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3 years ago

Find the equation of the graphed line.?

Mathematics

1 answer:

kiruha [24]3 years ago

7 0

Answer:

c. y = x - 6.

Step-by-step explanation:

It's a straight line whose general form is y = mx + c.

The slope is (0, -6) / (6, 0)

= -6 / -6

= 1 so the coefficient of x , (m) is 1.

The value of c ( the y-intercept) is -6.

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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

HELP ASAP! explain please <br> Find the sum of the Arithmetic sequence<br> 2 + 4 + 6+...+ 2n

alexira [117]

Sn=n/2(2+2n)shdheuxucuehehxhcxdwg

5 0

3 years ago

Consider the graph shown.

otez555 [7]

Answer:

y = $\frac{2}{3}$ x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 4)

m = $\frac{4-2}{3-0}$ = $\frac{2}{3}$

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = $\frac{2}{3}$ x + 2 ← equation of line

5 0

3 years ago

Convert 3 and 19/20 to a decimal

inysia [295]

3 is converted to 0.03
19/20 is converted to 0.95.

4 0

3 years ago

members of a soccer team raised $741.15 to go to a tournament. They rented a bus for $250 and budgeted $25.85 per player for mea

blsea [12.9K]

9514 1404 393

Answer:

19 players

Step-by-step explanation:

The total being spent is ...

bus cost + (per player cost) × (number of players) = total raised

250 + 25.85p = 741.15

25.85p = 491.15

p = 491.15/25.85 = 19

The team could bring 19 players to the tournament.

6 0

3 years ago