Select all of the correct solutions for the following equation

A baker cut a pie in half. He cut each half into 3 equal pieces and piece into 2 equal slices. He sold 6 slices. What fraction o

prisoha [69]

He sold one half of the pie because if you do it in your head split one half into 3 and get one sixth, then that slit in two is 1 twelfth so if he sold six pieces and six is one half of twelve then you get one half.

7 0

3 years ago

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Find the approximate area between the curve f(x) = -4x² + 32x and on the x-axis on the interval [0,8] using 4 rectangles. Use th

Doss [256]

Split up the interval [0, 8] into 4 equally spaced subintervals:

[0, 2], [2, 4], [4, 6], [6, 8]

Take the right endpoints, which form the arithmetic sequence

$r_i=2+\dfrac{8-0}4(i-1)=2i$

where 1 ≤ <em>i</em> ≤ 4.

Find the values of the function at these endpoints:

$f(r_i)=-4{r_i}^2+32r_i=-16i^2+64i$

The area is given approximately by the Riemann sum,

$\displaystyle\int_0^8f(x)\,\mathrm dx\approx\sum_{i=1}^4f(r_i)\Delta x_i$

where $\Delta x_i=\frac{8-0}4=2$ ; so the area is approximately

$\displaystyle2\sum_{i=1}^4(-16i^2+64i)=-32\sum_{i=1}^4i^2+128\sum_{i=1}^4i=-32\cdot\frac{4\cdot5\cdot9}6+128\cdot\frac{4\cdot5}2=\boxed{320}$

where we use the formulas,

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

6 0

2 years ago

Which statements must be true?

Lorico [155]

Take a look at the picture and note that the same tick marks represent that they are congruent parts.

A. UV is parallel to JL. Yes, this is correct. They are parallel because they don't intersect at any point.

B. UW = 12KL. This is incorrect. The truth is, UW = (1/2)(KL). If this is a typo error and there should've been a '/' in between 1 and 2, then this is acceptable.

C. UW = VW. As you can see, UKVW is a rectangle. They have two pairs of congruent sides. And UW≠VW, so this is incorrect.

D. UV = UK. The diagonal of a rectangle is never equal with one of its sides. So, this is incorrect.

E. JK = 2VW. Since VW=UK and we can see that twice the length of UK is equal to JK, then this is correct.

6 0

3 years ago

Please someone help I’m in the middle of my test and I don’t understand this question please someone help me answer it.

DENIUS [597]

Answer:

Freedom of the American people

broadened as a result of the Civil War.Freedom of the American people

broadened as a result of the Civil War.

Step-by-step explanation:

8 0

2 years ago

Find the derivative using the fundamental theorem of calculus part 1<img src="https://tex.z-dn.net/?f=g%28x%29%3D%5Cint%5Climits

QveST [7]

Unfortunately, my answer could not be saved. Please refer to the attachments below.

3 0

2 years ago