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3 years ago

Show FSS Find the area of the remaining pizza if the radius 10 centimeters.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

100π or about 314.16

Step-by-step explanation:

The formula for the area of a circle is (pi)*(radius^2)=area.

The radius is 10, so plugging that in you get pi*10^2=area.

Simplifying, you get Area=100π, or about 314.16

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A photograph is 4 inches high and 5 inches wide. You need to scale it up so it is 10 inches high. How wide should it be?

IrinaK [193]

Answer: 12.5 in. high

Step-by-step explanation: to get from 4 to 10, you have to muliplty by 2.5.

if you multiply 5 by 2.5, the answer is 12.5

8 0

3 years ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

What do u do when the question says what is an area of the rectangle Like

Anastaziya [24]

Answer:

multiply

Step-by-step explanation:

Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width.

6 0

2 years ago

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

Viktor [21]

Answer:

Therefore $k= \frac{ln2 }{18}$ , A=184

Step-by-step explanation:

Given function is

$T(t)=230 -e^{-kt}$

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

$138=230 -Ae^{-k\times 18}$

$\Rightarrow -Ae^{-18k}=138-230$

$\Rightarrow Ae^{-18k}=92$ .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

$184=230-Ae^{-k\times 36}$

$\Rightarrow Ae^{-36k}=230-184$

$\Rightarrow Ae^{-36k}=46$ .......(2)

Dividing (2) by (1)

$\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}$

$\Rightarrow e^{-18k}=\frac{46}{92}$

Taking ln both sides

$ln e^{-18k}=ln\frac{46}{92}$

$\Rightarrow -18k =ln (\frac12)$

$\Rightarrow -18k= ln1-ln2$

$\Rightarrow k= \frac{ln2 }{18}$

Putting the value k in equation (1)

$Ae^{-18\frac{ln2}{18}}=92$

$\Rightarrow A e^{ln2^{-1}}=92$

$\Rightarrow A.2^{-1}=92$

$\Rightarrow \frac{A}{2}=92$

$\Rightarrow A= 92 \times 2$

⇒A= 184.

Therefore $k= \frac{ln2 }{18}$ , A=184

7 0

3 years ago

Solve

liraira [26]

Answer:

y - 3 = (1/2)(x - 4)

Step-by-step explanation:

The graph is hard to read, but we can make assumptions about the x- and y-values shown. The y-intercept appears to be (0, 1) and the blue dot appears to be (4, 3). Let's try finding the equation of the line using this assumed data:

The point-slope equation is y - k = m(x - h), where (h, k) is a point on the line and m is the slope of the line.

We need the slope of the line. Recall that m = rise/run. Going from (0, 1) to (4, 3), x (the 'run') increases by 4 and y (the 'rise') increases by 2. Thus, the slope is m = rise/run = 2/4, or 1/2.

Substituting the known values into the point-slope equation y - k = m(x - h), we get:

y - 3 = (1/2)(x - 4)

7 0

3 years ago