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3 years ago

Write each number as a fraction and each fraction as a number 4 2/3

Mathematics

1 answer:

Viktor [21]3 years ago

6 0

I dont get the numbers write space beetween

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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

4 years ago

Find the volume of a cone with a base area 36pi and a height equal to twice the radius

beks73 [17]

The volume of a cone is $V= \frac{1}{3} A_{\text{basis}}\cdot H$ . Since $A_{\text{basis}}=36\pi$ and you know that basis is a circle you can conclude that $\pi R^2=36\pi$ and $R=6$ .

If height $H$ equal to twice the radius $R$ , then $H=2R=2\cdot 6=12$ .

The volume will be: $V= \frac{1}{3} \cdot 36\pi \12=144\pi$ cubic units.

8 0

4 years ago

Mr. Thomas spent $1600 on a television and 2/ 5 of the remainder on a refrigerator. He had 1/3 of his original amount of savings

quester [9]

So he spent 1600 so x will represent original savings so
x-1600
then he spent 2/5 of the remainder on a refrigerator so
[(x-1600)2]/5
he had 1/3 of original savings left
[(x-1600)2]/5=1/3x
distrubute
(2x-3200)/5=1/3x
multiply both sides by 15
3(2x-3200)=5x
distrubute
6x-9600=5x
subtract 5x from both sides
x-9600=0
add 9600 to both sides
x=9600

7 0

4 years ago

Evaluate the following expression. 53 Enter the answer

givi [52]

Answer:

125

Step-by-step explanation:

5^3 = 5 ✕ 5 ✕ 5, and 5 ✕ 5 ✕ 5 = 125

Hope this helps :)

3 0

3 years ago

Read 2 more answers

What is the radian measure of 75°?

Rainbow [258]

1.309 is the measure of 75

7 0

3 years ago