Mathematics, 09.07.2019 13:00 vvvvvvvv84

Can someone me with 19- i need it to be worked out and and you i really don't understand it, but it's due tomorrow morning so can someone

Can someone me with 19- i need it to be worked out and and you i really don't understand it, but

Answers: 1

Show answers

Answers

Answer from: michibabiee

Let me help you to understand this problem. Linear functions are those whose graph is a straight line. The form of a linear function is given by the following form:

$y=f(x)=ax+b \\ \\ where \ a \ and \ b \ are \ constants \\ \\ \\ a:Represents \ the \ slope \ of \ the \ line \\ \\ b:Represents \ the \ y-intercept$

The y-intercept occurs when x = 0.

So, our problem is to find the constants $a \ and \ b$ in each case. Therefore:

FIRST. (19)

$f(0)=2, \ f(2)=4$

The slope of a line can be found as follows:

$a=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ \\ f(x_{2})=f(2)=4 \\ \\ f(x_{1})=f(0)=2 \\ \\ \\ \therefore a=\frac{4-2}{2-0}=1$

As the y-intercept occurs when x = 0, therefore:

b=f(0)=2

Accordingly, the first linear function is:

$\boxed{y=f(x)=x+2}$

SECOND. (20)

$f(0)=7, \ f(3)=1$

Applying the same reasoning as in the first exercise, the slope is:

$f(x_{2})=f(3)=1 \\ \\ f(x_{1})=f(0)=7 \\ \\ \\ \therefore a=\frac{1-7}{3-0}=-2$

And the y-intercept is:

b=f(0)=7

Accordingly, the second linear function is:

$\boxed{y=f(x)=-2x+7}$

THIRD. (21)

$f(4)=-3, \ f(0)=-2$

The slope is:

$f(x_{2})=f(4)=-3 \\ \\ f(x_{1})=f(0)=-2 \\ \\ \\ \therefore a=\frac{-3-(-2)}{4-0}=-\frac{1}{4}$

And the y-intercept is:

b=f(0)=-2

Accordingly, the third linear function is:

$\boxed{y=f(x)=-\frac{1}{4}x-2}$

FOURTH. (22)

$f(5)=-1, \ f(0)=-5$

The slope is:

$f(x_{2})=f(5)=-1 \\ \\ f(x_{1})=f(0)=-5 \\ \\ \\ \therefore a=\frac{-1-(-5)}{5-0}=\frac{4}{5}$

And the y-intercept is:

b=f(0)=-5

Accordingly, the fourth linear function is:

$\boxed{y=f(x)=\frac{4}{5}x-5}$

FIFTH. (23)

$f(-2)=6, \ f(0)=-4$

The slope is:

$f(x_{2})=f(-2)=6 \\ \\ f(x_{1})=f(0)=-4 \\ \\ \\ \therefore a=\frac{6-(-4)}{-2-0}=-5$

And the y-intercept is:

b=f(0)=-4

Accordingly, the fifth linear function is:

$\boxed{y=f(x)=-5x-4}$

SIXTH. (24)

$f(0)=3, \ f(-6)=3$

The slope is:

$f(x_{2})=f(-6)=3 \\ \\ f(x_{1})=f(0)=3 \\ \\ \\ \therefore a=\frac{3-3}{-6-0}=0$

And the y-intercept is:

b=f(0)=3

Accordingly, the sixth linear function is:

$\boxed{y=f(x)=3} \\ \\ This \ is \ a \ constant \ function$

Answer from: Quest

Answer: 900°

good luck on your studies! : )

david edward.

Answer from: Quest

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

Questions in other subjects:

Social Studies, 22.04.2020 22:12

I need help with these 3 questions!...

Mathematics, 22.04.2020 22:12

History, 22.04.2020 22:12

How did Julius Caesar’s death affect the leadership of Rome? His supporters wanted to give power to a military triumvirate. The people demanded new elections in a...

Engineering, 22.04.2020 22:12

Consider a venture with a small hole drilled in the side of the throat. This hole is connected via a tube to a closed reservoir. The purpose of the venture is to create vacuum in t...

Mathematics, 22.04.2020 22:13

To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the...

Mathematics, 22.04.2020 22:13

Find the perimeter of the figure to the nearest hundredth.Please consider helping!Any help is appreciated!

Arts, 22.04.2020 22:13

Which composer wrote "The Captains Room"? *...

English, 22.04.2020 22:13

But, in a larger sense, we cannot dedicate—we cannot consecrate—we cannot hallow this ground. The brave men, living and dead, who struggled here have consecrated it, far above our...

Mathematics, 22.04.2020 22:13

To determine how a city's residents feel about building a new youth center, a group considers surveying 50 random children at a local elementary school. Why would this result in a...

Mathematics, 22.04.2020 22:13

What can be concluded about the line represented in the table? Check all that apply. x y –6 –7 2 –3 8 0 The slope is 2. The slope is One-half. The y-intercept is –4. The y-intercep...

More questions: Mathematics Another questions

Can someone me with 19- i need it to be worked out and and you i really don't understand it, but it's due tomorrow morning so can someone

Answers

Other questions on the subject: Mathematics

Questions in other subjects: