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Rasek [7]
3 years ago
10

The sales totals at Macy's food store have increased exponentially over the months. Which of these best shows the sales in the f

irst three months?
A:$1200 in the first month, $1220 in the second month, $1240 in the third month B:$1200 in the first month, $1272 in the second month, $1344 in the third month C:$1200 in the first month, $1285 in the second month, $1370 in the third month D:$1200 in the first month, $1224 in the second month, and $1248.48 in the third month
Mathematics
2 answers:
Phoenix [80]3 years ago
6 0

Answer:

D

Step-by-step explanation:

Tpy6a [65]3 years ago
3 0

An exponential or geometric function can be expressed as a power of t, where t is time.  

This means that if you can fit all three values into the formula  

S = S0 * (1+r)^t  

for a constant r, and t=1, 2, 3 (or 0, 1, 2 for simplicity), then it's exponential.  

You can see right away that the first and second sets of numbers are not exponential. These are linear, because each month is a fixed value greater than the previous one.  

If you look at the formula above, you can see that each successive time interval's growth can be calculated by multiplying a fixed value to the previous intervals. For example, the second month is given by:  

S(1) = S0 * (1+r)  

S(2) = S0 * (1+r)^2 = S0 * (1+r) * (1+r) = S(1) * (1+r)  

Since each month's sales is 102% the previous month's in the fourth set, this is the one you want.

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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
Please help. Thank you :)
mixer [17]

Okay, first let's look at what they give us!


The measure of angle 2 is 3x + 1


Measure of angle 3 is 2x + 4


And they give us that one angle is right which means it is 90°


Now if we use what we know of triangles, we know that all the angles in a triangle add up to equal 180 which means if we add angle 2, angle 3, and the right angle together we should get 180. Let's write an equation for it:


3x + 1 + 2x + 4 + 90 = 180


First we will add together liked terms!


3x + 2x = 5x


1 + 4 + 90 = 95


This gets us:


5x + 95 = 180


Second, let's get rid of that 95 by subtracting it from both sides, after doing this it should leave us with:


5x = 85


Third we need to get the x by itself and we can do it by dividing both sides by 5 to get:


x = 17


Now the question asks to find the measure of angle 2, given that angle 2 is 3x + 1 all there is left to do is to plug in 17 for x!

3(17) + 1


51 + 2 to get us 52!


Answer: 52

3 0
3 years ago
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