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morpeh [17]
2 years ago
8

In the triangle shown above, if theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in unit

s per minute when x equals 3 units
Mathematics
1 answer:
kvv77 [185]2 years ago
7 0
<span>X is increasing at the rate of 12 units per minute. Without the actual diagram of the triangle, this question is impossible to answer. However, doing a google search using your exact wording has given me several search results, some of which have a drawing of the triangle. I am going to assume that those drawings match the triangle you were given. If this is not the case, then this answer will be wrong, but should provide you enough information to be able to solve the problem on your own. First, the triangle is a right triangle with the hypotenuse having a length of 5 and X being the side opposite to angle theta. Now we need to create an equation that defines X in terms of theta. Since X is opposite to theta, and we know the length of the hypotenuse, the sine function comes to mind. So sin A = x/5 5sin A = x x = 5 sin A Now let's calculate the first derivative of that equation with respect to time. So d/dt[ x ] = d/dt[ 5 sin A ] dx/dt = 5 d/dt[ sin A ] dx/dt = 5 cos(A) * d/dt[ A ] dx/dt = 5 cos(A) * dA/dt Now we've been given dA/dt which is 3 radians per minute. But we need to calculate cos(A) when X equal 3. Since we know the hypotenuse, we can use the Pythagorean theorem to get the length of the adjacent side and from there calculate the cosine. So sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt(16) = 4. And since cosine = adjacent/hypotenuse, we have 4/5 = 0.8. Now substitute the known values into the equation and solve. dx/dt = 5 cos(A) * dA/dt dx/dt = 5 * 0.8 * 3 dx/dt = 12 Therefore X is increasing at the rate of 12 units per minute at the moment X equals 3. Note: If the triangle you've been given does not have a hypotenuse of 5. Then THIS ANSWER IS WRONG. If you've been given a hypotenuse, the general equation will be: dx/dt = H * cos(A) * dA/dt Where H = given hypotenuse, dA/dt = rate of change in theta. So dx/dt = H * cos(A) * 3 dx/dt = H * sqrt(H^2 - 3^2)/H * 3 dx/dt = sqrt(H^2 - 9) * 3 dx/dt = 3*sqrt(H^2 - 9) So just plug in whatever value of H you have and you'll get the answer. And if you plug in 5, you'll see that the answer is still 12.</span>
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A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so
mamaluj [8]

Answer:

1) Is the pattern an arithmetic sequence?​

Yes it is

2)Identify a and d.​

a = First term = 2

d = Common difference = 2

3) Write the 50th term of the sequence.​

50th term = 100

4) Find the total number of logs in the first 10 rows.​

= 1010 logs

Step-by-step explanation:

Is the pattern an arithmetic sequence?​

Yes it is

2) Identify a and d.​

A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on,

The formula for arithmetic sequence =

an = a+ (n - 1)d

a = First term

d = Common difference

For the above question:

a = 2

d = Second term - First term

= 4 - 2

d = 2

3) Write the 50th term of the sequence.​

Using the formula for arithmetic sequence

an = a+ (n - 1)d

a = 2

n = 50

d = 2

a50 = 2 + (50 - 1)2

= 2 + (49)2

= 2 + 98

= 100

The 50th term = 100

4)Find the total number of logs in the first 10 rows.​

Sum of first n terms = n/2(a + l)

n = 10

a = first term = 2

We are told that there are 200 logs in the bottom row, hence:

l = last term = 200 logs

Hence,

Sn = 10/2×[ (2 + 200

= 5(202)

= 1010 logs

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3 years ago
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Vinil7 [7]

Answer:

A: Measure of center, also known as the Median.

3 0
3 years ago
What is the equation for the line?
antoniya [11.8K]

Answer:

y=-4x+5

Step-by-step explanation:

the line goes down 4 for every 1 that x changes. the line crosses the y axis at 5.

(this might not be accurate, I can't really see if the line is on the exact point or not)

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3 years ago
Read 2 more answers
in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference​
allsm [11]

I believe there is no such AP...

Recursively, this sequence is supposed to be given by

\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}

so that

a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d

a_n=a_1+(n-1)d

33=8+(n-1)d

21=(n-1)d

n has to be an integer, which means there are 4 possible cases.

Case 1: n-1=1 and d=21. But

\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123

Case 2: n-1=21 and d=1. But

\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123

Case 3: n-1=3 and d=7. But

\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123

Case 4: n-1=7 and d=3. But

\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123

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3 years ago
Hello everyone, I was wondering if you guys could please go subscribe to my youtub/e, and stay subscribed. You don’t have too, b
Greeley [361]
Oh okay I will have a good day

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