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2 years ago

Is ( – 1, – 5) a solution to this system of equations? 7x+2y=13 4x+4y=14

Mathematics

1 answer:

Rus_ich [418]2 years ago

5 0

Answer:

yes

Step-by-step explanation:

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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

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

3 0

3 years ago

1. Find the slope between the given two points. (-1, -11) and (-6, -7) *

ZanzabumX [31]

Answer: Y=mx+b

m=-4/5

Step-by-step explanation:

3 0

2 years ago

If 15 books cost $90, what is the unit price?

creativ13 [48]

Answer:

$6/ book

Step-by-step explanation:

Unit price = Total cost/ total number of items

= 90/15

=$6 per book

4 0

3 years ago

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Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina

sukhopar [10]

Answer:

Possible C:

(1 , 1 + 3sqrt(3))

(1 , 1 - 3sqrt(3))

Step-by-step explanation:

AB = 6 units

Midpoint of AB is (1,1)

C would be at x = 1

So, (1,y)

(y-1)² + (1+2)² = 6²

(y-1)² = 36 - 9

(y-1)² = 27

y - 1 = 3sqrt(3)

y - 1 = -3sqrt(3)

y = 1 + 3sqrt(3)

y = 1 - 3sqrt(3)

7 0

3 years ago

What are all the factors of 32? A 2, 4, 8, 16 B 1, 2, 16, 32 C 1, 2, 4, 8, 16, 32 D 2, 4, 6, 8, 12, 16, 32

Natasha2012 [34]

What are all the factors of 32?

answer : ( C ) 1, 2, 4, 8, 16 and 32.....

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2 years ago

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