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natali 33 [55]
2 years ago
6

Alisa has a bunch of coins. She has pennies. She has nickels. She has dimes. She has quarters. They lie in one big pile. Alisa w

ants to organize her coins. So she goes into her cupboard and finds four jars. Each jar has a different shape and size. Alisa puts the pennies into one jar. She puts the nickels into another jar. She puts the dimes into another jar. She puts the quarters into another jar. Then she puts all four jars on the table and steps back. Looking at them, Alisa scratches her head.( look at pic! )

Mathematics
2 answers:
melisa1 [442]2 years ago
5 0
Not enough information is provided
Alona [7]2 years ago
3 0

Answer:

E. Not enough info.

Step-by-step explanation:

There could be 2 quarters 500 nickels and 7 pennies or 800 pennies 50 quarters and 2 nickels.

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f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans
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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}.

Step 1: Find \Delta{x}

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

f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527

f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0

f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527

Step 4: Apply the Left Riemann Sum formula

\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315

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

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