1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
katovenus [111]
3 years ago
8

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

Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
3 0

Answer:

A

Step-by-step explanation:

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

The angle in radians is defined by:

\displaystyle \tan(\theta)=\frac{h}{x}

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

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

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

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

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

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

\text{Hypotenuse}=\sqrt{h^2+x^2}

Since secant is the ratio of the hypotenuse to adjacent:

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

So:

\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}

By substitution, we have:

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

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

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

Therefore:

\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}

Our answer is A.

You might be interested in
What is the slope for the line that goes through the points?
sweet [91]

Answer: 2/1x

Step-by-step explanation:

you follow the graph from the y intercept to the next point

up 2 over 1

4 0
3 years ago
Read 2 more answers
9.)Cici went shopping and spent a total of $45.28. She paid
777dan777 [17]

Answer:

Cici received $54.72 dollars in change

Step-by-step explanation:

$100 (what she payed with) - $45.28 (how much she spent) = $54.72 (how much she got back in change)

8 0
3 years ago
At Clucker's Chicken, a bucket of 4 pieces of dark meat and 5 pieces of white meat costs 7.05. A bucket of 3 pieces of dark meat
Alenkinab [10]

Answer:

The cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.

Step-by-step explanation:

Given:

At Clucker's Chicken, a bucket of 4 pieces of dark meat and 5 pieces of white meat costs 7.05.

A bucket of 3 pieces of dark meat and 8 pieces of white meat costs 8.90.

Now, to find the cost of a piece of dark meat and the cost of a piece of white meat.

Let the cost of a piece of dark meat be x.

And the cost of a piece of white meat be y.

A bucket of 4 pieces of dark meat and 5 pieces of white meat costs $7.05.

So,

4x+5y=7.05

4x=7.05-5y  

x=\frac{7.05-5y}{4}   .......(1)

Now, a bucket of 3 pieces of dark meat and 8 pieces of white meat costs $8.90.

3x+8y=8.90

Substituting the value of x from equation (1) we get:

3(\frac{7.05-5y}{4})+8y=8.90

\frac{21.15-15y}{4} +8y=8.90

\frac{21.15-15y+32y}{4} =8.90

<em>Multiplying both sides by 4 we get:</em>

21.15-15y+32y=35.60

21.15+17y=35.60

<em>Subtracting both sides by 21.15 we get:</em>

17y=14.45

<em>Dividing both sides by 17 we get:</em>

y=0.85

<u>The cost of a piece of white meat = $0.85.</u>

Now, substituting the value of y in equation (1) we get:

x=\frac{7.05-5y}{4}

x=\frac{7.05-5\times 0.85}{4}

x=\frac{7.05-4.25}{4}

x=\frac{2.8}{4}

x=0.70.

<u>The cost of a piece of dark meat = $0.70.</u>

Therefore, the cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.

5 0
3 years ago
What is answer?<br><br> Not really good. At this
Rama09 [41]
J
Because 15 - 13 is 2 x (8 + 4 = 24 and divided by 6 is 4
8 0
2 years ago
As jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. convert this speed to miles per m
Mama L [17]
Did you look on quizlet
5 0
3 years ago
Other questions:
  • What is the sum of 2 ½ , 3 ¼ , and 7?
    5·2 answers
  • Can u help me answer this I am confused.
    12·1 answer
  • Connect Leon bought 8 CDs on sale for
    8·1 answer
  • Convert 17.47° to degrees, minutes, and seconds..
    7·1 answer
  • Max's grade on the first math exam was a 94. His grade on his seond math exam was an 89. What was the percent of change in Max's
    9·2 answers
  • 54.7912 Rounded to the nearest hundredth
    11·1 answer
  • What does interior angle A of the polygon in the figure equal?
    13·2 answers
  • A=0.75V−M solve for v
    6·1 answer
  • Suppose f(x)= x? - 6r? +9x and g(x)=10x-6.
    10·1 answer
  • If the sum of 3.5 and .02 is subtracted from the product of 11 and .05 the result is​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!