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3 years ago

8

Stan's, Mark's, and Wayne's ages are consecutive whole numbers. Stan is the youngest, and Wayne is the oldest. The sum of their

ages is 96. Find their ages.

1 answer:

Brums [2.3K]3 years ago

7 0

Stan is 20
mark is 32
wayne is 44

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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

Kruka [31]

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

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

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

5 0

3 years ago

12 = ____% of 160? Thank you!

beks73 [17]

7.5% of 160.

12 / 160 = 0.075

Move decimal 2 places to the left to convert it to a percent, or multiple by 100.

0.075 * 100 = 7.5

7.5% is your answer.

3 0

3 years ago

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please help this is a math question about geometry !!!! please view the attached images to see the question and the answer choic

jolli1 [7]

Answer:

It is the second picture.

Step-by-step explanation:

4 0

2 years ago

I don't really understand this can someone explain this to me

azamat

Find the measure of the arc or angle.

8 0

3 years ago

What are the solutions of the quadratic equation x2=9x+6

irina [24]

Question: What is the solution to the equation $\bold{x\cdot \:2=9x+6}$

Answer: $\boxed{\bold{x=-\frac{6}{7}}}$

Explanation: $\downarrow{\downarrow{\downarrow{}}}$

[ Step One] Subtract 9x From Both Sides Of Equation

$\bold{x\cdot \:2-9x=9x+6-9x}$

[ Step Two ] Simplify Equation

$\bold{-7x=6}$

[ Step Three ] Divide Both Sides By -7

$\bold{\frac{-7x}{-7}=\frac{6}{-7}}$

[ Step Four ] Simplify

$\bold{x=-\frac{6}{7}}$

$\bold{\rightarrow{}Rhythm \ Bot\leftarrow{}}$

5 0

3 years ago

Read 2 more answers