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viva [34]
3 years ago
10

All of the girls are Danielle's cabin at camp are the same age. Their counselor is 3 times their age. Danielle's age and her cou

nselor's ages at up to 28. Write an equation that can be used to find the ages of Danielle and her counselor.
Mathematics
1 answer:
FromTheMoon [43]3 years ago
8 0

Answer:

see the explanation

Step-by-step explanation:

Let

D -----> Danielle's age

C -----> Counselor's age

we know that

C=3D ----> equation A

D+C=28 ----> equation B

substitute

equation A in equation B

D+3D=28 ----> equation that can be used to find Danielle's age

Solve for D

4D=28

D=7

<em>Find the value of C</em>

C=3D  ---->  equation that can be used to find Counselor's age

substitute the value of D

C=3(7)=21

therefore

Danielle's age is 7 and Counselor's age is 21

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Answer:

\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558

Step-by-step explanation:

We want to find the Riemann sum for \int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)

where \Delta{x}=\frac{b-a}{n}.

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We have that a=0, b=\frac{3\pi }{4}, n=6

Therefore, \Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}

Step 2: Divide the interval \left[0,\frac{3 \pi}{4}\right] into n = 6 sub-intervals of length \Delta{x}=\frac{\pi}{8}

a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b

Step 3: Evaluate the function at the left endpoints

f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3

f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386

f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964

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Step 4: Apply the Left Riemann Sum formula

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