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3 years ago

What is the area of the polygon below?

Mathematics

2 answers:

mash [69]3 years ago

8 0

The answer to this problem is A

scZoUnD [109]3 years ago

4 0

A. 147

Explanation: 3×9 equals 27 and 10×12 equals 120.

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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.

8 0

4 years ago

Micah's gym is moving into a bigger space, where he can have more stationary bicycles and treadmills. Micah needs both stationar

marin [14]

Answer:

Options (2), (3), (5) and (6)

Step-by-step explanation:

Let the number of bicycles = x

and the number of treadmills = y

Since, number of new bicycles must be more than $\frac{1}{3}$ times of new treadmills,

Inequality representing the statement will be,

x > $\frac{1}{3}$ y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are,

Option (2)

Option (3)

Option (5)

Option (6)

3 0

3 years ago

The lengths of three

True [87]

Answer:

90 cm, 180 cm, 240 cm

Step-by-step explanation:

Let the lengths of sides of the triangle be 3x, 6x and 8x

$\therefore \: 3x + 6x + 8x = 5.1 \: m \\ \therefore \: 17x = 510 \: cm \\ \therefore \: x = \frac{510}{17} \\ \therefore \:x = 30 \: cm \\ \implies \\ 3x = 3 \times 30 = 90 \: cm \\ 6x = 6 \times 30 = 180 \: cm \\ 8x = 8 \times 30 = 240 \: cm$

Hence, lengths of the sides of the triangle are 90 cm, 180 cm and 240 cm.

4 0

3 years ago

Chicago, Illinois, has a longitude of 88 degrees W and a latitude of 42 degrees N. Indianapolis, Indiana, is located at 86 degre

Mashcka [7]

See the attached picture:

6 0

4 years ago

Explain how a points distance from 0 relates to the value of the number that it represents

Gnoma [55]

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative. Take a look at some examples. The distance from 5 to 0 is 5 units.

7 0

3 years ago