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3 years ago

Suppose that your net income for the month is $1,500 and that your total expenses are $2,500

Mathematics

1 answer:

Aleks [24]3 years ago

6 0

Answer:

You will need to double your net income in order to make a profit.

Step-by-step explanation:

1500 x 2 = 3000 - 2500 = 500 which is 500 dollars profit

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Integrate the following

enot [183]

I suppose you mean to have the entire numerator under the square root?

$\displaystyle\int_2^4\frac{\sqrt{x^2-4}}{x^2}\,\mathrm dx$

We can use a trigonometric substitution to start:

$x=2\sec t\implies\mathrm dx=2\sec t\tan t\,\mathrm dt$

Then for $x=2$ , $t=\sec^{-1}1=0$ ; for $x=4$ , $t=\sec^{-1}2=\frac\pi3$ . So the integral is equivalent to

$\displaystyle\int_0^{\pi/3}\frac{\sqrt{(2\sec t)^2-4}}{(2\sec t)^2}(2\sec t\tan t)\,\mathrm dt=\int_0^{\pi/3}\frac{\tan^2t}{\sec t}\,\mathrm dt$

We can write

$\dfrac{\tan^2t}{\sec t}=\dfrac{\frac{\sin^2t}{\cos^2t}}{\frac1{\cos t}}=\dfrac{\sin^2t}{\cos t}=\dfrac{1-\cos^2t}{\cos t}=\sec t-\cos t$

so the integral becomes

$\displaystyle\int_0^{\pi/3}(\sec t-\cos t)\,\mathrm dt=\boxed{\ln(2+\sqrt3)-\frac{\sqrt3}2}$

7 0

3 years ago

1 3 Which is the best estimate of 11. 113 2 4? O 4 O 6 o 22 O 33

JulsSmile [24]

Answer:22

Step-by-step explanation:

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3 years ago

SOLVE FAST BRAINLIEST ASAP <br><br> Y-9=41

Fudgin [204]

Answer:

Y = 50

Step-by-step explanation:

Solve for Y:

Y - 9 = 41

Add 9 to both sides:

Y + (9 - 9) = 9 + 41

9 - 9 = 0:

Y = 41 + 9

41 + 9 = 50:

Answer: Y = 50

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3 years ago

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Which table represents a linear function?

mars1129 [50]

o 16 30 one

as it forms a pattern

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2 years ago

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(-57)-(+12) <br>find the difference

Airida [17]

Answer:

siiiii

Step-by-step explanation:

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3 years ago

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