Х If two lines do not intersect, then they are parallel.

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

Convert from Standard Form to Slope Intercept Form 3x + 2y = 6

Ilia_Sergeevich [38]

Answer:

y = -3/2x + 3

General Formulas and Concepts:

Algebra I

Equality Properties

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step-by-step explanation:

Step 1: Define

Standard Form: 3x + 2y = 6

Step 2: Find slope-intercept form

Subtract 3x on both sides: 2y = 6 - 3x
Divide both sides by 2: y = 3 - 3/2x
Rewrite: y = -3/2x + 3

And we have our final answer!

5 0

2 years ago

Solve For X A 3 B 30 C 60 D 90

Anarel [89]

Answer:

sln

10x+10x+30+90=180

20x+120=180

20x=180-120

20x=60

x=3

the answer is A) 3

8 0

3 years ago

Find the circumference of each circle. Use 3.14 or 22/7 for T. Round to the

Ludmilka [50]

Answer:

4. Circumference = diameter × π

8× 3. 14= 25. 12 ~25. 1

5. 13×3. 14= 40. 82 ~40. 8

6. Diameter= radius ×2

3. 5×2=7

Diameter = 7

7× 3. 14= 21. 98 ~22

6 0

3 years ago

The measures of three angles of a triangle are given by (8x - 5), (2x)º, and (3x – 10). What is the measure of the largest angle

zhannawk [14.2K]

Answer: 115°

Step-by-step explanation:

We should note that the sum of the angles that are in a triangle is equal to 180°, therefore we will add the angles given and equate them to 180°. This will be:

(8x - 5) + (2x) + (3x - 10) = 180

8x - 5 + 2x + 3x - 10 = 180

Collect like terms

8x + 2x + 3x = 180 + 5 + 10

13x = 195

x = 195/13

x = 15

The angles are:

8x - 5 = 8(15) - 5 = 120 - 5 = 115°

2x = 2(15) = 30°

3x - 10 = 3(15) - 10 = 45 - 10 = 35°

Therefore, the largest angle is 115°

3 0

2 years ago