A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree.

Running consumes about 720 calories per hour about how many are used if you run for 40 minutes

Agata [3.3K]

Answer:

288

Step-by-step explanation:

0.40hrs × 720 calories = 288 calories burned

7 0

2 years ago

The sides of a square field are 28 meters. A sprinkler in the center of the field sprays a circular area with a diameter that co

Ulleksa [173]

Answer:

168.24784 m²

Step-by-step explanation:

Area of the square:

28 x 28=784 sq. m.

Area of the circle:

π(r²)=π(14)²=196π

=615.75216

Area not covered by the sprinkler:

784-615.75216=168.24784 m²

6 0

3 years ago

Read 2 more answers

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

A wise man once said, "400 reduced by 3 times my age is 163." Write and solve a two-step equation to determine his age.

emmainna [20.7K]

Answer:

hey

Step-by-step explanation:

let the age of man be x

400-3x=163

400-163=3x

237/3=x

x= 79

3 0

3 years ago

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Given f(x) = 2x2 - 4, find the average rate of change from x1 = -2 to x2 = 4.

Oduvanchick [21]

Answer:

The average rate of change = 4

Step-by-step explanation:

Given the function

$f\left(x\right)\:=\:2x^2\:-\:4$

x₁=-2, x₂=4

f(x₁) = f(-2) = 2x²-4 = 2(-2)²-4 = 8-4 = 4

f(x₂) = f(4) = 2x²-4 = 2(4)²-4 = 32-4 = 28

The average rate of change = f(x₂) - f(x₁) / x₂ - x₁

= (28-4)/(4-(-2))

= 24/6

= 4

Thus, the average rate of change = 4

4 0

2 years ago