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2 years ago

(03.05 LC)

Mathematics

2 answers:

vlabodo [156]2 years ago

8 0

3.14 * 3 * 6 = 56.52 cubic inches. Hope this helps. :)

Rama09 [41]2 years ago

8 0

V = 1/3 * a_base * height, a_base = pi * r^2

V = 1/3* pi * 3^2*6 = 56.54 cubic inch,

so ... Third one!!

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Pani-rosa [81]

x=months

so erica: 200+75x

darrell: 350+50x

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200+75x=350+50x

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3 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

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3 years ago

What is the relationship between the circumference of a circle and its diameter?

Hatshy [7]

The answer is A to the question

5 0

3 years ago

Read 2 more answers

Factor completely. 5x^2+44x-9

Leni [432]

Answer:

(x + 9)(5x - 1)

Step-by-step explanation:

Given

5x² + 44x - 9

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × - 9 = - 45 and sum = + 44

The factors are + 45 and - 1

Use these factors to split the x- term

5x² + 45x - x - 9 ( factor the first/second and third/fourth terms )

= 5x(x + 9) - 1(x + 9) ← factor out (x + 9) from each term

= (x + 9)(5x - 1) ← in factored form

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3 years ago

A computer randomly selects a number from the given set. {2, 4, 6, 9, 16, 44, 51, 60, 78} What is the probability that a number

nekit [7.7K]

You would find the probability of getting an answer less than 10 by counting all of the possible outcomes, or numbers that are less than 10 and compare them to the total number of possible outcomes, or the total number of numbers. You would write the ratio of predicted outcomes to total possibilities.

The answer would be 4/9.

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3 years ago