outside temperature over a day can be modelled as a sinusoidal function. suppose you know the high temperature for the day is 90 degrees and the low temperature of 80 degrees occurs at 5 am. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.
Answers
Therefore, the equation for the temperature in terms of t is: d = 5 sin(π/12 t - π/3) + 85.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables. They can also be used to represent relationships between different variables.
Here,
The temperature variation over the day can be modeled using a sine function of the form:
d = A sin(Bt + C) + D
where A is the amplitude (half the difference between the maximum and minimum temperatures), B is the angular frequency (2π divided by the period), C is the phase shift (the horizontal displacement of the wave), and D is the vertical shift (the average temperature over the day).
Using the given information, we can determine some of these values:
A = (90 - 80)/2 = 5
D = (90 + 80)/2 = 85
B = 2π/24 = π/12 (since the period of a day is 24 hours)
To find C, we need to know when the temperature reaches its maximum value. Since the maximum temperature occurs halfway between the minimum temperature and the next minimum temperature, it must occur at t = 12 (noon). Plugging in these values, we get:
80 = 5 sin(π/6 + C) + 85
Solving for C:
-5 = 5 sin(π/6 + C)
-1 = sin(π/6 + C)
π/6 + C = 7π/6 or 11π/6 (since these are the angles whose sine is -1)
C = 11π/6 - π/6 or 7π/6 - π/6
C = 2π/3 or -π/3
Since we want an equation for the temperature in terms of t, we can use C = -π/3 to get:
d = 5 sin(π/12 t - π/3) + 85
To know more about equation,
https://brainly.com/question/28243079
#SPJ4
Related Questions
Cindy tried to find the sum of the exterior angles of the hexagon. What was her error?
will mark brainiliest!
Answers
Step-by-step explanation:
Simple, she found the sum of the interior angles not exterior angles.
The exterior angles of any polygon add up to 360 degrees.
What Cindy did was found the total interior angle measure of a hexagon which is 720
Select the equation that is true.
6,714 ÷ 103 = 6.714
6,714 ÷ 103 = 67.14
6,714 ÷ 103 = 671.4
6,714 ÷ 103 = 6,714
Answers
Answer: None of the choices is correct.
6,714÷103 is about 65.184
Step-by-step explanation:
The closest answer is the second choice. But there must be a typo in the question.
6,714÷100 = 67.14
I hope this helps. You might be able to ask your teacher about the mistake in the question.
Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
Each pair of figures is similar. Find the value of the missing side (x). Round your answer to the nearest tenth if necessary.
Answers
Answer:
4.9 in
Step-by-step explanation:
6/11 = x/9
6/11 times 9 = x
x = 4.9
What is 3c4?
7
4
24
12
Answers
Answer:
3c4 Is equal to 12 because c means ×
please help!! 10+ points
Answers
Answer:
i dont see the question
Step-by-step explanation:
Collin mows lawns for a lawn service. He has 52 customers, each
paying $50.00 per month. He receives 24% of the money he collects.
How much should he earn for the month?
a. $240.00
b. $362.00
1.
c. $540.00 d. $624.00
Answers
Answer:
First, you need to find out how much money Collin collects from all his customers. To do this you can multiply the number of customers (52) by the amount each customer pays per month ($50.00).
52 * $50.00 = $2600.00
Then you need to find out Collin's commission which is 24% of the money he collects. To do this you can multiply the money he collects by 24% (24/100)
$2600.00 * (24/100) = $624.00
So Collin should earn $624.00 for the month.
Step-by-step explanation:
So we are given that Colin mows lawns, with 52 customers, each paying $50 a month. But Colin only keeps 24% of the money. Maybe his gf took the 76% and bought some nice clothes.
Anyway, to start, let’s find out how much Colin would make without losing 76% of the money. To do that, simply take the number of customers (52), and multiply it by the amount of money each pays ($50).
52x50=$2,600.
Colin would make $2,600 without losing that 76%.
Now let’s find how much money Colin actually gets to keep for some reason he loses majority of it. To do that, we would have to take the total amount of money he makes ($2,600) and times it by the percent he gets to keep (24%). If you remember, or if your teacher has taught you by now, how to convert percent into decimals, you should be able to know what 24% is in decimal form. If not then I’ll teach you now. Simply move the percentage sign two places to the left and replace it with a decimal, or divide the number by 100, which is 0.24.
2,600 x 0.24 = $624
The answer is d. $624.00
Colin should earn $624.00 for the month.
A market researcher analyzing the fast-food industry noticed the following: The historical average amount spent at an upscale restaurant was $150.30, with a standard deviation of $50. The researcher wishes to have a sampling error of $5 or less and be 95 percent confident of an estimate to be made about average amount spent at an upscale restaurant from a survey. What sample size should be used (round the number up)
Answers
Answer:
A sample size of 385 should be used.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
What sample size should be used (round the number up)
A sample of n should be used.
n is found when M = 5.
We have that \(\sigma = 50\)
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(5 = 1.96\frac{50}{\sqrt{n}}\)
\(5\sqrt{n} = 1.96*50\)
Simplifying by 10
\(\sqrt{n} = 1.96*10\)
\(\sqrt{n} = 19.6\)
\((\sqrt{n})^2 = (19.6)^2\)
\(n = 384.16\)
Rounding up
A sample size of 385 should be used.
fun quashen answer this you will get 20 pointes it must be corret a clue it not B , D have fun be fast
Answers
Answer:
A. no, the sale price is about 60% of $65 or $39. Because $38 is less than $39, you do not have enough money.
Step-by-step explanation:
Given parameters:
Discount on sales = 40%
Amount with me = $38
Original sales price = $65.99
Unknown:
Will you have enough money to buy the item = ?
Solution:
To solve this problem, let us find the discount amount on the selling price;
= \(\frac{40}{100}\) x 65.99
= $26.39
So, the price of the item now = Original sales price - discount amount
= $65.99 - $26.39
= $39.6
$39.6 can also be derived from 60% of $65.99
This amount is more than amount at hand.
What is a perfect square 6^1
Answers
A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.
However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.
need help with explanation will give brain list
Answers
Answer:
Option 4: 12.7
Step-by-step explanation:
You can look at the diagram as two 45º45º90º triangles.
By the properties of a 45º45º90º triangle:
OW=WL=a
OL=a√2
a√2 = 18
a=18/√2a≈12.728
1. Solve MMXXVII -MCMXCII
A.LV
B. XLV
C. XXXV
D. XXV
E. XV
Answers
Answer:
the answer is C. XXXV
Step-by-step explanation:
MMXXVII -MCMXCII= XXXV
Find the area of a sector with a central angle of 75 degrees and a radius of 12. Express your answer in terms of pi
Answers
Heeeelp please, Can be zero or not?
with all steps and explanay.
Answers
The value of integral is 3.
Let's evaluate the integral over the positive half of the interval:
∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx
Let u = 4 + 3sin(x), then du = 3cos(x) dx.
Substituting these expressions into the integral, we have:
∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du
Using the power rule of integration, the integral becomes:
∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]
Evaluating the definite integral at the limits of integration:
(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))
(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0
So, the value of integral is
= 3-0
= 3
Learn more about Definite integral here:
https://brainly.com/question/30760284
#SPJ1
Answer:
\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)
Step-by-step explanation:
First, compute the indefinite integral:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)
To evaluate the indefinite integral, use the method of substitution.
\(\textsf{Let} \;\;u = 4 + 3 \sin x\)
Find du/dx and rewrite it so that dx is on its own:
\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)
Rewrite the original integral in terms of u and du, and evaluate:
\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)
Substitute back u = 4 + 3 sin x:
\(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
Therefore:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.
Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.
\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)
Therefore, the curve of the function is:
Below the x-axis between -π and -π/2.Above the x-axis between -π/2 and π/2.Below the x-axis between π/2 and π.So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.
Integrate the function between -π and -π/2.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)
Integrate the function between -π/2 and π/2:
\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)
Integrate the function between π/2 and π.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)
To evaluate the definite integral, sum A₁, A₂ and A₃:
\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)
Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:
\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)
Therefore, the given expression cannot be zero.
how would I write an equation?
and what would my x and y represent?
Answers
The equation is x + y=z. X represents the number of hours for tutoring, and Y represents the total cost for the tutoring session. The equation does not represent direct variation, as the hourly rate is a fixed rate, not a variable rate.
How to write an equation for any data? To write an equation for any given data, first identify the independent and dependent variables in the data set. The independent variable is the variable that is changed or manipulated, while the dependent variable is the variable that is observed or measured. Once the independent and dependent variables have been identified, the equation can be written using the dependent variable in terms of the independent variable. For example, if the data set contains a set of values for the independent variable x and the corresponding values for the dependent variable y, then the equation can be written as y = f(x). The function f(x) represents the relationship between the two variables and can be determined by plotting the data points and finding the best fit line or curve. This line or curve is the equation that describes the data set.To learn more about equation refer to:
https://brainly.com/question/2972832
#SPJ1
What is the area of
the segment? Express
the answer in terms
of pi.
Answers
The area of the segment is 9( π-2) units²
What is area of segment?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.
Area of segment = area of sector - area of triangle
area of sector = 90/360 × πr²
= 1/4 × π × 36
= 9π
area of triangle = 1/2bh
= 1/2 × 6²
= 18
area of segment = 9π -18
= 9( π -2) units²
therefore the area of the segment is 9(π-2) units²
learn more about area of segment from
https://brainly.com/question/22599425
#SPJ1
What kind of transformation converts the graph of f(x) = -x - 10 into the graph of g(x)
-9x - 10?
horizontal stretch
vertical stretch
vertical shrink
horizontal shrink
=
Answers
Answer:
zeroay horizontal stretch vertical shrink
Step-by-step explanation:
1+1=2
Please help, I’ll mark your answer as brainliest.
Answers
Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.
What is a sound wave?When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.
When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.
Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.
Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.
Learn more about the sound wave here,
https://brainly.com/question/21995826
#SPJ1
Which inequality is represented by the graph?
Answers
The inequality on the graph is the third option:
(2/5)*x - 3/2 ≥ y
Which inequality is represented by the graph?Let's analyse the graph if the inequality.
We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:
y ≤ linear equation.
We know that the symbol "≤" must be used because of the solid line.
We also can see that when x = 0, y takes a velue between -1 and -2.
With that in mind the correct option is the third one:
(4/5)*x - 2y ≥ 3
Isolating y we get:
(4/5)*x - 3 ≥ 2y
(2/5)*x - 3/2 ≥ y
Changing the order:
y ≤ (2/5)*x - 3/2
That is the graphed inequality.
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
the population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Answers
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
To learn more about differential equations refer to:
brainly.com/question/1164377
#SPJ4
Lesson 17: Use the Four Operations to Solve Problems Cool Down: Andre's Balloons Andre has 125 balloons. He and 4 friends hung up some balloons for a party at school and now there are 80 balloons left. If each person hung up the same number of balloons, how many balloons did each person hang up? 1. Write an equation with a letter for the unknown quantity to represent the situation. 2. Solve the problem. Explain or show your reasoning.
Answers
a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.
b) An equation representing the situation is x = (125 - 80)/5.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
The mathematical operations provide solutions to mathematical problems using operands.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
The total number of balloons that Andre has = 125
The number of balloons remaining after hanging some for the school party = 80
The difference (number of balloons used) = 45 (125 - 80)
The number of friends who hang the balloons = 5
The number of balloons hung by each friend of Andre = 9 (45/5)
Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.
Learn more about mathematical operations at https://brainly.com/question/30715366.
#SPJ1
Which of the following coordinates is located in Quadrant I?
(-3,-4)
(-1,2)
(4,6)
O
(2,-1)
Answers
Answer:
(4,6)
Step-by-step explanation:
quadrant 1 always has positive coordinates so the only one with all positive coordinates is (4,6)
Sasha Cohen does a triple toe loop (rotating 1080 degrees) in 1.5 s. What is her average angular speed during this jump
360°/s
3.0 rad/s
12.6 rad/s
720 rad/s
Answers
9514 1404 393
Answer:
12.6 rad/s
Step-by-step explanation:
1080 degrees in 1.5 seconds is an angular rate of ...
(1080°)/(1.5 s) = 720 °/s
There are π radians in each 180°, so this angular speed is ...
720 °/s = 4×180 °/s = 4×π rad/s ≈ 12.6 rad/s
Sasha's average angular speed is 12.6 rad/s.
Select the interval(s) where the function is increasing:
f(x) = x ^ 4 - 5x ^ 2 - 3
(- 9.3, - 3)
(- ∞,- 1.5)
(0, 1.5)
(-1.5, 0)
(1.5, ∞)
(-∞, ∞)
(-9.3, ∞)
Answers
(-1.5, 0) and (1.5, ∞)
I need help very fast plz someone help
Answers
Answer:
4-9=-5
Step-by-step explanation:
do the work you get that
How do I simplify this expression
Answers
Where did u get the 55 and 88 from?
Answers
Answer:
11
Step-by-step explanation:
11 times 5 is 55
11 times 8 is 55
HELP ASAP! LOOK AT PIC PLS
Answers
Answer:
E
Step-by-step explanation:
well, yes we know what coins there are and that they’re in jars right? but to find which jar is worth the most, we need to know how many coins are in each. she could have 300 pennies, 2 quarters, 4 dimes, and 7 nickels. we need more information to answer this question so E is the only correct option!
Alice has 5 quarters and 2 nickels. How many cents does Alice have
Answers
Answer:
Alice has 135 cents, or $1.35.
Step-by-step explanation:
A quarter is worth 25 cents.A nickel is worth 5 cents.Multiply 25 by 5, since there are 5 quarters. That will give you 125.Multiply 5 by 2, since there are 2 nickels. That will give you 10.Add 125 and 10. That will give you 135, which is your answer!Which one I’ll mark you!!!
Answers
Answer:
D.
Step-by-step explanation:
99 multiplied by 1 = 99
99 multiplied by a number less than 1 = less than 99
99 multiplied by a number greater than 1 = greater than 99
In all choices, 99 appears as a factor and is multiplied by a fraction.
If the fraction that 99 is being multiplied by is less than 1, then that product is than 99. If the fraction is equal to 1, then the product is 99. If the fraction is greater than 99, then the product is greater than 99.
Look at the fractions:
A. 20/20 = 1, so 20/20 * 99 = 99
B. 16/15 * 99; 16/15 > 1, so 16/15 * 99 > 99
C. 12/7 * 99; 12/7 > 1, so 12/7 * 99 > 99
D. 10/11 * 99; Since 10/11 < 1, then 10/11 * 99 < 99
D. is the answer because it is the only choice with fraction that is less than 1 multiplying 99.
By which rule are these triangles congruent?
Answers
Answer:
S, S, S
Step-by-step explanation: