The ratio 216: x is equivalent to the ratio x^2: 216. What is the value of x?

I need help solving these problems

Delicious77 [7]

QUESTION 1

$4 {p}^{2} = 2 \times 2\times {p} \times p$

QUESTION 2

$39 {b}^{3} {c}^{2} = 3 \times 13 \times {b} \times b \times b\times {c} \times c$

QUESTION 3

$100 {x}^{3} y {z}^{2} = {2} \times 2 \times {5} \times 5 \times {x} \times x \times x\times y \times {z} \times z$

QUESTION 4

$66 {d}^{4} = 2 \times 3 \times 11 \times {d} \times d \times d \times d$

QUESTION 5

$85 {x}^{2} {y}^{2} = 5 \times 17 \times {x} \times x \times {y} \times y$

QUESTION 6

$18xy = 2 \times {3}^{2} \times x \times y$

$36 {y}^{2} = {2}^{2} \times {3}^{2} \times {y}^{2}$

The greatest common factor is the product of the least powers of the common factors;

$GCF=2 \times {3}^{2} \times y$

$GCF=18y$

QUESTION 7

$25mn = {5}^{2} \times m \times n$

$21m = 3 \times 7 \times m$

$GCF=m$

QUESTION 8

$15a = 3 \times 5 \times a$

$28a {b}^{2} = {2}^{2} \times 7 \times a \times {b}^{2}$

$GCF=a$

QUESTION 9

$24 {d}^{2} = {2}^{3} \times 3 \times {d}^{2}$

$30 {c}^{2} d = 2 \times 3 \times 5 \times d$

$GCF=2 \times 3 \times d$

$GCF=6d$

QUESTION 10

$20gh = {2}^{2} \times 5 \times g \times h$

$36 {g}^{2} {h}^{2} = {2}^{2} \times {3}^{2} \times {g}^{2} \times {h}^{2}$

$GCF= {2}^{2} \times g \times h$

$GCF=4gh$

QUESTION 11

$17 {c}^{3} {d}^{2} = 17 \times {c}^{3} \times {d}^{2}$

$5 {c}^{2} {d}^{2} = 5 \times {c}^{2} \times {d}^{2}$

$GCF= {c}^{2} \times {d}^{2}$

$GCF= {c}^{2}{d}^{2}$

4 0

3 years ago

Help meez 40 pts use surface area formula of cylinder that is for Lateral surface area and for total surface area

jeka94

Answer:So the radius of the cylinder is 2.65 cm.

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1. The two circles that make up the caps of the cylinder.

2. The side of the cylinder, which when "unrolled" is a rectangle.

The area of each end cap can be found from the radius r of the circle, which is given by:

A = πr2

Thus the total area of the caps is 2πr2.

The area of a rectangle is given by:

A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:

P = 2πr

Thus the rectangle's area is rewritten as:

A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr2 + 2πrh

where:

π is Pi, approximately 3.142

r is the radius of the cylinder

h height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.

Example 1: Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Solution:

SA = 2 × π × r2 + 2 × π × r × h

SA = 2 × 3.14 × 42 + 2 × 3.14 × 4 × 3

SA = 6.28 × 16 + 6.28 × 12

SA = 100.48 + 75.36

SA = 175.84

Surface area = 175.84 cm2

Example 2: Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Solution:

The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

TSA = 2πr(r+h)

TSA = 11π (5.5+10)

TSA = 170.5 π

TSA = 535.6 cm2

Example 3: Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution:

Again as in the previous example:

TSA = 2πr(r+h)

TSA = 2π× 17(17+3)

TSA = 2π×17×20

TSA = 2136.56 cm2

Example 4: Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Solution:

The radius of cylinder: r = 6 cm

The height of cylinder: h = 9 cm

Total surface area of cylinder is therefore:

TSA = 2πr(r + h)

TSA = 12π (6+9)

TSA = 180 π

TSA = 565.56 cm2

Example 5: Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.

Solution:

Lateral surface area of cylinder is given by:

LSA = 2πrh

Given that:

LSA = 150cm2

h = 9cm

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

LSA = 2πrh

150 = 2× π × r × 9

r = 150 / (2×9× π)

r = 2.65cm

So the radius of the cylinder is 2.65 cm.

5 0

2 years ago

Emily thinks the perfect tomato sauce has 888 cloves of garlic in every 500 mL . Raphael's tomato sauce has 12 cloves of garlic

Finger [1]

Answer:

Step-by-step explanation:

Choice A will be true, that is, Emily would fine the sauce too garlicky.

3 0

3 years ago

Unscramble the place value.write three forms of number 9 hundreds+4ten thousands+8 ones+7 tens

liubo4ka [24]

40,978 would be the answer hope it helped!

3 0

4 years ago

Read 2 more answers

Describe how to compare the two ratios 5:8 to 7:9. Tell each step to set up the ratios, then explain what to do to be able to co

lutik1710 [3]

Answer:

5/8 is smaller.

Step-by-step explanation:

A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777

Then to compare them you see which is smaller or bigger.

0.77777 is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.

3 0

2 years ago

Read 2 more answers