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Nimfa-mama [501]

3 years ago

10

Dexter paid $74.94 for 201/5 gallons of gas. What's the price of gas where Dexter filled up his vehicle?

1 answer:

densk [106]3 years ago

3 0

Answer:

$1.90 approx

Step-by-step explanation:

Given data

Amount paid= $74.94

Amount of gallons= 201/5 gallons of gas

= 201/5

=40.2 gallons

let us find the unit cost per gallons

Unit cost per gallon is = 74.94/40.2

Unit cost per gallon=$1.86

The price of gas is $1.90 approx

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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

Pedro has 3 boxes of 6 markers. Rafael has 5 boxes of 5 markers. One of the friends arranges all his markers into 2 equal groups

Komok [63]

Answer:

see below

Step-by-step explanation:

Pedro has 3 boxes of 6 markers.

3*6 = 18 markers

We can divide this by 2 because this is even

18/2 = 9

There are 9 in each group

Rafael has 5 boxes of 5 markers

5*5 = 25

We cannot divide this by 2 because this is odd

3 0

3 years ago

Professionals typically order 10% more than calculated. If w represents the minimum number of whole boxes needed, what expressio

d1i1m1o1n [39]

Number of Boxes ordered = w + w/10 or
w(1+0.1)=1.1 w

Answer
1.1 w

6 0

3 years ago

These two matrices are unable to be added due to dimensional mismatch? True, false, both, unable to answer with the info given

Hoochie [10]

Answer:

false

Step-by-step explanation:

$\left[\begin{array}{c}-4\end{array}\right] +\left[\begin{array}{c}7\end{array}\right] =\left[\begin{array}{c}3\end{array}\right]$

Both of the matrices are 1 x 1 ("one by one"), so they can be added to produce a 1 x 1 matrix.

To add (or subtract) two matrices, they must be the same size.

(m x n) + (m x n) = (m x n)

m x n means a matrix has m rows and n columns. Dimensions are always named in that order: rows, then columns.

6 0

3 years ago

Can someone tell me which one it is. I don’t understand what answer it is. Is it the first one, second, or third. Please help if

dolphi86 [110]

Answer:

The answer is where the line hits (0, -1) since that's the y-intercept

It's the answer choice right below the "No answer text provided"

6 0

3 years ago