What is the y-value of the solution of the system of equations given below?

A cylinder has a height h, and a radius (3h-2)

tekilochka [14]

Answer:

$V= 4\pi (9h^2 -12h + 4)$

Step-by-step explanation:

Given

Shape: Cylinder

$Radius = 3h - 2$

$Height = h$

$Base\ Area = \pi (3h - 2)^2$

Required

Simplify the volume

The volume is calculated as:

$Volume = Base\ Area * Height$

Substitute values for Base Area and Height

$V= \pi(3h-2)^2*h$

Expand the bracket

$V= \pi(3h-2)(3h-2)*h$

Open brackets

$V= \pi (9h^2 -6h - 6h + 4) *h$

$V= \pi (9h^2 -12h + 4) *h$

$V= 4\pi (9h^2 -12h + 4)$

6 0

3 years ago

For which value of x must the expression √37x be further simplified?

vekshin1

Answer:

37x

Step-by-step explanation:

Since it has a square root you can square it to get rid of it so your final answer is 37x

5 0

3 years ago

Can someone please help me please

Assoli18 [71]

A
Volume of the Cylinder
Givens
H = 60 yards.
Diameter = 20 yards
pi = 3.14

Formula
V = pi * r^2 * h

Calculations
r = d/2
r = 32/2
r = 16

V = 3.14 * 16^2 * 60
V = 48230 cubic yards [Cylinder's Volume]

Cone
Formula
V = 1/3 pi r^2 H

Givens
pi = 3.14
r = 16 yards
h = 20 yards

Sub and solve
V = 1/3 3.14 * 16^2 * 20
V = 5359 cubic yards.

Total Volume of the structure
48230 + 5359 = 53589 Cubic Yards

Water Content
The answer to this part requires a proportion.

1 Cubic yard will hold 201.97 gallons.
53589 yd^3 = x

1/201.97 = 53589 /x [ You should get a pretty big answer]
x = 201.87 * 53589
x = 10 819 092 gallons can be held by the tank.

10 819 092 gallons <<<< answer

B
If the height of both the cylinder and the cone remain the same. If the radius doubles in both the cylinder and the cone then the tank will hold 4 times as much.

Total volume before doubling the radius = pi * r^2 h + 1/3 pi r^2 h
New Total Volume = pi * (2*r)^2 h + 1/3 pi * (2r)^2 h
New Total volume = pi * 4r^2 h + 1/3 pi *4 r^2 h
New Total Volume = 4 [pi r^2 h + 1/3 pi r^2 h]
but pi r^2 h + 1/3 pi r^2 h is the total volume before doubling the radius

New volume = 4 original volume. <<<<< answer to part B

6 0

3 years ago

You have a garden in your backyard that measures 15 meters by 20 meters. You want to place stepping stones around the perimeter

Anettt [7]

Answer:

0.5 m

Step-by-step explanation:

Given that the dimensions of the garden are 15 meters by 20 meters.

The area of the new garden (original garden + stone placed around the perimeter) is 336m².

Let d be the width of the border having stepping stones as shown in the figure. The shaded region in the figure is the area having stepping stones.

The area including the shaded region $= (15+2d)(20+2d) m^2$

$\Rightarrow 336 = (15+2d)(20+2d) \\\\\Rightarrow 336 = 300+ 70 d +4d^2 \\\\\Rightarrow 4d^2 +70d+300-336=0 \\\\\Rightarrow 4d^2 +70d-36=0 \\\\\Rightarrow 2d^2 +35d-18=0 \\\\\Rightarrow 2d^2 +36d-d-18=0 \\\\\Rightarrow (2d-1)(d+18)=0 \\\\\Rightarrow (2d-1)=0, \; or \; (d+18) \\\\\Rightarrow d= 0.5\;or -18 \\\\$

As the width of the stone border can't be a negative value, so taking the positive value.

Hence, the width of the stone border is 0.5 m.

So, the wi

7 0

3 years ago

What is 10,000,000,000 in standard form?

Flauer [41]

Answer:

10 billion

Step-by-step explanation:

4 0

3 years ago