Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!

Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

With this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

How to solve

To solve this problem, we will need to find the time of flight and the horizontal velocity. We can use the following kinematic equations:

Vertical motion:

Maximum height: h = (v^2 * sin^2(angle)) / (2 * g)

Time of flight: t = 2 * v * sin(angle) / g

Horizontal motion:

Range: R = v * t * cos(angle)

Given:

Initial velocity (v) = 20 m/s

Angle = 45 degrees

Acceleration due to gravity (g) = 9.81 m/s²

Calculations:

Convert angle to radians: 45 degrees = 45 * (π/180) = 0.785 radians

Calculate time of flight: t = 2 * 20 * sin(0.785) / 9.81 = 2.04 seconds

Calculate horizontal range: R = 20 * 2.04 * cos(0.785) = 28.98 meters

So, with this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

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A ball is thrown with an initial velocity of 20 meters per second at an angle of 45 degrees with respect to the horizontal. How far does the ball travel horizontally (range) before it hits the ground? Assume no air resistance.


Related Questions

Consider the two-loop circuit shown below:

Ignore the red and pencil markings, just worry about the printed questions

Answers

Answer:

  (I₁, I₂) = (1, 1)

Step-by-step explanation:

You want the matrix version of the given circuit equations, and the solution by matrix methods and by Cramer's rule.

15I₁ +5I₂ = 2025I₁ +5I₂ = 30

(a) Matrix equation

The coefficients of the variables fill matrix A; the constants fill matrix (column vector) B:

  AI = B

  [tex]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}20\\30\end{array}\right][/tex]

(b) Matrix algebra

The solution to this matrix equation can be found by left-multiplying both sides by the inverse of matrix A. The inverse of a 2×2 matrix is the transpose of the cofactor matrix, divided by its determinant. It can be written down, as the form is simple: diagonal elements are swapped; off-diagonal elements are negated.

  [tex]A^{-1}=\dfrac{1}{15(5)-25(5)}\left[\begin{array}{cc}5&-5\\-25&15\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\\\\\textsf{Multiplying by $A^{-1}$, we have ...}\\\\\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{c}20\\30\end{array}\right][/tex]

  [tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}(-0.1)(20+(0.1)(30)\\(0.5)(20)+(-0.3)(30)\end{array}\right]\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

(c) Cramer's rule

Cramer's rule requires we find three determinants. We already found the determinant of the coefficient matrix, above. It is D = -50. The other two are ...

  [tex]D_1=\left|\begin{array}{cc}20&5\\30&5\end{array}\right|=(20)(5)-(30)(5)=-50\\\\\\D_2=\left|\begin{array}{cc}15&20\\25&30\end{array}\right|=(15)(30)-(25)(20)=-50\\\\\\I_1=\dfrac{D_1}{D}=\dfrac{-50}{-50}=1\qquad I_2=\dfrac{D_2}{D}=\dfrac{-50}{-50}=1\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

find the surface area of the figure

Answers

Answer:

The answer for Surface area is 332m²

Step-by-step explanation:

S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle

S.A=2×1/2×4×3 + 2(20×5) + 20×6

S.A=12+2(100)+120

S.A=12+200+120

S.A=212+120

S.A=332m²

find the truth set of *-1/2 《 5/2 + 2​

Answers

The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)

How to Solve the Inequality?

Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:

x > -2*(5/2 + 2)

x > -5 - 4

x > -9

Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:

(-9, ∞)

Below is the complete question:

Find the truth set of x*(-1/2) < 5/2 + 2

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Can someone please help me?

Answers

Answer:i think it is c

Step-by-step explanation:

answer ASAP pls with as as much detail in how to complete it as possible :))


in general, if you have the ratio of the volume of two figures how do you find the ratio of their edge lengths? And does how to do this differ between shapes (if so could you explain for triangles pls?)

Answers

To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

Finding the volume

To find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.

If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:

(Volume of A) / (Volume of B) = (a^3) / (b^3) = k

We can then solve for the ratio of edge lengths:

a / b = (k)^(1/3)

Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.

This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.

For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.

If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:

a / b = sqrt(Area of first triangle / Area of second triangle)

So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

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I need help with questions 1,2, and 3. This class is microeconomics

Answers

Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.

What is budget?

A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.

What is consumption?

Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.

According to the given information:

To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.

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A 3 scoops ice-cream cone cost 4.80. A single Scoop ice-cream cost $2. Which one cost less for each scoop of ice cream ? How much less?

Answers

A single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.

To compare the cost of each scoop of ice cream in a 3-scoop cone and a single scoop, we need to calculate the cost per scoop for each option.

In a 3-scoop cone, the cost of each scoop can be found by dividing the total cost by the number of scoops. Therefore, the cost of each scoop in a 3-scoop cone is:

4.80 ÷ 3 = 1.60

On the other hand, a single scoop of ice cream costs $2. Therefore, the cost of each scoop in a single scoop is:

2 ÷ 1 = 2

Comparing the two options, we can see that a single scoop of ice cream costs less per scoop than a 3-scoop cone. Specifically, a single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.

Therefore, choosing a single scoop of ice cream over a 3-scoop cone will result in a cost savings of $0.40 per scoop.

In conclusion, when comparing the cost per scoop of ice cream, a single scoop is cheaper than a scoop in a 3-scoop cone. The cost savings per scoop is $0.40.

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PLEASEE HELP ITS URGENT

Answers

The ratio of the areas is given as follows:

1:5.8.

How to obtain the ratio of the areas?

The ratio of the areas is obtained applying the proportions in the context of the problem.

When a prism is dilated by a scale factor of k, we have that:

The ratio of the perimeters is k, as both the side lengths and the perimeter are measured in units.The ratio of the areas is k², as the side lengths are measured in units, while the areas are in units squared.The ratio of the volumes is k³, as the side lengths are measured in units, while the volumes are in units cubed.

Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:

(14²)^(1/3) = 5.8.

Hence:

1:5.8.

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NO LINKS!!! URGENT HELP PLEASE!!!!

Express the statement as an inequality. Part (2a^2)

d. c is between 1/7 and 1/5
1. 1/5 ≥ c ≥ 1/7
2. 1/7 < 1/5 < c
3. c < 1/7 < 1/5
4. 1/7 < c < 1/5
5. 1/7 ≤ c ≤ 1/5


e. p is not greater than -6
1. p ≤ -6
2. p < -6
3. p ≥ -6
4. p > -6
5. p = -6

f. The negative of m is not less than -2
1. m ≤ -2
2. m < 2
3. -m < -2
4. m < -2
5. -m ≥ -2

Answers

Answer:d. The inequality that represents "c is between 1/7 and 1/5" is:

1/7 ≤ c ≤ 1/5

e. The inequality that represents "p is not greater than -6" is:

p ≤ -6

f. The inequality that represents "the negative of m is not less than -2" is:

-m ≥ -2

Note that we need to flip the inequality when we multiply or divide both sides by a negative number, which is the case in part (f).

Step-by-step explanation:

the answer to d is 5

the answer to e is 1

the answer to f is 5

Un problema de derivadas de la vida cotidiana utilizando la siguiente función:

f(x)= 2x^3-3x^2-12x+1

Answers

Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

How can we use the derivative of a function to analyze a car's motion?

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

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Please help!!!!! Help please!! what is the value of x? is this right???​

Answers

Bro the subtraction is wrong

Answer:

x = 68

Step-by-step explanation:

X + 22 = 90 degrees

90 - 22 = 68 degrees

In need of assistance! If possible, I'd appreciate it!

Answers

The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.

How to determine parametric equation?

Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:

x(t) = 2 - t

y(t) = (t+3)²

To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.

When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.

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Operations with Fractions
Solve for x.
2/5+x=1

Answers

Answer:

Hello... im exhausted but ill solve it i guess

To solve for x in the equation 2/5 + x = 1, we can follow these steps:

Subtract 2/5 from both sides of the equation to isolate the x term:

2/5 + x - 2/5 = 1 - 2/5

This simplifies to:

x = 1 - 2/5

Find a common denominator for 1 and 2/5, which is 5:

x = 5/5 - 2/5

Subtract 2/5 from 5/5:

x = 3/5

So, the solution for x in the given equation is x = 3/5.

if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1?

Answers

Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.

What is mathematical induction?

It is a  a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:

Base case: Prove that the statement is true for the first positive integer (usually 1).Inductive step: Assume that the statement is true for some arbitrary positive integer k, and then prove that it must also be true for the next positive integer (k+1).

We can calculate like this:

Base case: Show that the inequality holds for n=1.

When n=1, we have σ(1) = 1 and H1 = 1, so the inequality 1 ≤ 2^(σ(1)/H1) becomes 1 ≤ 2^(1/1), which is true.

Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).

Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).

Using the inductive hypothesis, we have:

k ≤ 2^(σ(k)/Hk),

So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:

k^(1/(kH(k+1))) ≤ 2^((k+1)/(kH(k+1)) * σ(k)/Hk).

By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get

k^(1/H(k+1)) ≤ 2^(σ(k+1)/H(k+1)).

Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.

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The students in Mrs. Fishers class planted seeds. Each seed was given sunlight and water. Mrs. Fisher measured one plants height each week.

* After 4 weeks, the height was 2 centimeters.
* After 7 weeks the height was 4.5 centimeters.
* After 9 weeks, the height was 6 centimeters.

A student noticed the data suggest a linear association between the height of the plant, y, in centimeters, after x weeks.

What is a reasonable value for n?

Please answer as soon as possible due in an hour. Thank you.

Answers

Answer:

-9.5.

Step-by-step explanation

To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:

2 = m(4) + b

Solving for b, we get:

b = 2 - 4m

Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:

4.5 = m(7) + 2 - 4m

Solving for m, we get:

m = 0.5

Now we have the slope and the y-intercept of the line. The equation is:

y = 0.5x + 2 - 4(0.5)

Simplifying, we get:

y = -1.5x + 4

To find n, we need to plug in x = 9 and solve for y:

y = -1.5(9) + 4

y = -9.5

81 smartphones is 45% of what number of smartphones? Please show work

Answers

Answer:

Let s be the number of smartphones.

81 = .45s, so s = 180

Answer:

36.45

Step-by-step explanation:

You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.

Find the value of x. Then find the area of the triangle.

Answers

Step-by-step explanation:

first of all, remember, the sum of all angles in a triangle is always 180°.

now, we see that both bottom angles are 45°.

that means

180 = 45 + 45 + top-angle

90° = top-angle

aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).

via Pythagoras

c² = a² + b²

where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.

in our case both legs are 7×sqrt(2) units long.

so,

baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =

= 98 + 98 = 196

baseline = sqrt(196) = 14 units

x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.

so, one side of the baseline from x is 14/2 = 7 units.

and now Pythagoras for that sub-triangle :

(7×sqrt(2))² = 7² + x²

98 = 49 + x²

49 = x²

x = sqrt(49) = 7 units

the area of the triangle is

baseline × height / 2

in our case

14 × 7 / 2 = 7×7 = 49 units²

Solve for x. I attached the question. Pls help me :(

Answers

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

a) Use your calculator to solve sin x = 0.79 for 0° ≤ x ≤ 90°
b) Use the graph below to solve sin x = 0.79 for 90° ≤ x ≤ 180°
Give your answer to the nearest degree

Answers

Answer:

  (a)  52°

  (b)  128°

Step-by-step explanation:

You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].

a) Inverse sine

The inverse sine function is used to find the angle when its sine is known.

  sin(x) = 0.79

  x = arcsin(0.79) ≈ 52°

x ≈ 52° in the domain 0 ≤ x ≤ 90°.

b) Other values

The sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.

  180° -52° = 128°

x = 128° in the domain 90° ≤ x ≤ 180°.

__

Additional comment

The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.

<95141404393>

HELP ASAP if ur good with non-linear and increasing lines and choose a letter A,B,C,D,E
(Please see the picture!)
Extra points nd brainlist!

Answers

Answer:

A nonlinear line is a line that is not straight. So the answers for these question include B and D

B and D  are not straight lines and they are increasing

Step-by-step explanation:

Hope this helps! =D

Mark me brainliest! =D

what are 3 differnt types of rocks

Answers

Answer:

Step-by-step explanation:

sedimentary, igneous, metamorphic

Answer: sedimentary, igneous, metamorphic.

have an amazing day and crush that homework/class!

branliest?

If the nth partial sum of a series n = 1 as it approaches infinity an is sn = 6 - n5^-n, find an and n = 1 as it approaches infinity an.

Answers

By using the partial sum of series is

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .

How to find the nth term?

To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.

The formula for the series' nth partial sum is as follows:

[tex]sn = 6 - n*5^{-n}[/tex]

The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,

a = sn+1 - sn

When we substitute the formula for sn, we get:

[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

As a result, the formula for the series' nth term is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

To calculate the series total, take the limit of the nth partial sum as n approaches infinity:

lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]

lim(n->inf) [n*5(-n)] = 6

= 6 - 0

= 6

As a result, the series' sum is 6.

As a result, the formula for the nth term in the series is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

And the series' total is:

a = sum(n=1 to inf) = 6

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PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️

Answers

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

What is the vertical displacement of the basic graph to produce a graph of
y =pi-3 cos(x-2)?

Answers

The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

What is Displacement?

In physics, displacement refers to the distance and direction of an object's change in position from its starting point. It is a vector quantity that measures the overall change in position of an object, regardless of the path it took to get there. Displacement can be positive, negative, or zero depending on the direction and distance of the movement.

To find the vertical displacement of the basic graph to produce a graph of y = pi - 3 cos(x - 2), we need to compare the given equation with the general cosine function y = A cos(Bx - C) + D.

Here, A = 3, B = 1, C = 2, and D = pi - 3.

The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

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Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.
sin^8(x)

Answers

The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]

What is trignomatric functions?

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

What is multiple angles?

If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.

Answer is attached as a image must check:

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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

What is power reducing formula?

Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.

We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:

sin²x = 1 - cos²x   (first power-reducing formula)

sin⁴x = (sin²x)² = (1 - cos²x)²

      = 1 - 2cos²x + cos⁴x   (second power-reducing formula)

sin⁶x = (sin⁴x)(sin²x)

      = (1 - 2cos²x + cos⁴x)(1 - cos²x)

      = 1 - 3cos²x + 3cos⁴x - cos⁶x   (third power-reducing formula)

sin⁸x = (sin⁶x)(sin²x)

      = (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)

      = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

Now we can substitute the expression for sin⁸x into the given expression and simplify it:

1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)

= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)

= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)

= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

     = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

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Lighthouse B is 9 miles west of lighthouse A. A boat leaves A and sails 4 miles. At this​ time, it is sighted from B. If the bearing of the boat from B is N65degreesE, how far from B is the​ boat? Round to the nearest tenth
(Note: Needs 2 Answers)

PLEASE HELP I'M GOING INSANE
*please include work/formulas for every step when needed*

Answers

Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

How to find the distance?

The boat has moved 4 kilometers from point A to point x. The distance between B and x is what we're looking for.

Trigonometry can be used to overcome this issue. Let's abbreviate the distance "d" from A to x. Then, we can apply the following formula:

tan(65°) = (9 / d)

We can rearrange this formula to solve for d:

d = 9 / tan(65°)

We find that:

tan(65°) = 2.1445

So, d = 9 / 2.1445

= 4.195 miles (rounded to the nearest tenth)

or  6.749755 km.

Hence, Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

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In a large population of students, 60% feel like they can do better in their math class. In a random sample of 5 students, what is the probability that at least 2 students feel like they can do better in their math class?

0.0870

0.2304

0.3174

0.6826

0.9130

Answers

The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.

How to calculate the probability

To find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:

P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024

P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680

Therefore,

P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296

Rounding this to four decimal places, we get: 0.9130

Therefore, the answer is option E: 0.9130.

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how do I find the IQR for the numbers 7,9,8,9,6

Answers

Answer:

There are three steps to find IQR

1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.

2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.

1 and 2 are the first quartile, or Q1

3 and 4 are the second quartile, or Q2

5 and 6 are the third quartile, or Q3

7 and 8 are the fourth quartile, or Q4

3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.

The formula is written as: Q3 – Q1 = IQR.

Answer:

the answer would be 2.5

Explanation:

The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).

What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9

Answers

To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.

What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9?

3/9 = 1/3, which is not a multiple of 1/9

4/9 cannot be simplified further and is therefore a multiple of 1/9

9/12 can be simplified to 3/4, which is not a multiple of 1/9

9/10 cannot be simplified further and is therefore a multiple of 1/9

2/9 cannot be simplified further and is therefore a multiple of 1/9

9/9 = 1, which is not a multiple of 1/9

Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.

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Use the given information to find a formula for the exponential function N = N(t). (Round the values to three decimal places.)
The initial value of N is 14. If t is increased by 6, the effect is to multiply N by 59.

Answers

the formula for the exponential function N(t) is N(t) = 14 * 59in power (t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

How to solve the question?

Let N(t) be the exponential function we are trying to find, where N is the population at time t.

From the given information, we know that when t=0, N(0) = 14, which is the initial value of N.

We also know that when t is increased by 6, N is multiplied by 59. In other words,

N(t+6) = 59N(t)

We can use this relationship to express N(t+6) in terms of N(t) by substituting N(t+6) with 59N(t) in the above equation, giving us:

59N(t) = N(t+6)

Now, we can use this equation to solve for N(t) in terms of N(0) by repeatedly substituting N(t) with 59N(t-6), 59²N(t-12), 59³N(t-18), and so on.

N(t) = 59  in power (t/6) * N(0)

Using the initial value of N(0) = 14, we get:

N(t) = 14 * 59 in power (t/6)

Therefore, the formula for the exponential function N(t) is N(t) = 14 * 59^(t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

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