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4 years ago

6

Alice make 2 bunches of balloons turre are the same Numbers of red balloons and the same Numbers of blue ballons in each did sir

ve use all of the ballons

1 answer:

german4 years ago

4 0

She put 8 balloons in each color group

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Through: (4,4), slope<br> 9/4

faltersainse [42]

Answer:

y - 4 = (9/4)(x - 4)

Step-by-step explanation:

Here we're given the slope (9/4) of a line and one point (4, 4) on the line. The easiest form of the equation of a straight line to use here is the point-slope form:

y - k = m(x - h).

Here h = 4 and k = 4; the slope is m = 9/4.

Thus, the desired equation is

y - 4 = (9/4)(x - 4)

4 0

3 years ago

Need help with AP CAL

anzhelika [568]

Answer: Choice C

$\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)$

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve $y = e^{-x}$

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is $e^{-x}$ where 0 < x < 1

Let's compute the area of each general cross section.

$\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\$

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

$\displaystyle \int_{0}^{1}e^{-2x}dx\\\\$

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

If x = 0, then u = -2x = -2(0) = 0
If x = 1, then u = -2x = -2(1) = -2

This means,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\$

I used the rule that $\displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx$ which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

$\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

In short,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

This points us to choice C as the final answer.

5 0

2 years ago

Using the point-slope formula, what is the equation of the line that passes through the points (1,5) and (0, 0)?

DerKrebs [107]

Answer:

y =5x

Step-by-step explanation:

$y_{1}-y_{2} = m(x_{1} - x_{2} )$

(5 - 0) = m(1 - 0)

5 = m(1)

5 = m

$y_{1}-y_{2} = m(x_{1} - x_{2} )$

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x -5 + 5

y = 5x

7 0

3 years ago

1. Latoya baked b cookies, her family ate 13 of them. Using b write an expression for the number of cookies that remained :)

fiasKO [112]

Answer:

b-13

Step-by-step explanation:

I'm pretty sure this is right? Unless I'm missing something, if I am I am terribly sorry.

5 0

3 years ago

Read 2 more answers

Find the area of the figure

MakcuM [25]

9514 1404 393

Answer:

24.885 in²

Step-by-step explanation:

Use the formula for the area of a triangle.

A = 1/2bh . . . . . . . where b is the base length and h is the height perpendicular to the base

A = 1/2(7.9 in)(6.3 in) = 24.885 in²

_____

<em>Additional comment</em>

The given side lengths cannot form a triangle, as the side shown as 14.7 is too long for the ends of the other segments to connect to. The attachment shows that side should be 11.97 in.

5 0

3 years ago