What is the value of x to the nearest tenth? 29.6 X 73° 33°

Andru [333]

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Before performing any calculation it's good to recall a few properties of integrals:

$\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}$

$\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }$

So we apply the first property in the first expression given by the question:

$\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}$

And we solve the second integral:

$\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }$

Then we take the last equation and we subtract 10 from both sides:

$\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}$

And we divide both sides by 2:

$\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}$

Then we apply the second property to this integral:

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}$

Then we use the other equality in the question and we get:

$\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}$

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}$

We substract 8 from both sides:

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}$

• $\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}$

7 0

2 years ago

Jason helped his dad put plastic and aluminum items into the recycling container. The container is a large cube with a length, w

igor_vitrenko [27]

Answer:

its 216 cubic feet.

Step-by-step explanation:

6x6x6 is 216

6 0

3 years ago

How do you estimate 289 and 7

padilas [110]

You first round 289 and get 290 then multiply it by 7

7 0

3 years ago

Read 2 more answers

Someone please help me on this math problem!

Galina-37 [17]

Look at the picture.

Therefore we have the equation:

10y - 29 = 7y + 19 add 29 to both sides

10y = 7y + 48 subtract 7y from both sides

3y = 48 divide both sides by 3

y = 16

3x + 7 = 5x - 21 subtract 7 from both sides

3x = 5x = -28 subtract 5x from both sides

-2x = -28 divide both sides by (-2)

x = 14

3 0

3 years ago

How would you convert a measurement given in fluid onuces into pints

Alexus [3.1K]

Multiply the quantity in ounces (including the unit) by the fraction

(1 pint) / (16 fl oz) .

4 0

3 years ago