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3 years ago

18.4 ÷ 2.3 × 3.4 + 13.812

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

the answer is 41.012

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The volume of fuel in a tank changes at a rate given by the equation V'\left(t\right)=\frac{4t}{\sqrt[3]{t^2+3}},\:t\ge0 V ′ ( t

Ksju [112]

$V'(t)=\dfrac{4t}{\sqrt[3]{t^2+3}}$

The volume of fuel in the tank after 9 hours is given by

$\displaystyle\int_0^9V'(t)\,\mathrm dt=\int_0^9\dfrac{4t}{(t^2+3)^{1/3}}\,\mathrm dt$

To compute the integral, substitute $u=t^2+3$ , so that $\mathrm du=2t\,\mathrm dt$ . Then when $t=0$ , $u=0^2+3=3$ ; when $t=9$ , $u=9^2+3=84$ .

$\displaystyle\int_0^9V'(t)\,\mathrm dt=2\int_{t=0}^{t=9}\frac{2t}{(t^2+3)^{1/3}}\,\mathrm dt=2\int_{u=3}^{u=84}u^{-1/3}\,\mathrm du$
$=2\cdot\dfrac32u^{2/3}\bigg|_{u=3}^{u=84}=3(84^{2/3}-3^{2/3})\approx51.3$

So the volume of fuel after 9 hours is about 51.3 gallons.

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4 years ago

The volume of the following figure is

Svetradugi [14.3K]

Answer:

C. 8 in

Step-by-step explanation:

(5)(6)(x)=240

solve for x

30x=240

x=240/30

x=8

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3 years ago

Can anyone help me please?

lions [1.4K]

Answer:

first one

Step-by-step explanation:

put the numbers together so 1/5 becomes 15

thats an example

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3 years ago

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Your center would be (3,-4)

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Answer:can you show a picture?

Step-by-step explanation:

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