Part 3: Hitting the baseball over the lights


Meanwhile at the ballpark Juan was practicing his hitting while talking to some friends. He started telling them how he hit the ball over the 50 foot light tower yesterday.



The formula for this hit is h(x) = -16xsquared + 60x + 4 , where h is the height of the ball and x is the number of seconds the ball is in the air.



How can Juan provide proof to the friends that he actually hit the ball over the tower?








How high did Juan actually hit the ball? Is Juan able to mathematically back up how high he says he hit the ball?

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

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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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

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.

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]

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]

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]

The range of the function is all real numbers.

In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We know,

The x-values (Input values) on the graph define the domain of the function.

and, The y-values (output values) on the graph determine the range of a function.

From the graph attached,

Here the x value start from +1 to ∞.

Thus, the range of the function is all real numbers.

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The value of y in the triangle is 20.

What is the triangle?

A triangle is a polygon with three sides and three angles. It is the simplest and most basic polygon in Euclidean geometry.

According to the given information:

From the figure, we can say that ΔABC and ΔABI are similar.

we can write proportions as

[tex]\frac{y}{30} =\frac{30}{y+25}[/tex]

y(y+25) = 30*30

[tex]y^{2}[/tex]+25y=900

[tex]y^{2}[/tex]+25y-900 = 0

On solving we can use quadratic formula y = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation y^2 + 25y - 900 = 0, we can identify a = 1, b = 25, and c = -900.

Plugging these values into the quadratic formula, we get:

y = (-25 ± √(25^2 - 4 * 1 * -900)) / (2 * 1)

Simplifying further:

y = (-25 ± √(625 + 3600)) / 2

y = (-25 ± √(4225)) / 2

y = (-25 ± 65) / 2

Now we can solve for two possible values of y:

y = (-25 + 65) / 2 = 40 / 2 = 20

y = (-25 - 65) / 2 = -90 / 2 = -45

So the two possible values of y that satisfy the given equation are y = 20 and y = -45.

distance cannnot be negative, so the value of y is 20.

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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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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.

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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The ratio of the areas is given as follows:

1:5.8.

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:

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

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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Answer:

Step-by-step explanation:

sedimentary, igneous, metamorphic

Answer: sedimentary, igneous, metamorphic.

have an amazing day and crush that homework/class!

branliest?

The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.

The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.

By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:

Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm

Perimeter of semicircle = 6 cm + 3 pi cm

Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:

Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm

Perimeter of quarter circle with radius 14 cm = 7 pi cm

And, the perimeter of the quarter circle with radius 30 cm is:

Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm

Perimeter of quarter circle with radius 30 cm = 15 pi cm

Therefore, the total perimeter of the given shape is:

Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm

Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)

Perimeter = 22 cm + 25 pi cm.

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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

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)

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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2. The total dollar amount for each cash dividend is $23,700.

 1. Calculation of outstanding common shares on each cash dividend date:

2.

Calculation of total dollar amount for each cash dividend:

Therefore, the total dollar amount for each cash dividend is $23,700.

3.

Calculation of the capitalization of retained earnings for the stock dividend:

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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)

Common stock—$4 par value, 100,000 shares

authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000

Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000

Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000

Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000

Stockholders’ Equity (December 31, 2017)

Common stock—$4 par value, 100,000 shares

authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600

Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200

Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000

768,800

Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)

Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800

The following transactions and events affected its equity during year 2017.

Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.

Mar. 20 Purchased treasury stock for cash.

Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.

July 5 Declared a $0.50 per share cash dividend, date of record July 10.

July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.

Aug. 14 Issued the stock dividend that was declared on July 31.

Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.

Required

1. How many common shares are outstanding on each cash dividend date?

2. What is the total dollar amount for each of the four cash dividends?

3. What is the amount of the capitalization of retained earnings for the stock dividend?

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).

Answer:i think it is c

Step-by-step explanation:

The complete table for the pie chart is;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            198

Comedy                         5                            90

From the given table used to form the pie chart, we see that;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            

Comedy                         5

We know that the angles in a circle is equal to 360 degrees. Thus;

Angle composed of horror and comedy = 360 - 72 = 288°

Thus;

Angle for horror film = (11/(4 + 11 + 5)) * 360°

= (11/20) * 360°

= 198°

Thus;

Angle for comedy = 288° - 198° = 90°

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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.

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:

We can calculate like this:

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

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:

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

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

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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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.

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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Answer:

L = (14x^2 - x - 3) / (2x - 1)

Step-by-step explanation:

The area of the rectangular lane is given as 14x^2 - x - 3 square feet.

Let's assume that the length of the lane is L feet. Then the formula for the area of a rectangle is:

Area = Length x Width

Substituting the values given in the question, we have:

14x^2 - x - 3 = L x (2x - 1)

To find an expression for the length of the lane, we can rearrange the equation to solve for L:

L = (14x^2 - x - 3) / (2x - 1)

Therefore, the expression that represents the length of the lane is:

L = (14x^2 - x - 3) / (2x - 1)

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.

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

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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Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

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 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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When we solve the radical equation, we can see that the value of x is -113.

A radical equation is an equation in which one or more variables are under a radical sign, such as a square root, cube root, or higher-order root. These equations involve expressions with radicals that contain the variable, and the goal is usually to isolate the variable on one side of the equation.

Given that;

10 + √2x + 1 = -5

√2x + 1 = - 5 - 10

√2x + 1 = - 15

Square both sides;

2x + 1 = -225

2x = -225 - 1

2x = -226

x = -113

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