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3 years ago

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The jars of paint in the art room have different amounts of paint.the green paint jar is 4/8 full. The purple paint jar is 4/6 f

ull. Which paint jar is less full?

1 answer:

ruslelena [56]3 years ago

8 0

The green paint is less full

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Leah is 2 less than 3 times Rachel's age. 3 years from now, Leah will be 7 more than twice Rachel's age. How old will Rachel be

Irina-Kira [14]

Answer:

15

Step-by-step explanation:

Let's call Leah's age l and Rachel's age r. We can write:

l = 3r - 2 (1)

l + 3 = 2(r + 3) + 7 (2)

Substituting (1) into (2) we get:

(3r - 2) + 3 = 2(r + 3) + 7

3r + 1 = 2r + 13

r = 12

In 3 years Rachel will be 12 + 3 = 15 years old.

8 0

3 years ago

How to solve this integration problem? the answer should be -π/12

ivann1987 [24]

$\displaystyle\int_{-1}^{-\sqrt2/2}\frac{\mathrm dy}{y\sqrt{4y^2-1}}$

Try setting $y=\dfrac12\sec t$ , so that $\mathrm dy=\dfrac12\sec t\tan t\,\mathrm dt$ . The interval then changes from $-1\le y\le-\dfrac{\sqrt2}2$ to $\dfrac{2\pi}3\le t\le \dfrac{3\pi}4$ .

Now, the integral is

$\displaystyle \int_{2\pi/3}^{3\pi/4} \frac{\dfrac12\sec t\tan t}{\dfrac12\sec t\sqrt{4\left(\dfrac12\sec t\right)^2-1}}\,\mathrm dt=\int_{2\pi/3}^{3\pi/4}\frac{\tan t}{\sqrt{\sec^2t-1}}\,\mathrm dt$

The Pythagorean identity lets you reduce the denominator:

$\sqrt{\sec^2t-1}=\sqrt{\tan^2t}=|\tan t|$

Since $\tan t$ for the given interval, you have $|\tan t|=-\tan t$ , which means the integral is equal to

$\displaystyle\int_{2\pi/3}^{3\pi/4}\frac{\tan t}{-\tan t}\,\mathrm dt=-\int_{2\pi/3}^{3\pi/4}\mathrm dt=-\dfrac\pi{12}$

8 0

3 years ago

Given three noncollinear points in space, how many lines can be drawn

Serhud [2]

Four lines can be drawn!

5 0

3 years ago

Read 2 more answers

Help? I wasn't able to attend class so I don't understand the work..these are the practice problems

Rzqust [24]

It must be equal to BQ

8 0

3 years ago

Alexeev081 [22]

Answer:

y = 18

Step-by-step explanation:

3.23(y – 18) - 19.17 = -19.17

3.23y - 18 x 3.23 = -19.17 + 19.17

3.23y - 58.14 = 0

3.23y = 58.14

3.23y/3.23 = 58.14/3.23

y = 18

3 0

3 years ago