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2 years ago

10

Lindsay has to read a 72-page book in 6 days. If she reads an equal number of pages each day, how many pages will Lindsay need t

o read each day to complete the book?
A. 9
B. 10
C. 11
D. 12

2 answers:

svet-max [94.6K]2 years ago

6 0

Answer : D. 12

Explanation: 72÷6 = 12

◊ YusuCr ◊

NISA [10]2 years ago

5 0

Answer:

D.12

Step-by-step explanation:

72 divided by 6 is 12

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Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

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3 years ago

Halp me please. This questions is killing me. I need the answer. Solve $3a + 4b = a - 8b + 24$ for $a$ in terms of $b$.

Anuta_ua [19.1K]

Answer:

a=12-6b

Step-by-step explanation:

move b and a to their respective sides, getting a = -6b+12

tada :)

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2 years ago

PLEASE HELP Which expression represents the difference quotient of the function f (x) = negative StartRoot 2 x EndRoot?

natali 33 [55]

Answer:

c is the correct option

Step-by-step explanation:

from,

f'(x) = h >0 <u>f</u><u>(</u><u>x</u><u> </u><u>+</u><u> </u><u>h</u><u>)</u><u> </u><u>-</u><u> </u><u>f</u><u>(</u><u>x</u><u>)</u><u> </u>

h

f(x) = - √2x

f(x + h) = - √(2x + h)

f'(x) = h>0 <u>-</u><u>√(2x + h) - √2x</u>

h

rationalize the denominator

= h>0 <u>-</u><u>√</u><u>(</u><u>2</u><u>x</u><u> </u><u>+</u><u> </u><u>h</u><u>)</u><u> </u><u>+</u><u> </u><u>√</u><u>2</u><u>x</u><u> </u><u> </u><u>(</u><u>-</u><u>√</u><u>(</u><u>2</u><u>x</u><u> </u><u>+</u><u> </u><u>h</u><u>)</u><u> </u><u>-</u><u> </u><u>√</u><u>2</u><u>x</u><u>)</u>

h (-√(2x + h) - √2x)

= h>0 <u>4</u><u>x</u><u> </u><u>+</u><u> </u><u>2</u><u>h</u><u> </u><u>-</u><u> </u><u>4</u><u>x</u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u>

h(-√(2x + h) -√2x)

= h>0 <u>2</u><u>h</u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u>

h(-√(2x+h) - √2x)

= h>0 <u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u>2</u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u>

-√(2x+h) - √2x

5 0

3 years ago

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Juan has 4 1/2 gallons of blue paint. Each wall in his house will need 3/4 of a gallon of paint. How many walls can Juan paint b

Lostsunrise [7]

We know that

<span>4 1/2 gallons-------> (4+2+1)/2-----> 9/2 gallons
</span>
1 <span> wall in the house will need --------> 3/4 of a gallon of paint
</span> X wall-----------------------------------> 9/2 gallons
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the answer is
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3 years ago

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Yuki888 [10]

Area= length * height
21*9 = 189cm^2

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2 years ago

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