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3 years ago

Simplify 2 (csc ^2 0-cot^2 0).

Mathematics

1 answer:

GarryVolchara [31]3 years ago

3 0

Answer:

Step-by-step explanation:

answer is 2 because cosec^2 theta-cot^ theta is 1and when u multiply 1 and 2 answer is 2

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Y = (4/9) x

frez [133]

Answer:

V = 8.06 cubed units

Step-by-step explanation:

You have the following curves:

$y_1=\frac{4}{9}x^2=f(x)\\\\y_2=\frac{13}{9}-x^2=g(x)$

In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:

$V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx$ (1)

To determine the limits of the integral you equal both curves f=g and solve for x:

$f(x)=g(x)\\\\\frac{4}{9}x^2=\frac{13}{9}-x^2\\\\\frac{4}{9}x^2+x^2=\frac{13}{9}\\\\\frac{13}{9}x^2=\frac{13}{9}\\\\x=\pm 1$

Then, the limits are a = -1 and b = 1

You replace f(x), g(x), a and b in the equation (1):

$V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units$

The volume of the solid of revolution is approximately 8.06 cubed units

8 0

3 years ago

Frank has a sheet of paper which is 1/624 inch thick. If the sheet is folded in half, the total thickness will be 1/312 inch A s

netineya [11]

Answer:

The thickness of the sheet will be 16/39 inch after folded 8 times

Step-by-step explanation:

* Lets explain how to solve the problem

- Frank has a sheet of paper of 1/624 inch thick

- The sheet is folded in half, the total thickness is 1/312 inch

- The sheet folded in half again and the total thickness is 1/156 inch

- We need to know the thickness of the sheet after folded 8 times

∵ The 1st thickness is 1/624 inches

∵ The 2nd thickness is 1/312 inch ⇒ after 1st fold

∵ The 3rd thickness is 1/156 inch⇒ after 2nd fold

∵ 1/312 ÷ 1/624 = 2

∵ 1/156 ÷ 1/312 = 2

∴ There is a common ratio 2 between each two fold

∴ The thicknesses of the sheet after each fold formed a

geometric series

∵ Any term of the geometric series is $a_{n}=a(r)^{n-1}$ , where

a is the first term, r is the ratio between each two consecutive

terms and n is the position of the term

∵ a = 1/312 because it is the thickness of the 1st fold

∵ r = 2 , n = 8

∴ $a_{8}=\frac{1}{312}(2)^{8-1}=\frac{16}{39}$

∴ The thickness of the sheet will be 16/39 inch after fold 8 times

8 0

4 years ago

Read 2 more answers

Its a word problem. Jann just started a new job. For every 4 hours he works, Jann earns $60. What is the unit rate for how much

Pepsi [2]

Answer:

$15

Step-by-step explanation:

unit rate means how much he earns in 1 hour

so if he earns $60 in 4 hours

then you have to divide 60 by four

which gives you $15

that means he earn $15 in one hour

7 0

3 years ago

Simplify: 5^2(3d - 2)

stiks02 [169]

Answer: 25d

Step-by-step explanation:

3d - 2 = 1d

5(5) = 25

25(1d) = 25d

5 0

3 years ago

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Use the multiplier method to incrases £258 by 43%

pochemuha

Answer:

Answer is 368.94

Step-by-step explanation:

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3 years ago