The phrase that completes the sentence is "determined by."
Dependent variable is always _________ independent variable in a function. In a mathematical function, the dependent variable is determined by the value of the independent variable. This means that when you input a value for the independent variable, the function will output a corresponding value for the dependent variable. The relationship between the two variables is often described using an equation, and it can be visualized on a graph. By understanding the relationship between the independent and dependent variables in a function, you can better understand how the function behaves and make predictions about its outputs for different inputs.Learn more about variable
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If y^3+y=x^2, then dy/dx=
A. 0
B. x/2
C. 2x/3y^2
D. 2x-3y^2
E. 2x/1+3y^2
If [tex]y^3+y=x^2[/tex], then [tex]dy/dx=2x/1+3y^2[/tex]. The correct answer is option e.
To find dy/dx, we first need to implicitly differentiate [tex]y^3 + y = x^2[/tex]with respect to x. Applying the chain rule, we have:
[tex]3y^2(dy/dx) + dy/dx = 2x[/tex]
Now we can solve for dy/dx:
[tex]dy/dx = (2x) / (3y^2 + 1)[/tex]
Substituting [tex]y^3 + y = x^2[/tex], we have:
[tex]dy/dx = (2x) / (3y^2 + 1) = (2x) / (3(x^2 - y))[/tex]
Therefore, the answer is E. [tex]2x/(1+3y^2)[/tex].
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What is the area of triangle abc if a = 12, b = 17, and C = 100°?
Explain the importance of understanding place value
before you learn how to do multi-digit multiplication.
Answer it is important understanding place value because if u put the number in the wrong place the math will be messed up so it is important to understand we're the place value is before multiplying or any math.
Step-by-step explanation:
A student runs 100 yards in 12 seconds at the same speed how many feet will he run in 8 seconds?
Step-by-step explanation:
since 1 yard =3feet
then 100yards= 300feet
which means 100yards=300feet=12seconds
let B be the number of feet in 8seconds
if 300feet=12seconds
then B feet= 8 seconds
if we cross multiply
300×8=12×B
2400=12B
B=2400/12
B= 200feet
OR
put it in ratio
feet/it's sec= feet/it's sec
300/12=B/8
then cross multiply to get your answer.
In SPSS, the "grouping variable" is the _______ and the "test variable" is the _____________.
a. extraneous variable: confound
b. classification variable: treatment variable.
c. IV: DV
d. DV:IV
In SPSS, the "grouping variable" is the classification variable , and the "test variable" is the treatment variable.
So, the correct answer is B.
What's grouping variable and test variableThe grouping variable, also known as the independent variable (IV), is the factor you manipulate in an experiment to observe its effect on the dependent variable (DV).
The test variable, also called the treatment variable, is the variable that represents the outcome or effect you are measuring, which depends on the IV.
These variables are essential in statistical analyses to determine whether there is a significant relationship between the manipulated factor and the observed outcome.
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if a=60 and n०b=40,find n(AuB), if A is subset of b.
ASAP
The value of expression n (A ∪ B) is,
⇒ n (A ∪ B) = 60
We have to given that;
⇒ n (A) = 60
⇒ n (B) = 40
And, A is subset of b.
Hence, We get;
⇒ n (A ∪ B) = LCM of {60, 40}
⇒ n (A ∪ B) = 60
Thus, The value of expression n (A ∪ B) is,
⇒ n (A ∪ B) = 60
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Sea z∈C definido como z= (5−2i)n+(5+2i)n con n∈N. Demuestre que Im(z) = 0
Answer:
Para demostrar que Im(z) = 0, debemos expresar z en términos de su parte real y su parte imaginaria. Desarrollando los términos de la suma, obtenemos:
z = (5−2i)n + (5+2i)n
z = (5^n)(cos(θ)-i sen(θ)) + (5^n)(cos(θ)+i sen(θ)) [Donde θ es el ángulo cuyo tangente es 2/5]
z = 2(5^n)cos(θ)
Entonces, la parte imaginaria de z es cero, ya que no hay términos que involucren la unidad imaginaria i. Por lo tanto, Im(z) = 0, como se quería demostrar.Para demostrar que Im(z) = 0, debemos expresar z en términos de su parte real y su parte imaginaria. Desarrollando los términos de la suma, obtenemos:
z = (5−2i)n + (5+2i)n
z = (5^n)(cos(θ)-i sen(θ)) + (5^n)(cos(θ)+i sen(θ)) [Donde θ es el ángulo cuyo tangente es 2/5]
z = 2(5^n)cos(θ)
Entonces, la parte imaginaria de z es cero, ya que no hay términos que involucren la unidad imaginaria i. Por lo tanto, Im(z) = 0, como se quería demostrar.
Lin charges $5. 50 per hour to babysit. The amount of money earned, in dollars, is a function of the number of hours that she babysits
If she babysits for 5 hours, the amount of money she earns is 27.50 dollars.
The function that represents the amount of money Lin earns for babysitting is:
E(h) = 5.50h
where h is the number of hours she babysits, and E(h) is the amount of money she earns in dollars.
For example, if she babysits for 3 hours, the amount of money she earns is:
E(3) = 5.50(3) = 16.50 dollars
Similarly, if she babysits for 5 hours, the amount of money she earns is:
E(5) = 5.50(5) = 27.50 dollars
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Lin charges $5. 50 per hour to babysit. The amount of money earned, in dollars, is a function of the number of hours. What is the mathematical relationship between the number of hours Lin babysits and the amount of money she earns?
Patrick carried the football on two plays. He lost two yards then gained 6. What was his net gain or loss for the two plays? what is the answer
Patrick's net gain for the two plays is 4 yards.
To determine Patrick's net gain or loss for the two plays, we need to calculate the difference between the total yards gained and the total yards lost.
Yards lost on the first play: -2
Yards gained on the second play: 6
To find the net gain or loss, we add the yards gained and subtract the yards lost:
Net gain or loss = Yards gained - Yards lost
= 6 - 2
= 4
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math.ceil(5.5) evaluates to ________.
math.ceil(5.5) evaluates to 6.
The CEILING. MATH function rounds a number up to the nearest integer or to the nearest multiple of specified significance. It also specifies whether the number is rounded toward or away from 0 depending on the mode. The ceiling function is a mathematical function that rounds a number up to the nearest integer. It is denoted by the symbol "⌈x⌉" and is also known as the least integer function or the smallest integer not less than x.
The ceiling function of a number x is defined as the smallest integer that is greater than or equal to x. Mathematically, we can express it as:
⌈x⌉ = the smallest integer n such that n ≥ x
For example, the ceiling function of 4.2 is 5, because 5 is the smallest integer that is greater than or equal to 4.2. Similarly, the ceiling function of -1.8 is -1, because -1 is the smallest integer that is greater than or equal to -1.8.
The ceiling function is commonly used in computer programming and engineering to round up values to the nearest integer.
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A triangle has two sides of lengths 7 and 12. What value could the length of
the third side be?
Check all that apply.
A. 7
B. 9
C. 17
D. 3
E. 5
F. 11
Select the correct answer.
Consider the functions graphed below.
-5
b
-3 -2
4
3
2
+
2
-3
4
5
a
1
2
C
3 4 S
X
Determine which function has the greatest rate of change over the interval [0, 2].
We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.
How is this correct?Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula:
m = (y2 - y1 /(x2 - x1)
Rate of change of a :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of :
m = (4-1)/2-0)
m = 1.5
The average rate of change of the function over the interval [0,2] is 1.5
Rate of change of b :
Here the end points are (0,0) and (2,2)
m = (2-0)/2-0)
m = 2/2
m=1
The average rate of change of the function over the interval [0,2] is 1
Rate of change of c:
Here the end points are (0,-1) and (2,0)
m = (0-(-1)/2-0)
m = 1/2
m= 0.5
The average rate of change of the function over the interval [0,2] is 0.5
Rate of change of d:
Here the end points are (0,0.5) and (2,2.5)
m = (2.5-0.5)/2-0)
m = 2/2
m= 1
The average rate of change of the function over the interval [0,2] is 1
We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.
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Full Question:
Determine which function has the greatest rate of change over the interval [0, 2].
See attached image.
Find the solution to the system of equations by graphing.
(Use the answer box with the graph) y = -2x+4 and 6x+3y = 12
Answer:
To graph the system of equations:
1. Rewrite the equations in slope-intercept form (y = mx + b):
y = -2x + 4
3y = -6x + 12
y = -2x + 4
2. Plot the y-intercept of the first equation, which is (0, 4). Then use the slope of -2 (rise of -2 and run of 1) to plot additional points and draw the line.
3. Plot the y-intercept of the second equation, which is (0, 4). Then use the slope of -2 (rise of -2 and run of 1) to plot additional points and draw the line.
The solution to the system of equations is the point where the two lines intersect. From the graph, we can see that the lines intersect at the point (2, 0).
Therefore, the solution to the system of equations by graphing is:
x = 2
y = 0
Answer box: (2, 0)
5÷1/3
as a fraction
ima just do random words now so that i can post it
Answer:
15
Step-by-step explanation:
We can use the saying "KCF", which is keep change flip to divide:
Keep the first number:
5
Change the sign:
x
And flip the fraction:
3/1
Now write an equation:
5x3=15
Hope this helps :)
An investment portfolio is shown below.
Investment Amount Invested ROR
$2,600
1.7%
$3,700
3.2%
Preferred Stock
$575
12.9%
Common Stock A $1,225
-5.6%
Savings Account
Municipal Bond
Using technology, calculate the weighted dollar amount of the municipal bond.
$44.20
O $74.18
O $118.40
$184.00
The weighted dollar amount of the municipal bond is $118.4
Calculating the weighted dollar amount of the municipal bond.From the question, we have the following parameters that can be used in our computation:
Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 -5.6%
Using the above as a guide, we have the following:
Weighted dollar = Amount Invested * ROR
For the municipal bond, we have
Weighted dollar = 3700 * 3.2%
Evaluate
Weighted dollar = 118.4
Hence, the weighted dollar is $118.4
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A set of data with 100 has a mean of 267. there are six outliers in the data set, which have a mean of 688. if the six outliers are removed what is the new mean?
The new mean after removing the outliers is approximately 231.14.
The mean of the data set with outliers is 267, and there are 6 outliers with a mean of 688. To find the new mean after removing the outliers, we need to subtract the total value of the outliers from the total value of the original data set and then divide by the remaining number of data points.
Let's start by finding the total value of the original data set. We know that the mean is 267 and there are 100 data points, so the total value is:
267 x 100 = 26700
Next, we need to find the total value of the outliers. We know that there are 6 outliers with a mean of 688, so the total value of the outliers is:
688 x 6 = 4128
Now we can subtract the total value of the outliers from the total value of the original data set to find the total value of the remaining data points:
26700 - 4128 = 22572
Finally, we can divide the total value of the remaining data points by the number of remaining data points to find the new mean:
(22572)/(100-6) = 231.14
Therefore, the new mean after removing the outliers is approximately 231.14.
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1.11 Jared and Leah both have bank accounts. The balance in Jared's bank account is -$5.50. The balance in Leah's bank account is $5.50. Which statement is true? A. Jared and Leah both have the same amount of money available in their accounts. B. Jared and Leah both owe the bank the same amount of money. C. Jared has money available in his account, but Leah owes the bank money. D. Leah has money available in her account, but Jared owes the bank money.
Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for pi.
The volume of the solid where the cone and the half sphere are hollow is 3839 in³.
What is volume?Volume is the space occupied by a 3D object.
To find the volume of the solid where the cone and the half sphere are hollow, we use the formula below
Folrmula:
V = πr²H-(πr²h/3)-(2/3πr³)................ Equation 1Where:
V = Volume of the solidH = Height of the solidh = Height of the coner = Radius of the base of the solid = Radius of the half coneFrom the question,
Given:
H = 29 inh = 29/2 = 14.5 inr = 8 inπ = 3.14Substitute these values into equation 1
V = (3.14×8²×29)-(3.14×8²×14.5/3)-(2×3.14×8³/3)V = 5827.84-971.31-1071.79V = 3838.74 in³V ≈ 3839 in³Learn more about volume here: https://brainly.com/question/1972490
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6. Carina has 24 apples, 36 bundles of bananas and 12 lemons. She wants to put all of the fruit into plastic containers, each with the same number of pieces of fruit in it. What is the greatest number of pieces of fruit she can put in each plastic container?
pls ayuda no entiendo ingles Flo
Solution:
Find the Highest Common Factor of 12, 24, and 36.
Highest Common Factor = 12
Divide.
[tex]12\div12=1[/tex]
[tex]24\div12=2[/tex]
[tex]36\div12=3[/tex]
12 symbolizes the amount of baskets there are.
---------------------------------------------
Answer:
1 lemon per basket.
2 apple's per basket.
3 banana's per basket.
---------------------------------------------
There is no possible way that there can be the same amount of fruit in each basket.
---------------------------------------------
To find the greatest number of pieces of fruit that can be put in each plastic container, we need to find the greatest common divisor (GCD) of the given numbers. The GCD is the highest number that divides all the numbers evenly. In this case, the GCD is 12.
Explanation:To find the greatest number of pieces of fruit that can be put in each plastic container, we need to find the greatest common divisor (GCD) of the given numbers. The GCD is the highest number that divides all the numbers evenly. In this case, we want to find the GCD of 24, 36, and 12.
The prime factorization of 24 is 2 * 2 * 2 * 3. The prime factorization of 36 is 2 * 2 * 3 * 3. The prime factorization of 12 is 2 * 2 * 3.
The GCD is found by taking the common factors with the lowest exponent. So the GCD of 24, 36, and 12 is 2 * 2 * 3 = 12. Therefore, Carina can put 12 pieces of fruit in each plastic container.
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Consider the following linear transformation
T(x1, x2, x3)= (2x1-3x2, -x1+4x2)
What is the co-domain of T? Select all options that are correct.
2
3
R3
R2
The co-domain of T is R2. So the correct option is: R2.
In linear algebra, a linear transformation is a function that maps vectors from one vector space to another while preserving certain properties.
In this case, the given linear transformation T takes a vector in [tex]$\mathbb{R}^3$[/tex] as input and outputs a vector in [tex]$\mathbb{R}^2$[/tex].
The notation T: [tex]$\mathbb{R}^3$[/tex] [tex]$\to$[/tex] [tex]$\mathbb{R}^2$[/tex] indicates that the domain of T is [tex]$\mathbb{R}^3$[/tex] and the co-domain (or range) is [tex]$\mathbb{R}^2$[/tex].
The co-domain is the set of all possible output values that can be obtained from the linear transformation.
The co-domain of a linear transformation is the set of all possible outputs that can be obtained by applying the transformation to any input.
In this case, the linear transformation T maps a vector in R3 to a vector in R2.
Therefore, the co-domain of the given linear transformation T is [tex]$\mathbb{R}^2$[/tex], which means that the output of T is a two-dimensional vector.
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Please answer with all work I need it asap
Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.
Count the number of distinct islands. An island is considered to be the same as another if they have the same shape, or have the same shape after rotation (90, 180, or 270 degrees only) or reflection (left/right direction or up/down direction).
To count the number of distinct islands in a non-empty 2D array grid of 0's and 1's, we need to first identify the islands. An island is a group of 1's that are connected 4-directionally. We can use depth-first search or breadth-first search to identify the islands.
Once we have identified the islands, we need to check if they have the same shape or not. To check the shape of an island, we can use a hash function that takes into account the shape of the island. The shape of an island can be represented as a sequence of directions that we follow to traverse the island. For example, if we start at the top-left corner of the island and traverse it in a clockwise direction, the shape of the island can be represented as "up-right-down-left".
To check if two islands have the same shape, we can compare their hash values. If the hash values are the same, the islands have the same shape. However, we also need to consider the rotations and reflections of the islands. To handle rotations, we can generate all possible rotations of an island (90, 180, and 270 degrees) and compute their hash values. To handle reflections, we can flip the island horizontally and vertically and compute their hash values. We can then compare the hash values of the original island with the hash values of the rotated and reflected islands to determine if they have the same shape or not.
Finally, to count the number of distinct islands, we can store the hash values of all the islands in a set. The size of the set gives us the number of distinct islands.
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The radius of a quarter is 1.21 centimeters. if a quarter is rolled so that it travels in a straight line for exactly 7 revolutions, how far would the quarter travel? express your answer in exact form and as an approximation to the nearest hundredths place.
The circumference of the quarter is approximately 7.60516 centimeters.
To find the distance traveled by the quarter, we need to calculate the circumference of the quarter and then multiply it by the number of revolutions.
The circumference of a circle is given by the formula:
C = 2πr
where C is the circumference and r is the radius.
Given that the radius of the quarter is 1.21 centimeters, we can substitute this value into the formula:
C = 2π(1.21)
Now, let's calculate the circumference:
C = 2 × 3.14159 × 1.21
C ≈ 7.60516 centimeters
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Explain why sin^ -1 (sin ( 3 pi 4 )+ 3 pi 4 when y = sin x and y = sin^1(x) are inverses
Answer:
The inverse function of a trigonometric function, such as the sine, is called arcsine or sin^-1. To show that the inverse function of sine, sin^-1(x), and the value of x when y = sin(x) are inverses, we can use the definition of the inverse function.
When y = sin(x), this means that x = sin^-1(y). Substituting sin(3π/4) in place of y gives x = sin^-1(sin(3π/4)).
Using the trigonometric identity of the inverse function, we have that:
cos^-1(cos(x)) = x
This means that sin^-1(sin(3π/4)) = 3π/4. Therefore, x = sin^-1(sin(3π/4)) + 3π/4, which means that the value of x is equal to the sum of sin^-1(sin(3π/4)) and 3π/4.
In summary, it can be shown that sin^-1(sin(3π/4)) + 3π/4 = 3π/4, which shows that the inverse function of sine and the value of x when y = sin(x) are reverse. This is because the inverse sine function takes the y value and returns the corresponding x value, and the sine function takes the x value and returns the corresponding y value.
Step-by-step explanation:
Views the system from the inside:
a. JVM
b. implementer
c. client
d. user
e. eclipse
The term that best fits "Views the system from the inside" is the implementer. An implementer is responsible for creating, developing, and integrating software systems, and thus has an intimate understanding of the system from the inside out.
When viewing a system from the inside, the Java Virtual Machine (JVM) is responsible for executing Java bytecode, acting as a layer between the compiled code and the host operating system. An implementer is the person who develops and writes the software, working on the internal components of the system. The client interacts with the system through its provided user interface or API, while the user is an individual who utilizes the system to accomplish their goals. Eclipse is an integrated development environment (IDE) often used by implementers for writing, debugging, and deploying Java applications, which can help in understanding the inner workings of the system.The other terms listed, such as JVM, client, user, and eclipse, may interact with the system in various ways, but do not necessarily have the same level of insight as the implementer.
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Complete the square to re-write the quadratic function in vertex form:
Answer:
[tex]y = {(x - 2)}^{2} - 11[/tex]
i explain the steps in the pic
We are unable to use a method like gradient descent for classifying error in classification because
Gradient descent cannot be used directly for classifying error in classification because the error rate is not a smooth function of the model parameters and gradients cannot be computed.
Gradient descent is an optimization algorithm that is commonly used in machine learning to minimize a cost function. The cost function is a measure of how well the model performs on the training data, and the goal of the optimization algorithm is to find the model parameters that minimize this cost function.
In classification tasks, the cost function is typically a measure of the error rate or misclassification rate of the model. However , the error rate is not a smooth function of the model parameters, and it is not possible to compute gradients with respect to the model parameters. This makes it difficult to use gradient descent directly for optimizing the parameters of a classification model.
Instead, specialized optimization algorithms such as stochastic gradient descent (SGD) and its variants are used to train classification models. These algorithms are designed to work with non-smooth, non-convex cost functions and are able to handle the discrete nature of the output labels in classification tasks. Additionally, other metrics such as accuracy, precision, recall, and F1 score can be used as evaluation metrics instead of the error rate.
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how do I find the inverse function of [tex]f(x)=\sqrt[3]{x-1}+4[/tex]
The inverse function of f(x) = ∛(x-1) + 4 is f⁻¹(x) = (x - 4)³ + 1
What is the inverse of the given function?Given the function in the question:
f(x) = ∛(x-1) + 4
To find the inverse of f(x), we need to switch the roles of x and y in the equation and then solve for y.
f(x) = ∛(x-1) + 4
Let y = f(x) = ∛(x-1) + 4.
y = ∛(x-1) + 4
Now, we can rewrite this equation in terms of x as follows:
x = ∛(y-1) + 4
Subtracting 4 from both sides, we get:
x - 4 = ∛(y-1)
Cubing both sides, we get:
(x - 4)³ = y - 1
Adding 1 to both sides, we get:
y = (x - 4)³ + 1
Replace y with f⁻¹(x)
f⁻¹(x) = (x - 4)³ + 1
Therefore, the inverse function is f⁻¹(x) = (x - 4)³ + 1.
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What is the relationship between wavelength and period? (both in words and mathematically)
The relationship between wavelength and period is such that as the wavelength of a wave increases, its period also increases, given that the wave speed remains constant. This means that longer wavelengths result in longer periods, while shorter wavelengths correspond to shorter periods.
Mathematically, this relationship is expressed through the formula v = λf, where v represents the wave speed, λ is the wavelength, and f is the frequency. Since frequency (f) is the reciprocal of period (T), i.e., f = 1/T, we can rewrite the formula as v = λ(1/T). By rearranging this equation, we can find the relationship between wavelength and period: λ = vT.
In summary, the relationship between wavelength and period is directly proportional, with longer wavelengths resulting in longer periods and vice versa, given a constant wave speed. The mathematical relationship is expressed as λ = vT, where λ is the wavelength, v is the wave speed, and T is the period.
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You are going to a Brooklyn nets game with your advisory. During a timeout, the performers are launching t shirts into the crowd! You are sitting in a balcony that is 64 feet above the ground, and you can see that a man is aiming the t-shirt gun right towards your section! The height of the t-shirt in feet can be modeled by the function h(t) = -16t + 80t, where t is the time in seconds since he shot the t-shirt.
A: is the performer launching the t-shirt from a platform or from the court (ground level)? How do you know?
B: After how many seconds will the shirt reach you? Explain whether your solution make sense in context
A: The performer is launching the t-shirt from the court (ground level). We can tell this because the initial height of the t-shirt is 0 feet when t = 0. The height of the t-shirt in feet can be modeled by the function h(t) = -16t^2 + 80t.
B: To find out when the shirt will reach you, we need to solve for t in the equation h(t) = 64. Substituting h(t) with 64, we get 64 = -16t^2 + 80t. Solving this quadratic equation, we get two solutions: t = 1 and t = 4. Since it doesn’t make sense for the shirt to reach you before it’s launched (t < 0), we can conclude that the shirt will reach you after 4 seconds.
