City Bank paid more interest than First National Bank over the 5-year period.
What is compound interest?
Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.
We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:
Amount of interest with First National Bank = [tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.
Amount of interest with First National Bank
=[tex]$500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$[/tex]
= $235.15 (rounded to two decimal places)
Amount of interest with City Bank =[tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.
Amount of interest with City Bank
=[tex]$500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$[/tex]
= $240.45 (rounded to two decimal places)
The difference in the amounts of interest paid by the two banks is:
$240.45 - $235.15 = $5.30
Therefore, City Bank paid more interest than First National Bank over the 5-year period.
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Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 600 and 700
(inclusive), the number of upperclassmen (11th and 12th graders) must fall between 500 and 600 (inclusive), and the number of students cannot
exceed 1200. Let a represent the number of underclassmen and let b represent the number of upperclassmen. Write a set of inequalities that
models the constraints on the composition of the student body.
number of underclassmen:
number of upperclassmen:
Total number of students:
:: 600 < a < 700
000
:: 600 ≤ a ≤ 700
:: 500 ≤ b ≤ 600
:: a + b ≤ 1200
:: 500 < b < 600
:: a + b > 1200
= a + b < 1200
:: a + b > 1200
The correct set of inequalities that model the constraints on the composition of the student body are:
600 ≤ a ≤ 700, 500 ≤ b ≤ 600 and a + b ≤ 1200
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The correct set of inequalities that model the constraints on the composition of the student body are:
600 ≤ a ≤ 700 (the number of underclassmen must fall between 600 and 700, inclusive)
500 ≤ b ≤ 600 (the number of upperclassmen must fall between 500 and 600, inclusive)
a + b ≤ 1200 (the total number of students cannot exceed 1200)
Note that the inequalities 600 < a < 700 and 500 < b < 600 are not correct, as they do not take into account the inclusive limits of the ranges for the number of underclassmen and upperclassmen. Also, the inequality a + b > 1200 is not correct, as it contradicts the previous inequality a + b ≤ 1200.
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Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
what is angle ?Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.
given
The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.
The information provided in the problem can then be used to create an equation as follows:
m∠A = 5(m∠B + 7.2°)
Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:
180 - m∠B = 5(m∠B + 7.2°)
The right side is being widened:
180 - m∠B = 5m∠B + 36
Simplifying and putting all the mB words to one side:
6m∠B = 144
m∠B = 24
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
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Use the formula KE= mv^2/2 where m=mass, V= velocity, KE = kinetic energy. If dev has a mass of 60kg and is running at a constant velocity with 150 J of KE. What is his velocity?
Dev's velocity is [tex]\sqrt{5}[/tex]. Thus option B.
What is kinetic energy?Kinetic energy is a amount of energy possessed when an object is in motion. Such that;
KE = 1/2 m v^2
Where m = mass, v = velocity
It is measured in Joules.
From the given question, we have;
KE = 1/2 m v^2
2KE = m v^2
v^2 = 2KE/ m
= (2*150)/ 60
= 300/ 60
= 5
V = (5)^1/2
The velocity of Dev is B. [tex]\sqrt{5}[/tex].
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Y=2x to the power of 2 plus 4x minus one
at a store 40% of all the refrigerators are silver. there are 50 silver refrigerants at the store . how many refrigerants are at the store?
Answer:
125
Step-by-step explanation:
50 refrigerators are 40% of all the refrigerators in the store.
5 refrigerators are 4% of refrigerators in the store
125 refrigerators are 100% of refrigerators in the store
therefore there are 125 refrigerators at the store.
in the figure below lines m and n are parallel m2= 62 and m3=73
Answer: 135
Step-by-step explanation:
A 40" screen television at a popular electronics retailer is priced at $600. The wall mount for this sized television costs $29.99.
Part A: If Jamie purchases the television and the wall mount and has a coupon for 30% off, how much will her subtotal be? Show all necessary work. (4 points)
Part B: If Jamie makes the purchase in a state with a 7% state sales tax, what will her final total be? Show all necessary work. (2 points)
Part C: The electronics retailer is extending a special offer to install the wall mount and television for free. However, Jamie decides to tip the installation specialist 10% of the original purchase price before the discount is applied. How much would her new total be, including tax, discount, and tip? Show all necessary work. (4 points)
The cost of the television and wall mount before discount is $600 + $29.99 = $629.99
After a 30% discount, the subtotal is:
$629.99 x 0.70 = $440.99
The sales tax is 7% of the subtotal:
$440.99 x 0.07 = $30.87
The final total is the subtotal plus the sales tax:
$440.99 + $30.87 = $471.86
The original purchase price before discount is $600.
10% of $600 is $60.
So Jamie decides to tip the installation specialist $60.
After the discount, the subtotal is $440.99 (as calculated in Part A).
The sales tax is 7% of the subtotal:
$440.99 x 0.07 = $30.87
The new total is the subtotal plus the sales tax and the tip:
$440.99 + $30.87 + $60 = $531.86
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Andrea is playing a board game with her friends. A player spins the spinner shown below and receives the number of points indicated in the section where the arrow stops. A negative value means a loss of points.
What is the expected payoff, in points, for landing on a space of the board game?
The expected payoff for landing on a space of the board game is 2.67 points.
How to find the expected payoff?We need to multiply each possible outcome by its probability of occurring and then add all the products to get the expected payoff.
Let's begin by determining the likelihood of each outcome:
The number 8 appears four times, so the probability of getting an 8 is 4/12 = 1/3.
The number 1 appears four times, so the probability of getting a 1 is also 1/3.
The number -2 appears twice, so the probability of getting a -2 is 2/12 = 1/6.
The number - 4 shows up two times, so the likelihood of getting a - 4 is likewise 1/6.
After that, we add up each outcome by multiplying it by its probability:
Expected payoff = (8 * 1/3) + (8 * 1/3) + (8 * 1/3) + (8 * 1/3) + (1 * 1/3) + (1 * 1/3) + (-2 * 1/6) + (-2 * 1/6) + (-4 * 1/6) + (-4 * 1/6)
Expected payoff = 2.67
As a result, the expected reward for landing on a board game space is 2.67 points.
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Each side of a square office is 3 meters long. It will cost $87.41 per square meter to replace the carpet in the office. What would be the total cost to replace the carpet?
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
what is a square?The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.
given
The square office's area is:
[tex]C = 9 \times $87.41 = $786.69[/tex]
A = s2 = 3 2 = 9 metres square
To completely replace the carpet, it would cost:
Cost per square meter equals C = A.
where a square meter costs $87.41. When we change the values, we obtain:
As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.
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An item is worth $240 now. This is 30% of what it was originally worth. What was it originally worth?
A cow is tethered to one corner of a square barn, 8 feet by 8 feet, with a rope 130 feet long. What is the maximum grazing area for the cow?
The maximum grazing area for the cow is approximately 53,343.08 square feet.
How to Find the maximum Grazing Area?The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.
Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.
To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.
Area of circle = π(130)^2 square feet = 53,407.08 square feet
Area of barn = 64 square feet
Maximum grazing area = Area of circle - Area of barn
= 53,407.08 - 64
= 53,343.08 square feet (rounded to two decimal places)
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Gabriella is 53 5/6
inches tall. Sheila is 1 1/3
inches shorter than Gabriella and Jane is 1 1/4
inches shorter than Sheila. How tall is Jane?
A flagpole is 12 feet fall. Its shadow is
11 feet long. How far is it from the top of the flagpole to the end of its shadow?
Step-by-step explanation:
You are looking for the hypotenuse of a right triangle with legs of 12 and
11 feet
Using Pthagorean theorem
hypot^2 = 12^2 + 11^2
hypot^2 = 265
hypot = sqrt (265) = 16.28 ft
if you multiplied a number by 1/2 , the result would be Responses
Answer:
half the number you started with
Step-by-step explanation:
8 times 1/2 would be 4....6 times 1/2 would be 3!
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Select all that apply
b. Symmetric with respect to the x-axis
The ones that are symmetric with respect to the x-axis is:
y = -7x^2Checking the symmetric for all equationsA function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the equation. In other words, if the graph of the function is the same when reflected across the x-axis.
y = -7x^2 is symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y and the equation remains the same.y = 6x² - 9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = 6x² - 9, which is not the same as the original equation.x=1/4y^2 is not a function, since it does not pass the vertical line test and has multiple values of x for some values of y.y=x^3-1 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = x^3 - 1, which is not the same as the original equation.x=-y^2+9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to x = -(-y)^2 + 9, which is not the same as the original equation.y=sqrt(x) is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x), which is not the same as the original equation.y=sqrt(x)-6 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x) - 6, which is not the same as the original equation.Therefore, only the equation y = -7x^2 is symmetric with respect to the x-axis.
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determina el volumen cuyo diametro es de 8 y su altura de 15 cm
Answer:
3016 centímetros cúbicos.
Step-by-step explanation:
El radio del cilindro es de 8 cm y la altura es de 15 cm. Sustituya 8 por r y 15 por h en la fórmula . Simplifique. Por lo tanto, el volumen del cilindro es de alrededor de 3016 centímetros cúbicos.
Need help on this please
Answer:
Step-by-step explanation:
(-50, -20), (-60, 40)
(40 + 20)/(-60 + 50) = 60/-10= -6
y - (-20) = -6(x - (-50))
if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
The correct option is B .solution of given problem with the help of integrating the given function is 3xLn3
what is integration and function ?The area under a curve in a given range can be calculated mathematically via integration. To locate the region between the curve and the x-axis, it is necessary to find a function's antiderivative and evaluate it twice.
A function is a rule that gives each input value a distinct output value. It can be compared to a machine that processes inputs into outputs in accordance with a predetermined rule or formula.
According to given informationTo find f'(x), we need to take the derivative of f(x), where f(x) is the antiderivative of k(x).
Since k(x) = 3x, we can find f(x) by integrating 3x with respect to x:
f(x) = ∫ 3x dx = 3/2 x² + C
where C is a constant of integration.
Now we can find f'(x) by taking the derivative of f(x):
f'(x) = d/dx (3/2 x² + C) = 3x
Therefore, the answer is (B) 3xLn3. Option (A) is incorrect because there is no natural logarithm term in the derivative of f(x). Option (C) is incorrect because the derivative of 3x is 3, not 3/Ln(x). Option (D) is incorrect because there is no x in the denominator of the natural logarithm term.
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please help pleaseee i need dis good grade
Answer:62.8 units
Step-by-step explanation:
Find the value of x. Write your answer in simplest form.
76√2
The value of x which is the hypotenuse of the triangle is 107.48
How to find missing side of a right angle triangle using Pythagoras theorem[tex]\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{Hyp = x}[/tex]
[tex]\text{opp} = 76\sqrt{2}[/tex]
[tex]\text{adj} = \text{x}[/tex]
substitute into the equation[tex]\text{x}^2 = (76\sqrt{2})[/tex]
[tex]\text{x}^2 = 11552[/tex]
[tex]\text{x}^2 = \sqrt{11552}[/tex]
[tex]\text{x} = 107.48[/tex]
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Q3: Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
the direction and angle of rotation between the two polygons is 180° clockwise rotation.
How to solve the question?
Based on the given information, we can determine the direction and angle of rotation between the two polygons.
First, let's look at the initial positions of the polygons. The graph of triangle ABC is located in Quadrant 4, which means that it is in the bottom-right portion of the coordinate plane. On the other hand, the second polygon A'B'C' is located in Quadrant 3, which is in the bottom-left portion of the coordinate plane.
To find the direction and angle of rotation between the two polygons, we need to imagine rotating one polygon onto the other. We can see that the two polygons are mirror images of each other across the y-axis. Therefore, we can infer that there is a horizontal line of symmetry between the two polygons.
If we rotate polygon A'B'C' 180 degrees clockwise around the origin, it will overlap perfectly with triangle ABC. This is because a 180-degree rotation is equivalent to a half-turn or a flip, which is exactly what we need to make the two polygons overlap. Therefore, the answer is 180° clockwise rotation.
In summary, the direction and angle of rotation between the two polygons is 180° clockwise rotation.
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solve as a fraction -2 1/3 - (-5) = ?
Answer:
-2 1/3 - (-5) = -2 1/3 + 5
To add these two numbers, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-2 1/3 can be written as -7/3 using the rule that a mixed number is equal to the sum of the whole number and the fraction.
So, we have:
-7/3 + 5
To add these two fractions, we need to find a common denominator. The common denominator of 3 and 1 is 3.
-7/3 can be written as -7/3 x 1/1 = -7/3.
So, we have:
-7/3 + 15/3 = 8/3
Therefore, -2 1/3 - (-5) = 8/3.
Where are the x-intercept(s) of the graph?
The x-intercept of the graph is (0,0).
What is an illustration of an x-intercept on a graph?
On a graph, the x-intercept is the point at which a line crosses the x-axis. At that time, the y coordinate has no value. The y-intercept is the point where the line crosses the y-axis. The x coordinate has no value. For example, y = x + 5 would intersect the x-axis at (-5, 0), forming the x-intercept.
From the figure, it is clear that the line crosses the X-axis at the origin, which means that x - coordinate 0 keeping y -coordinate is also zero.
Which means that the x-intercept of the graph is (0,0).
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Express the statement as an inequality part 7a^2
The statement, "t is not less than 7" as an inequality is E. t ≥ 7.
The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .
How to represent as inequalities ?The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:
t ≥ 7
Therefore, the correct inequality for the statement is t ≥ 7.
Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:
-z ≤ 8
Multiplying both sides of the inequality by -1 gives:
z ≥ -8
Therefore, the correct inequality for the statement is z ≥ -8.
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Answer:
e) The correct option is: t≥7
The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.
here's an explanation of each option:
t = 7: This statement indicates that the value of t is exactly 7. If this statement is true, then t cannot be greater than or less than 7.t > 7: This statement indicates that the value of t is greater than 7. If this statement is true, then t can be any value that is greater than 7.t < 7: This statement indicates that the value of t is less than 7. If this statement is true, then t can be any value that is less than 7.t ≤ 7: This statement indicates that the value of t cannot be greater than 7, but it can be less than or equal to 7. If this statement is true, then t can be 7 or any value less than 7.t ≥ 7: This statement indicates that the value of t cannot be less than 7, but it can be greater than or equal to 7. If this statement is true, then t can be 7 or any value greater than 7.To express the statement t≥7 as an inequality in terms of 7a^2, we can simply multiply both sides by 7a^2, like this:t * 7a^2 ≥ 7 * 7a^2
Simplifying the right-hand side of the inequality, we get:49a^2
Therefore, the inequality in terms of 7a^2 is:t * 7a^2 ≥ 49a^2
Note that this inequality is equivalent to t ≥ 7, which is what we started with.
f) The correct option is:-z ≤ 8
The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:
Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.
The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:
-z ≤ 8
Since we cannot multiply or divide by a negative number when we are working with inequalities, we will multiply both sides of the inequality by -1. Remember that whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality symbol. So, we have:z ≥ -8
Multiplying both sides by 7a^2, we get:7a^2 * z ≥ -8 * 7a^2
Simplifying the right-hand side, we get:-56a^2
Therefore, the inequality in terms of 7a^2 is:7a^2 * z ≥ -56a^2
So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.
A quadratic function yields negative values between x = 2 and x = 6. Its minimum value is −2. What are the coordinates of the y-intercept? Enter your answer by filling in the boxes.
Answer:
Since the quadratic function has a minimum value at some point between x = 2 and x = 6, its graph is a downward-facing parabola.
Let's assume that the function is of form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Since the minimum value of the function is −2, we know that the vertex of the parabola lies on the line y = -2. Also, we know that the x-coordinate of the vertex is the average of 2 and 6, which is 4.
Therefore, the equation of the parabola can be written as f(x) = a(x-4)^2 - 2.
Since the y-intercept is the value of y when x = 0, we can find it by plugging in x = 0 into the equation of the parabola:
f(0) = a(0-4)^2 - 2
f(0) = 16a - 2
We know that the function yields negative values between x = 2 and x = 6, so the parabola must intersect the y-axis below the x-axis. This means that the y-intercept is negative.
To find the y-intercept, we need to solve the equation 16a - 2 = 0, which gives us a = 1/8.
Therefore, the equation of the parabola is f(x) = (1/8)(x-4)^2 - 2.
Finally, we can find the y-intercept by plugging in x = 0:
f(0) = (1/8)(0-4)^2 - 2
f(0) = 8 - 2
f(0) = 6
So the coordinates of the y-intercept are (0, 6).
A six sided dice is rolled. What is the probability of rolling a number greater than 2?
The probability of rolling a number greater than 2 is 2/3
Calculating the probability of rolling a number greater than 2?From the question, we have the following parameters that can be used in our computation:
Rolling a number cube once
Using the above as a guide, we have the following:
Sample space, S = {1, 2, 3, 4, 5, 6}
In the above sample space, we have
Outcomes greater than 2 = {3, 4, 5, 6}
So, we have
P(greater than 2) = n(Outcomes greater than 2)/n(Sample space)
Substitute the known values in the above equation, so, we have the following representation
P(greater than 2) = 4/6
When evaluated, we have
P(greater than 2) = 2/3
Hence, the probability is 2/3
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What angle(s) on the Unit Circle make this equation true?
-√3 csc(2θ) = 2
a. Using only the graph of the given equation on Desmos, what angle(s) on the Unit Circle make this equation true? You must include a detailed, labeled screenshot as your explanation or detailed, labeled drawing of the graph as you solution.
b. Even though Desmos found the angle(s) that make the equation true in part (a), you must now show why the angle(s) are true. Provide a clear, convincing argument why the angles you stated in part (a) are true without the use of Desmos in anvway.
The angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.
How to calculate the valueFrom the information, the following can be deduced:
-√3 csc(2θ) = 2
csc(2θ) = -2/√3
sin(2θ) = -√3/2
We know that sin(2θ) = 2sin(θ)cos(θ) by the double-angle identity for sine,
2sin(θ)cos(θ) = -√3/2
2sin(θ)cos(θ) = -√3/2
sin(θ)cos(θ) = -√3/4
sin(θ)cos(θ) = sin(π/3)sin(θ)
cos(θ) = sin(π/3)
θ = π/6 + 2πn, 5π/6 + 2πn
Therefore, the angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer
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What 4×4/3 in its simplest form
Answer:
5 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]
You can re-write [tex]\frac{16}{3}[/tex] as
[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.
1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]
Helping in the name of Jesus.
pls!! :(( a golf ball has been hit off of the tee at an angle of elevation of 30 degrees and an initial velocity of 128 ft/sec
how long is the ball in the air (hang time)?
what is the maximum height of the ball?
how far, horizontally, does the ball travel in the air?
According to the information, the horizontal distance traveled by the ball is 443.404 feet.
How to calculate the distance traveled by the ball?We can use the kinematic equations of motion to solve for the hang time, maximum height, and horizontal distance traveled by the golf ball.
First, we need to resolve the initial velocity vector into its horizontal and vertical components. The vertical component will determine the maximum height and hang time, while the horizontal component will determine the horizontal distance traveled.
The initial velocity can be represented as:
v0x = v0 cos(theta) = 128 cos(30) = 110.851 ft/secv0y = v0 sin(theta) = 128 sin(30) = 64 ft/secwhere v0 is the initial velocity, theta is the angle of elevation, v0x is the horizontal component of the initial velocity, and v0y is the vertical component of the initial velocity.
Now we can use the kinematic equations to solve for the hang time, maximum height, and horizontal distance traveled.
Hang time (time in air):
We can use the vertical motion equation to solve for the time when the ball reaches its maximum height:
v = v0y - gt0 = 64 - 32tt = 2 secondsSince the ball will be in the air for twice the time it takes to reach its maximum height, the hang time is:
2t = 4 secondsMaximum height:
We can use the vertical motion equation to solve for the maximum height reached by the ball:
y = v0y t - 1/2 gt^2y = 64(2) - 1/2 (32)(2)^2y = 64 ftTherefore, the maximum height of the ball is 64 feet.
Horizontal distance traveled:
We can use the horizontal motion equation to solve for the horizontal distance traveled by the ball:
x = v0x t
x = 110.851(4)
x = 443.404 ft
Therefore, the horizontal distance traveled by the ball is 443.404 feet.
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[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
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