Mathematics High School

Find the equation of this line.

Answers

Answer 1

f(x)=-2/5x+1

using the two dots Rise/run =-4/10 simplifies tp -2/5 y-intercept is 1

Related Questions

CAN SOMEONE HELP WOTH THISPLS RIGHT ANSWER GETS BRAINLIEST Q4

Answers

Answer: yes

Step-by-step explanation:

Answer:

a. no

b. yes

not sure about the rest though

Simplify.
-7+8i / 10i

A) 2i+4 / 5
B) - i / 5
C) 7i+8 / 10
D) 4i+4 / 5

Answers

The outcome of the complex number given is 7i+8/10 in its most basic form. Option C

Simplifying complex expressions

Complex numbers are referred to as the square root of negative numbers. For instance √-1 = i.

In this expression 'i" is a complex number.

Given the expression below;

-7+8i / 10i

Rationalise

-7+8i / 10i * 10i/10i

= 10i(-7+8i)/10(i²)

= -70i+18(-1)/10(-1)

= -70i - 18/-10

= 7i+1.8

Hence the result of the given complex number in its simplest form is 7i+8/10

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I need help with this please

Answers

The segment AB is a radius and the notation is ↔ AB

Writing the notation with the term that best describes the segment AB

From the question, we have the following parameters that can be used in our computation:

The circle

On the circle, we can see that

The segment AB goes from the center of the circle to a point on the circle

A line that goes from the center of the circle to a point on the circle is the radius of the circle

This means that the segment AB is a radius and the notation is ↔ AB

Answers

The expression where the greatest common factor (GCF) is factored completely is $2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)$

The expression completely factored in is

$2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)$

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

$2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)$

Part B:

To completely factor the expression, we can further factor the quadratic term.

$2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)$

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is $2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)$

The expression completely factored in is

$2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)$

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The average wait time to get seated at a popular restaurant in the city on a Friday night is 8 minutes. Is the mean wait time greater for men who wear a tie

Answers

This isn’t a real question right?

sin 2
x+cos 2
x=1,2sinxcosy=sin(x−y)+sin(x+y)
2sinxsiny=cos(x−y)+cos(x+y),2cosxcosy=cos(x−y)−cos(x+y)
∫xsinxdx=sinx−xcosx,∫xcosxdx=xsinx+cosx,∫sin 2
xdx= 2
x

− 4
1

sin2x
∫x 2
cosxdx=(x 2
−2)sinx+2xcosx,∫x 2
sin 2
xdx= 6
x 3

− 8
2x 2
−1

sin2x− 4
x

cos2x

An infinite square well confines a particle of mass m
˙
to the region −a/2
(x)= ⎩
⎨
⎧

a
2

cos( a
nπx

)
a
2

sin( a 2
nπx

)

for n=1,3,5,…
for n=2,4,6…

Therefore, ψ n

(−x)=(−1) n−1
ψ n

(x), a relationship that holds [with (−1) n−1
replaced by (−1) n
in cases where the ground state is labeled n=0 rather than n=1] for any potential satisfying V(−x)=V(x). Throughout the questions below, take advantage of symmetries and other simplifications to minimize the number of integrals that you must perform by brute force. minimize the number of integrals that you must perform by brute force. 1. Calculate ⟨x⟩,⟨x 2
⟩, and σ x

in the n th stationary state.

Answers

The expectation value ⟨x⟩, the expectation value of $x^2$⟨$x^2$⟩, and the standard deviation σx in the n-th stationary state of the particle in an infinite square well can be calculated using symmetries and simplifications.

In the n-th stationary state, the wave function ψn(x) has a specific form based on the given conditions. For odd values of n (n = 1, 3, 5, ...), ψn(x) = (a/2) * cos[(nπ/a)x]. For even values of n (n = 2, 4, 6, ...), ψn(x) = (a/2) * sin[(nπ/2a)x].

To calculate the expectation value ⟨x⟩, we need to evaluate the integral ∫ψn*(x) * x * ψn(x) dx, where ψn*(x) represents the complex conjugate of ψn(x). However, due to the symmetry property ψn(-x) =$(-1)^(n-1)$ * ψn(x), we can simplify the integral. Since x is an odd function and ψn(x) is an even or odd function depending on n, the product ψn*(x) * x * ψn(x) is an odd function. Thus, the integral over the entire well, from -a/2 to a/2, is zero. Therefore, ⟨x⟩ = 0 for all n.

To calculate ⟨$x^2$⟩, we evaluate ∫ψn*(x) *$x^2$ * ψn(x) dx. Here, using the same symmetry property, we find that ψn*(-x) = $(-1)^(n)$ * ψn(x). As$x^2$ is an even function and ψn(x) is even or odd depending on n, the product ψn*(x) * $x^2$* ψn(x) is an even function. Hence, the integral from -a/2 to a/2 gives a $x^2$non-zero result. The integral evaluates to (a^2)/4 for odd n and ($a^2$)/8 for even n. Therefore, ⟨$x^2$⟩ = (a^2)/4 for odd n and ⟨$x^2$⟩ = ($a^2$)/8 for even n.

Finally, the standard deviation σx is given by the square root of the variance, where the variance is defined as ⟨$x^2$⟩ -$⟨x⟩^2$. Since ⟨x⟩ = 0 for all n, the variance simplifies to just ⟨$x^2$⟩. Therefore, σx = sqrt(⟨$x^2$⟩) = a/2 for odd n and σx =sqrt⟨$x^2$⟩ = a/(2$\sqrt{2}$) for even n.

In summary, for the n-th stationary state in an infinite square well, ⟨x⟩ is always zero, ⟨$x^2$⟩ is ($a^2$)/4 for odd n and ($a^2$)/8 for even n, and σx is a/2 for odd n and a/(2$\sqrt{2}$) for even n. These results are obtained by utilizing symmetries and taking advantage of simplifications, which reduce the need for extensive calculations.

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Use the simple interest formula 1=prt find the amount that needs to be invested at 7%per year for 12 years in order to earn 2500$in interest

Answers

the answer is 1358.70

if i were to roll a dice one time what is the probability of it landing on an even number?

Answers

Answer:

50% chance, 3/6

Step-by-step explanation:

there are 6 numbers on a die, 1,2,3,4,5,6. 3 even and 3 odd

Answer:

50%

Step-by-step explanation:

even numbers on a dice: 2,4,6

odd numbers:1,3,5

3/6= 0.5

probability is 50%

you want to treat some of your friends to the movies, and you have $75 to spend. If each ticket costs $10, and you want to purchase $25 worth of snacks, how many friends can you take to the movies?

Answers

Answer:

5 friends

Step-by-step explanation:

Since the snacks are worth $25, it is deducted from the total

10x=75-25

10x=50

x=5

The formula for finding the volume of a rectangular prism is V = lwh. The height h of a rectangular prism is 12 centimeters. The prism has a volume of 10,800 cubic centimeters. The prism's length l is modeled by 3x centimeters and its width w by (2x + 1) centimeters. What is the value of x? What are the dimensions of the length and the width?

Answers

Answer:

x = 12

prism's length = 36 centimeters

Prisms width = 25 centimeters

Step-by-step explanation:

volume of a rectangular prism, V = length × width × height

volume = 10,800 cubic centimeters

prism's length = 3x

Prisms height = 12 centimeters

Prisms width = (2x + 1)

volume of a rectangular prism, V = length × width × height

10,800 = 3x * 2x + 1 * 12

10,800 = 6x² + 3x * 12

10,800 = 72x² + 36x

72x² + 36x - 10,800 = 0

2x² + x - 300 = 0

Using quadratic formula

x = -b ± √b² - 4ac / 2a

= -1 ± √1² - 4*2*-300 / 2*2

= -1 ± √1 - (-2400) / 4

= -1 ± √1 + 2400 / 4

= -1 ± √2401 / 4

= -1 ± 49 / 4

x = (-1 + 49)/4 or (-1 - 49)/4

= 48/4 or -50/4

x = 12 or -12.5

x cannot be a negative value

Therefore, x = 12

prism's length = 3x

= 3(12)

= 36 centimeters

prism's length = 36 centimeters

Prisms width = (2x + 1)

= 2(12) + 1

= 24 + 1

= 25 centimeters

Prisms width = 25 centimeters

Given 2 = ln(x + In y), evaluate Zx, Zy.

Answers

The partial derivatives Zx and Zy are:
Zx = 1/(x + ln y)
Zy = (1/y)/(x + ln y)

Given the equation 2 = ln(x + ln y), we need to evaluate the partial derivatives Zx and Zy with respect to x and y, respectively.
Differentiate the equation with respect to x.
For Zx, we treat y as a constant and differentiate the equation with respect to x:
Zx = d/dx[ln(x + ln y)].

Using the chain rule, we get:
Zx = 1/(x + ln y) * d/dx(x + ln y)4
Since the derivative of x with respect to x is 1 and the derivative of ln y with respect to x is 0 (as y is treated as a constant):
Zx = 1/(x + ln y)
Step 2: Differentiate the equation with respect to y.
For Zy, we treat x as a constant and differentiate the equation with respect to y:
Zy = d/dy[ln(x + ln y)]
Using the chain rule, we get:
Zy = 1/(x + ln y) * d/dy(x + ln y)
Since the derivative of x with respect to y is 0 (as x is treated as a constant) and the derivative of ln y with respect to y is 1/y:
Zy = 1/(x + ln y) * (1/y).

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suppose that the random variable x has a exponential distrbution with = 3

Answers

The random variable x follows an exponential distribution with a parameter λ = 3. This distribution is commonly used to model the time between events occurring at a constant average rate.

The exponential distribution is characterized by its probability density function (PDF) and cumulative distribution function (CDF).

In the exponential distribution, the parameter λ represents the rate parameter or the average number of events occurring per unit of time. In this case, with λ = 3, we can interpret it as an average of 3 events occurring per unit of time.

The PDF of the exponential distribution with parameter λ is given by f(x) = λe^(-λx), where x is a non-negative value. This function describes the probability of observing a specific value of x.

The CDF of the exponential distribution is given by F(x) = 1 - e^(-λx). It represents the probability that x is less than or equal to a given value.

The exponential distribution is widely used in various fields such as reliability analysis, queueing theory, and survival analysis. It is particularly useful when modeling the time between events with a constant average rate.

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3. The line segment below is a reflection over which line?O y-axisO y =xO y = -xO x-axis

Answers

Remember that

The rule of a reflection over the line y=-x is equal to

(x,y) ------> (

Find the slope of the line passing through the points (-6, -5) and (4,4).

Answers

Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

Jonathan purchased 120 pieces of candy for Valentine's Day . He gives 2 pieces to each of his friends. When he finishes handing out candy he has 30 pieces left. How many friends did you give the candy to?

Answers

Answer:

45 friends

Step-by-step explanation:

Consider the infix expression: 16/(5+3). The equivalent postfix (reverse Polish notation) expression is:
16/8
16/5+3
1653+/
53+/16

General-purpose architectures are divided into three groups: memory-memory, register-memory, and load-store stack addressing, accumulator addressing, and register addressing Von Neumann, parallel, and quantum Windows, Mac, and Linux A stack-organized computer uses addressing. indirect zero indexed direct

Answers

The equivalent postfix (reverse Polish notation) expression is: 16 /8. Stack-organized computers are computers that use stack addressing. They employ direct, indirect, and zero-indexed addressing.

The infix expression is: 16/(5+3). To find its equivalent postfix expression (in reverse Polish notation), we need to follow the following steps:Step 1: Consider the left parentheses, which has the lowest precedence. Since it does not involve any calculation, just put it in the stack. Stack: {(Step 2) Step 2: We have 16 and the division operator. Since there is nothing in the stack, just add them to the stack. Stack: {16, /}Step 3: Now, we have a left parenthesis and the numbers 5 and 3. Since the left parenthesis has the lowest precedence, just put it in the stack. Stack: {16, /, (} Step 4: We have two numbers 5 and 3 and an addition operator. We can solve this expression now. So, we pop 5 and 3 from the stack, add them, and put the result (8) back into the stack. Stack: {16, /, (, 8}Step 5: Finally, we have a right parenthesis. Now, we can solve the expression inside the brackets. We pop 8, and the left parenthesis from the stack and place them in the postfix expression as 8. We now have the postfix expression 16 8 /, which is the equivalent postfix expression of 16/(5+3).Therefore, the equivalent postfix (reverse Polish notation) expression is: 16 8 /In general-purpose architectures, Von Neumann, parallel, and quantum are the three groups. Stack-organized computers are computers that use stack addressing. They employ direct, indirect, and zero-indexed addressing.

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3) Find the simple interest.

Rafael borrowed $12,000 at 6% interest to be paid back in 7 years. How much interest will that cost him?
Please help asap

Answers

Step-by-step explanation:

Simple interest = prt÷100

Here,

Principle = 12000

Rate = 6

Time = 7

So to find the simple interest,

You just apply the formula.

$\frac{p \times r \times t}{100} = \frac{12000 \times 6 \times 7}{100} = 5040$

Interest = 5040

A human cell has an approximate mass of 2.7 × 10-11 grams.
Use these values to estimate the number of human cells in a newborn baby.
Give your answer in standard form, correct to 2 significant figures.

Answers

To estimate the number of human cells in a newborn baby, we need to divide the mass of a newborn baby by the mass of a single human cell.

Given that the mass of a human cell is approximately 2.7 × 10^(-11) grams, we'll need to know the mass of a newborn baby. However, without that information, it's challenging to provide an accurate estimate. The number of cells in a newborn baby can vary significantly based on factors such as birth weight and individual variability.

If we assume an average newborn weight of around 3.5 kilograms (3500 grams), we can set up the following calculation:

Number of cells = Mass of newborn baby / Mass of a single cell

Number of cells ≈ 3500 grams / (2.7 × 10^(-11) grams)

Calculating this, we get:

Number of cells ≈ 1.296 × 10^14

Therefore, an estimate of the number of human cells in a newborn baby would be approximately 1.3 × 10^14, expressed in standard form with two significant figures.

what is (4,5) rotated 90 degrees clockwise?
(pls help)

Answers

Answer:

(5,-4)

Step-by-step explanation:

⅓m-2/x÷9-y² ÷2x²m-12x÷9x+3xy

Answers

The simplified form of the expression (⅓m - 2/x) ÷ (9-y²) ÷ (2x²m-12x) ÷ (9x+3xy) is (x-3m)/(4mx (mx-6) (3-y)).

Mathematical expression is a mathematical statement involving numerical values, mathematical operations, variables, power of variables and combination of that.

The expression is = (⅓m-2/x)÷(9-y²) ÷(2x²m-12x)÷(9x+3xy)

We have to simplify the expression.

Simplifying the expression we get,

(1/3m - 2/x) ÷ (9 -y²) ÷ (2x²m -12x) ÷ (9x +3xy)

= ((x-3m) / 6mx)*(1 / (3²-y²)) ÷ ((2x (mx-6)) / (3x (3+y)))

= ((x-3m) / 6mx (3+y) (3-y)) * (3x (3+y) /2x (mx-6)) [Since, a²- b² = (a+b)(a-b)]

= (x-3m)/(4mx (mx-6) (3-y))

Hence the simplified expression is = (x-3m)/(4mx(mx-6)(3-y)).

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-1/2=y-1 solve for y and I need to know how you solved it

Answers

Solution:

$y = \frac{1}{2}$

Process of Solution:

1. Switch sides.

$y-1=-\frac{1}{2}$

2. Add 1 to both sides.

$y-1+1=-\frac{1}{2} +1$

3. Simplify.

$y = \frac{1}{2}$

Hope this helps!

I need help pls...ty :)

Answers

Answer:

132

Step-by-step explanation:

because area is when you multiply 2 numbers and if you multiply 12 and 11 you will get 132 u welcome

the points (-5,r) and (2,13) lie on a with slope 3 find the missing coordinate r

Answers

Answer:

r = - 8

Step-by-step explanation:

calculate the slope m using the slope formula , then equate to 3

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 5, r ) and (x₂, y₂ ) = (2, 13 )

m = $\frac{13-r}{2-(-5)}$ = $\frac{13-r}{2+5}$ = $\frac{13-r}{7}$

then equating gives

$\frac{13-r}{7}$ = 3 ( multiply both sides by 7 )

13 - r = 21 ( subtract 13 from both sides )

- r = 8 ( multiply both sides by - 1 )

r = - 8

Which expression simplifies to 5v3?

Answers

Answer:

Step-by-step explanation:

Answer:

D. V15

Step-by-step explanation:

HELPPP SOMEBODY PLEASEEE WITH THIS MATHHHH

Answers

The correct statement is given as follows:

The function g(t) reveals the market value of the house increases by 3.6% each year.

How to define an exponential function?

An exponential function has the definition presented as follows:

$y = ab^x$

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

The parameter b for this problem is given as follows:

b = 1.036.

As the parameter b has an absolute value greater than 1, the function is increasing, with a rate given as follows:

1.036 - 1 = 0.036 = 3.6% a year.

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Right Angle Trig Including Problem Solving Question 4.2.

What's the X1 value and X2?

Answers

The value of x1 and x2 in the given triangle is 11.28 and 3.70 respectively.

What are trigonometric functions?

The first six functions are trigonometric, with the domain value being the angle of a right triangle and the range being a number. The angle, expressed in degrees or radians, serves as the domain and the range of the trigonometric function (sometimes known as the "trig function") of f(x) = sin. The domain and range of the other functions are similar. In calculus, geometry, and algebra, trigonometric functions are often utilised.

The value of x1 and x2 can be determined using the trigonometric identity that relates the adjacent side and hypotenuse.

Cos (a) = adjacent side / Hypotenuse

Cos (27.3) = x1/ 12.7

0.88(12.7) = x1

x1 = 11.28

Now, the trigonometric identity that relates the opposite side and hypotenuse is sine function.

Thus,

sin (19.2) = x2 / 11.28

0.32(11.28) = x2

x2 = 3.70

Hence, the value of x1 and x2 in the given triangle is 11.28 and 3.70 respectively.

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Congratulations! You won a free grill in sweepstakes! You know that you can fit a rectangular grill in your truck that has a width of 212 feet. The length of the grill can be up to three times the width. What is the largest possible perimeter your new grill can have to fit in your taco truck? Show your work.

Answers

Answer:

by5b5ybyb54

Step-by-step explanation:

yb5ybyby

How are the properties of exponents used when dividing a polynomial by a monomial?

Answers

Answer:

a couple different obes

Step-by-step explanation:

there are five

4. Find the value of f(2)-f(0), if a. 3 b. -1 c. 2 d. 0 e. 1 (2-x, f(x) = (x²-x+1, x < 1 x 21

Answers

The correct answer is b. -1.we need to evaluate the function f(x) at x = 2 and x = 0, and then subtract the results.

To find the value of f(2) - f(0),

Let's first calculate f(2):

$f(x) = (2 - x)^2 - (2 - x) + 1$

Substituting x = 2:

$f(2) = (2 - 2)^2 - (2 - 2) + 1$

= 0^2 - 0 + 1

= 1

Now let's calculate f(0):

$f(x) = (2 - x)^2 - (2 - x) + 1$

Substituting x = 0:

$f(0) = (2 - 0)^2 - (2 - 0) + 1$

= 2^2 - 2 + 1

= 4 - 2 + 1

= 3

Finally, we can find the value of f(2) - f(0) by subtracting the results:

f(2) - f(0) = 1 - 3

= -2

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The work done in moving an object through a displacement of d meters is given by W = Fd cos 0, where 0 is the angle between the displacement and the force F exerted. If Lisa does 1500 joules of work while exerting a 100-newton force over 20 meters, at what angle was she exerting the force?

Answers

Lisa was exerting the force at an angle of 41.41 degrees.

The formula given to calculate the work done, W = Fd cosθ, involves the force F, the displacement d, and the angle θ between the force and the displacement. We are given that Lisa does 1500 joules of work (W), exerts a force of 100 newtons (F), and moves the object through a displacement of 20 meters (d). We need to find the angle θ.

Rearranging the formula, we have:

W = Fd cosθ

Substituting the known values, we get:

1500 = 100 * 20 * cosθ

Simplifying, we have:

1500 = 2000 * cosθ

Dividing both sides by 2000, we find:

0.75 = cosθ

To find the angle θ, we need to take the inverse cosine (cos⁻¹) of 0.75. Using a calculator or a trigonometric table, we find that the angle whose cosine is 0.75 is approximately 41.41 degrees.

Therefore, Lisa was exerting the force at an angle of approximately 41.41 degrees.

This means that the force she exerted was not directly aligned with the displacement, but rather at an angle of 41.41 degrees to it. The cosine of the angle determines the component of the force in the direction of the displacement. In this case, the cosine of 41.41 degrees is 0.75, indicating that 75% of the force was aligned with the displacement, resulting in the given amount of work.

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