Need help #3. The answer is shown, but I don’t know how to get to the answer. Please teach and show steps.

Answers

Answer 1

Answer:

Step-by-step explanation:

We are given a right triangle with a base of x feet and a height of h feet, where x is constant and h changes with respect to time t.

The angle in radians is defined by:

[tex]\displaystyle \tan(\theta)=\frac{h}{x}[/tex]

And we want to find the relationship that describes dθ/dt and dh/dt.

So, we will differentiate both sides with respect to t where x is a constant:

[tex]\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big][/tex]

Differentiate. Apply the chain rule on the left. Again, remember that x is just a constant, so we can move it outside the derivative operator. Therefore:

[tex]\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

Since we know that tan(θ)=h/x, h is the opposite side of our triangle and x is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:

[tex]\text{Hypotenuse}=\sqrt{h^2+x^2}[/tex]

Since secant is the ratio of the hypotenuse to adjacent:

[tex]\displaystyle \sec(\theta)=\frac{\sqrt{h^2+x^2}}{x}[/tex]

So:

[tex]\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}[/tex]

By substitution, we have:

[tex]\displaystyle \Big(\frac{x^2+h^2}{x^2}\Big)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

By multiplying both sides by the reciprocal of the term on the left:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{1}{x}\Big(\frac{x^2}{x^2+h^2}\Big)\frac{dh}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}[/tex]

Our answer is A.

Related Questions

An understanding of statistics is necessary in any job. The use of statistics can help provide answers to many questions. Write a question you think that statistics may help you answer and explain why statistics can help provide an accurate answer.

Answers

Answer:

Statistics can help solving data quantitative analysis data.

Step-by-step explanation:

Statistics can help solving data quantitative analysis data.

Examples of questions, that statistics can help provide answers to

What is the measure of central tendency, that is representative of entire statistical data.

Ans : It can be found out by calculating mean , median , mode

How widely dispersed or spread off is the data

Ans : It can be found out by calculating standard deviation, variance

An example of a question statistics can help you answer is: What is are the socio-economic characteristics of people living in Texas?

Using frequency count and percentage, we can determine the gender, age distribution, occupation and other demographics of the population of people living in Texas.

What is Statistics?Statistics involves the collection, collation, analysis, and interpretation of data to form valid conclusions about problems and give answers to questions raised.We have descriptive and inferential statistics as the two types of statistics.For descriptive statistics, frequency count and percentage can be used to describe the socio-economic characteristics of a population.

Therefore:

An example of a question statistics can help you answer is: What is are the socio-economic characteristics of people living in Texas?Using frequency count and percentage, we can determine the gender, age distribution, occupation and other demographics of the population of people living in Texas.

Learn more about statistics on:

https://brainly.com/question/12150562

7/y = 3x make y the subject

Answers

Answer:

7/y=3x

(3x)y=7

y=7/3x

i don't really understand, please help!!

Answers

Step-by-step explanation:

the proof is given above

Step-by-step explanation:

In Triangle ICU,

Angle 2 = 180° - Angle 1 (Angles on a straight line)

CR = CU - RU

In Triangle ISR,

Angle 3 = 180° - Angle 4(Angles on a straight line)

SU = RS - RU

Angle 1 = Angle 4

Therefore, Angle 2 is equal to Angle 3

CU = RS

Therefore, CR is equal to SU

Triangle ICR and Triangle ISU

IC = IS

Angle 2 = Angle 3

CR = SU

Therefore, Triangle ICR and Triangle ISU are congruent (SAS congruency).

As the two triangles are congruent, Angle CIR = Angle SIU

Please help ASAP! Will give brainlist

Answers

2x+12=3x
2x-3x=-12
-x=-12
x=12

2% as a decimal plssssssssssss help brainliest!

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All you have to do is move the % to the left 2 so it would be 0.02

An airplane makes a 2,748-mile flight in 6 hours. What is the airplane's average rate of speed in miles per hour?

Answers

Answer:

speed=16,480 miles per hour or 16,480/hour.

Step-by-step explanation:

Distance=speed ×time

The diagram shows a square.
(7x + 3) cm
Find the length of the side of the square.
(5x + 8) cm

Answers

The length of each side of the square is; 20.5cm

Squares and equal sides

Since, all sides of a square have equal lengths;

We can assume that the the sides given are equal so that we have;

7x +3 = 5x +8

2x = 8 -3

2x = 5

x = 5/2

x = 2.5

By substituting x into either of the expressions! we have;

7x + 3

7(2.5) + 3 = 17.5 + 3

= 20.5

Answers

Answer:

C. 5d - 5 = 5-5d

Step-by-step explanation:

The answer is B. 5b-5 = -5+5b

how many hours and minutes are there between 9:30 and 1:50

Answers

Answer:

4 hours and 20 minutes!

Answer:

Step-by-step explanation:

PM or AM?

If it is 9:30 AM to 1:50 PM, it is 4 hours and 20 minutes.

if it is 9:30 PM to 1:50 AM, it is also 4 hours and 20 minutes.

If it is 9:30am to 1:50 AM, it is 16 hours and 20 minutes.

A 24-foot by 72-foot rectangular dance floor is completely tiled with 1-foot by 1-foot square tiles. Two opposite corners of the dance floor are connected by a diagonal. This diagonal passes through the interior of exactly how many tiles

Answers

Answer:

do do do do to stop do so at to do do d

John is putting together Christmas gift bags. If he has 20 Kit Kats and 35 bracelets, what is the greatest number of bags he can make in order to have the equal number of KitKats and bracelets in each bag? Hint: Find the GCF

Answers

Answer:5

Step-by-step explanation: the gcf for both number are 5, 20: 5*4. 35: 5*7

PLZ HELP!!
What quadrant is (0, 4)
A.1
B.2
C.3
D.4
E.x-axis
F.y-axis

Answers

Answer:

F.y-axis

Step-by-step explanation:

y axis is the answer because 0 is starting.

The given point

(0,4)

is on the positive segment of the y-axis.

so I really need help. you have to set fractions equal to each other and try and find out how many prefer sweaters and whatnot. Also, the answer isn't supposed to be a fraction, it's supposed to be a whole number, you find the answer by using fractions with the information provided in the word problem above ^
I hope that makes sense. lol, thank you :)

Answers

I can’t help you with that movie

3+(-4) on a number line iready

Answers

Answer:

it minus one or -1

Step-by-step explanation:

because 4 has more minus than 3 plus

A number y has a minimum of -2.5

a.>
b.<
c.≥
d.≤

Answers

Answer:

c.≥

Step-by-step explanation:

Minimum of means the number y can be -2.5 and higher, but it cannot be lower than -2.5.

≥ means more than or equal to.

> means more than only.

< means less than only.

≤ means less than or equal to.

how is the graph of f(x)=-3x^2-4 different from the graph of f(x)=-3x^2 ?

Answers

Answer:

Step-by-step explanation:

rules:

add outside the function : f(x) ± a; will shift a + up / a- down

add inside the function: f(x ± a); will shift a + left / a- right

so if

f(x) becomes f(x) -4 will be shifting down 4 units

5/8 - 1/2 =

1/8
2/3
1/2

Answers

answer:

5/8 - 1/2 = 1/8

I will give brainiest to whoever answers correctly !!

Answers

Answer:

it is not clear .... please add the question and send the link of the question

Answer:

$712.79

Step-by-step explanation:

Solve 72 = 3v^2, where v is a real number

Answers

Answer:

v is equal to 6

Step-by-step explanation:

Answer: v=2√6 or v=−2√6

Step-by-step explanation:

-2v3 + v75

How do I solve this and what would be the answer

Answers are either
3 √3
25 √3
-25 √3
-3 √3

Answers

Answer:

a) [tex]3\sqrt{3}[/tex]

Step-by-step explanation:

Step(i):-

Given - 2 √3 + √75

we know that 25 × 3 = 75

- 2 √3 + √75

= -2 √3 + [tex]\sqrt{25 X 3}[/tex]

By using

[tex]\sqrt{ab} = \sqrt{a} \sqrt{b}[/tex]

= [tex]-2\sqrt{3} + \sqrt{25} X \sqrt{3}[/tex]

= [tex]-2\sqrt{3} + 5 \sqrt{3}[/tex]

= [tex](-2 + 5 ) \sqrt{3}[/tex]

= [tex]3\sqrt{3}[/tex]

The sum of four times a number and fifteen is forty-seven. Find the number.

Answers

It is 8 because 47-15= 32 & 32/4 =8 (please give me brainliest)

Answer:

8 is the number

Step-by-step explanation:

I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47

It probably took me a really long time because I am tired, and I am not using a calculator.

Factor.

x^2−8x+16

(x−4)2

(x+8)^2

(x−8)^2

(x+4)^2

Answers

Answer:

Step-by-step explanation:

In ΔVWX, x = 160 cm, v = 150 cm and ∠W=77°. Find the length of w, to the nearest centimeter. PLEASE HURRY

Answers

Answer:

193

Step-by-step explanation:

according to the question

w²=x²+v²-2xv.cos(<w)

w=√160²+150²-2.160.150.cos(77)°

w=√48100-48000cos(77°)

w=193

Answer:

193

Step-by-step explanation:

delta math

Evaluate if a = 2 , b = 3, and c = -4 :

ab +3c-b

Answers

Answer:

Evaluate if a = 2 , b = 3, and c = -4 :

Step-by-step explanation: that the answer

Use the drawing tool to form the correct answer on the provided graph plot the x-intercept y-intercept and axis of symmetry for the function below g(x) = x2+4x+3

Answers

Answer:

x-intercepts: x =-1, x=-3 when y=0

y-intercept, y=3, when x =0

axis of symmetry x = -2

Step-by-step explanation:

We are given the function: [tex]g(x) = x^2+4x+3[/tex]

We need to draw the graph for

x-intercept y-interceptaxis of symmetry

of the given function.

x-intercept

For finding x-intercept put y=0, in the given function, we will put g(x) =0

We know that: g(x)=y

[tex]y=x^2+4x+3[/tex]

Putting y=0, we get:

[tex]0=x^2+4x+3[/tex]

Now, we need to solve the equation by factorization, to find value of x

[tex]0=x^2+4x+3\\We\:can\:write\\x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+1)(x+3)=0\\x+1=0\:or\:x+3=0\\x=-1\:or\:x=-3[/tex]

So, we get x-intercepts: x =-1, x=-3 when y=0

y-intercept

For, finding y-intercept, put x =0

Putting x=0

[tex]g(x)=x^2+4x+3\\We\:know\:g(x)=y\\y=x^2+4x+3\\y=(0)^2+4(0)+3\\y=3[/tex]

So, we get y-intercept, y=3, when x =0

Axis of symmetry

The formula used to calculate axis of symmetry is: [tex]x = \frac{-b}{2a}[/tex]

We have b=4 and a = 1

Putting values and finding axis of symmetry

[tex]x =-\frac{b}{2a} \\x=-\frac{4}{2(1)}\\x=-2[/tex]

So, we get axis of symmetry x = -2

We will also be requiring vertex of the function:

We can find h = -b/2a (same as axis of symmetry) we get h =-2

k can be found as k=f(h)

Put h=-2 in the function:

g(-2)=(-2)^2+4(-2)+3

g(-2)=4-8+3

g(-2)=-1

So, we get k = -1

The vertex (h,k) is (-2,-1)

Now, the graph is attached in figure below.

Hamda and Layla get paid per project.

Hamda is paid a project fee of AED 25 plus AED 10.50 per hour.

Layla is paid a project fee of AED 18 plus AED 14.25 per hour.

Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.

Show your steps

Answers

Answer:

[tex]Company: 43 + 24.75h[/tex]

Step-by-step explanation:

Given

Hamda:

[tex]Project\ Fee = 25[/tex]

[tex]Hourly\ Rate = 10.50[/tex]

Layla:

[tex]Project\ Fee = 18[/tex]

[tex]Hourly\ Rate = 14.25[/tex]

Required

Derive an expression for total pay

Represent the number of hours with h.

For Hamda and Layla, their pay for h hours is:

[tex]Pay = Project\ Fee + Hourly\ Rate * h[/tex]

For Hamda, we have:

[tex]Hamda : 25 + 10.50 * h[/tex]

[tex]Hamda : 25 + 10.50 h[/tex]

For Layla, we have:

[tex]Layla: 18 + 14.25 * h[/tex]

[tex]Layla: 18 + 14.25 h[/tex]

For h hours, the company will pay:

[tex]Company: Hamda + Layla[/tex]

[tex]Company: 25 + 10.50h + 18 + 14.25h[/tex]

Collect like terms

[tex]Company: 25 + 18 + 10.50h + 14.25h[/tex]

[tex]Company: 43 + 24.75h[/tex]

how do you simplify this radical (4x^2y)^1/3 and have no negative exponents?

Answers

Answer:

4^(1/3) x^(2/3) y^(1/3)

Step-by-step explanation:

why would you expect negative exponents? Just pultiply powers

Solve for s.
3 = s - 2
s=

Answers

The answer is 5 because 5-2=3. S=5

Answer:

3 = s - 2

s = 3 - 2

s = 1

what was hard lol

i need help plz
State the coordinates of the point.

Answers

Answer:

(-5,8)

Step-by-step explanation:

Hope this helps ;)

Find the value of this expression if x=-9.

Answers

Answer:

if x = -9

then, (-9)×(-9) + 3

= 81 +3

= 84

(-9) + 6

= -3

so, ans is = 84/(-3)

= (-84)/3

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