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3 years ago

8

Write an equation showing that the distance traveled on the first day plus the distance traveled on the second day is equal to 4

25 miles.

2 answers:

Alexandra [31]3 years ago

8 0

It's simple you did not asked to solve this problem, but the equation for this is x+y = 425 X is the distance traveled on the first day, and Y is the distance traveled on the second day

Radda [10]3 years ago

4 0

X+y=425. This is as simple it can be, unless theres more information. x is the distance traveled on the first day and y is the distance traveled on the second day.

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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

2 years ago

Order from least to greatest 6.03 6.3 6.305 6.035

Masja [62]

Answer:

6.03 6.035 6.3 6.305

not 100% sure

let me know if im correct thank you!

7 0

2 years ago

Is 1/8<-1/2 a solution or no?

miv72 [106K]

It is not because always remember, a positive is greater than a negative. This equation is showing a negative being greater than a positive. That's like saying I'm taller than you.

5 0

3 years ago

"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.) f (x) = c

Oliga [24]

$\bf f(x)=cos\left( \frac{\pi x}{2} \right)\implies \cfrac{df}{dx}=\stackrel{chain~rule}{-sin\left( \frac{\pi x}{2} \right)\cdot \frac{\pi }{2}}$

now, what is the value of the derivative at any extrema on the original function? well, by definition, if the original function has an extrema anywhere, the derivative will be the derivative of a horizontal tangent line to it, and by definition it'll be 0.

8 0

2 years ago

A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than

Reptile [31]

The probability that a randomly selected customer takes more than 10 minutes will be 8.38%

<em><u>Explanation</u></em>

The average or mean $(\mu)$ is 8.56 minutes and standard deviation $(\sigma)$ is 1.04 minutes.

<u>Formula for finding the z-score</u> is: $z= \frac{X-\mu}{\sigma}$

So, the z-score for $X=$ 10 minutes will be.....

$z(X=10)=\frac{10-8.56}{1.04}=\frac{1.44}{1.04}=1.3846... \approx 1.38$

Now, according to the standard normal distribution table, $P(z$ . So.....

$P(X>10)=P(z>1.38)= 1-P(z$

So, the probability that a randomly selected customer takes more than 10 minutes will be 8.38%

3 0

3 years ago