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3 years ago

The cost of a customer smartphone bill can be modeled by the equation c=10g+50

Mathematics

1 answer:

Vika [28.1K]3 years ago

6 0

Answer:

c=10(g+5)

Step-by-step explanation:

Given that,

The cost of customer smartphone bill is given by the equation as follows :

c=10g+50

Where

g is the number of gigabits of data the customer per month

We need to factor this cost polynomial

The common between 10 and 50 is 10

Taking 10 common. So,

c=10(g+5)

Hence, the required factor is equal to c=10(g+5).

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A local animal shelter has many cats and dogs. The shaded part represents the percent of animals that are dogs. If there are 82

frutty [35]

Answer:

weel if you divide 82 by 2 then it you will get the number of cats which is 41 then add 82 + 41 =123

Step-by-step explanation:

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3 0

2 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

2 years ago

What is the fractional equivalent of the repeating decimal n = 0.5151...?

slava [35]

Answer:

I believe that it is 2, I'm not 100% but ill take the guess

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Can anyone plz help me

Andrew [12]

Let's solve number 7 step-by-step.
y/23=7
Step 1: Multiply both sides by 23.
y/23=7
(y23)*(23)=(7)*(23)
y=161 is our answer.

Let's solve number 8 step-by-step.
n−4.85=12.6
Step 1: Add 4.85 to both sides.
n−4.85+4.85=12.6+4.85
n=17.45 is our answer.


Let's solve number 12 step-by-step.
m/5=8
Step 1: Multiply both sides by 5.
m/5=8
(m/5)*(5)=(8)*(5)
m=40 is our answer.


Let's solve number 16 step-by-step.
a/12=8
Step 1: Multiply both sides by 12.
a/12=8
(a/12)*(12)=(8)*(12)
a=96 is or answer.

6 0

3 years ago

The formula for the volume of this rectangular prism is:

juin [17]

Answer:

Step-by-step explanation: Explanation:

and

represent the length, height and width of the prism, then the volume of the rectangular prism is :

............. (1)

Given :

−

;

............... (2)

(

−

)

;

(

)

Let

(

)

be the expression for the length, then the RHS of equation (1) becomes

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

−

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

;

−

;

Therefore

(

)

8 0

2 years ago