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2 years ago

Find the area of the shape below

Mathematics

1 answer:

maks197457 [2]2 years ago

3 0

Answer:

204 ft^2

Step-by-step explanation:

triangle on the left:

A= l x w x 1/2

A = 12 x 5 x 1/2

A = 30 ft^2

triangle on the right:

Same thing

A = 30 ft^2

square in the middle:

A = l x w

A = 12 x 12

A = 144 ft^2

Add them up:

30 + 30 + 144 = 204 ft^2

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A student athlete run 3 1/3 miles in 30 minutes A professional runner can run 1 1/4 times as far in 30 minutes . how far can the

IrinaK [193]

The professional runner can run 4 1/6 miles in 30 minutes.

Since the professional can run 1 1/4 times as far in 30 minutes, we multiply 3 1/3 by 1 1/4:

(3 1/3)(1 1/4)

Convert each to an improper fraction (multiply the whole number by the denominator and add the numerator):
10/3(5/4) = 50/12 = 25/6 = 4 1/6.

4 0

3 years ago

Two cars start at a given point and travel in the same direction at average speeds of 45 miles per hour and 52 miles per hour (s

Citrus2011 [14]

Answer:

half apart

Step-by-step explanation:

hope it help you

7 0

2 years ago

Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma

Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}$

The total surface area is,

$\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}$

Volume is,

$\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}$

Now, differentiate with respect to x,

$\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}$

Now,

$\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}$

Now, differentiate (1) with respect to x again,

$\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}$

Since, the double derivative is negative.

$So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}$

So, the volume becomes,

$\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}$

Answer: maximum volume of the cylinder is,

6 0

1 year ago

What are factors of the expression (y-2)(x+3)

Savatey [412]

They have a common factor of 6

4 0

3 years ago

Erica is playing Target one fractions. She has three cards: 1, 2, 3, 4, 6. Which three cards should she choose to make a whole n

cluponka [151]

Answer:

They are 1, 2 and 6

Step-by-step explanation:

To make a whole number and a fraction that have a product closest to 1. We need to find the smalles whole number and a fraction

- For the whole number, only card 1 has the smallest value

- For a fraction, we need to find the smallest numerator , it is card 2, and the greatest denominator, it is card 6 to have the smallest value in the fractoon.

So finally, our product areL 1 2/6 = 8/6 which is closest to 1.

Hope it will find you well.

Thanks

6 0

2 years ago