A type of bacterium triples in population every hour. Assuming you start with

A company makes a cone-shaped container with a height of 15 in. The area of its base is about 78.8in.2 Approximately what is the

MakcuM [25]

Answer:

Approximately the volume of cone-shaped container is 393 in³.

Step-by-step explanation:

Given:

A company makes a cone-shaped container with a height of 15 in.

The area of its base is about 78.8 in².

Now, to get the cone-shaped container volume.

So, we find the radius first by using formula:

Let the radius be $r.$

(Using the value π = 3.14)

$A_{B}=78.8\ in^2.$

$A_{B}=\pi r^2$

$78.8=3.14\times r^2$

Dividing both sides by 3.14 we get:

$25.09=r^2$

Using square root on both sides we get:

$5.00=r$

$r=5\ in.$

Thus, the radius ( $r$ ) = 5 in.

The height ( $h$ ) = 15 in.

Now, to get the volume of the cone-shaped container we put formula:

$Volume=\pi r^2\frac{h}{3}$

$Volume=3.14\times 5^2\times \frac{15}{3} \\\\Volume=3.14\times 25\times 5\\\\Volume=392.50\ in^3.$

Therefore, approximately the volume of the cone-shaped container is 393 in³.

7 0

3 years ago

Solve the following problems. Remember that all reasoning must be explained, and all steps of math work must be shown!

iris [78.8K]

Answer to Question 1:

<OGE (also m˚) = 19˚

Step-by-step explanation:

We know that all the angles in a triangle add up to 180˚.

Given:

<EGO = 71˚

<OEG = 90˚ (the angle forms a right angle because line EG is perpendicular to point O)

To Solve:

⇒ Since we know two angles, we should know the third; and they all add up to 180˚. This can be written as:

71˚ + 90˚ + <OGE = 180˚

⇒ Solve for <OGE by simplifying:

161˚ + <OGE = 180˚

⇒ Subtract 161˚ from both sides to get:

161˚ − 161˚ + <OGE = 180˚ − 161˚

⇒ Isolate <OGE:

<OGE = 19˚

Answer: <OGE (also m˚) = 19˚

Answer:

<OAC (also x˚) = 50˚

<OCB (also y˚) = 90˚

Step-by-step explanation:

–How to solve for <OCB (also y˚)

Just by looking, you can already tell that <OCB equals 90˚ because it forms a right angle.

Answer: <OCB (also y˚) = 90˚

–How to solve for <OAC (also x˚)

Given (and what we can already know):

<AOC = 40˚

<OCA = 90˚

⇒ Reason: Line AB is a straight line and a straight line equals 180˚. We already know on side of the line because <OCB is 90˚, and so the other side, <OCA, should also be 90˚, since the both sides that make up the straight line equal 180˚ (90˚ + 90˚ = 180˚). You can also tell that <OCA forms a right angle in the triangle because line AB is perpendicular to point O, and right angles are 90˚.

To Solve:

⇒ Since we know two angles in the triangle, we should know the third; and they all add up to 180˚. This can be written as:

40˚ + 90˚ + <OAC = 180˚

⇒ Solve for <OAC by simplifying:

130˚ + <OAC = 180˚

⇒ Subtract 130˚ from both sides to get:

130˚ − 130˚ + <OAC = 180˚ − 130˚

⇒ Isolate <OAC:

<OAC = 50˚

Answer: <OAC (also x˚) = 50˚

I hope you understand and that this helps with your question! :)

3 0

2 years ago

If f(x)=logx, explain the transformation that occurs when f(0.25(x-5))+3

nevsk [136]

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

6 0

2 years ago

A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

Advocard [28]

Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)

Now the function that represents the cost to construct the can will be

C = 2πr²(0.027) + 2πrh(0.015)

C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

$h=\frac{16}{\pi r^{2}}$ -------(2)

Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

$C=0.054\pi r^{2}+0.03(\frac{16}{r})$

$C=0.054\pi r^{2}+(\frac{0.48}{r})$

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

$C'=0.108\pi r-(\frac{0.48}{r^{2} })$

Now for C' = 0

$0.108\pi r-(\frac{0.48}{r^{2} })=0$

$0.108\pi r=(\frac{0.48}{r^{2} })$

$r^{3}=\frac{0.48}{0.108\pi }$

r³ = 1.415

r = 1.12 inch

and h = $\frac{16}{\pi (1.12)^{2}}$

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

$C"=0.108+\frac{0.48}{r^{3}}$ which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

5 0

3 years ago

Which of the following is the equation of a line perpendicular to the line

Taya2010 [7]

Answer:

A. - 2x + 3y = 21

Step-by-step explanation:

The perpendicular lines have opposite reciprocal slopes.

The given line has a slope of:

m = -3/2

The perpendicular slope is:

m = 2/3

And its y-intercept is:

9 = 2/3*3 + b
b = 7

The line is:

y = 2/3x + 7

Convert this into standard form and compare with answer choices:

3y = 2x + 21
- 2x + 3y = 21

Correct choice is A

3 0

2 years ago