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2 years ago

Write and solve an equation for the following:

Mathematics

1 answer:

IrinaVladis [17]2 years ago

7 0

Answer:

x = (180 - [71 + 9]) ÷ 2

Step-by-step explanation:

71 + 9 = 80

180 - 80 = 100°

100° ÷ 2 = 50°

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If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

Choose the equation that could be used to solve this problem.

Naddik [55]

Answer:

425

Step-by-step explanation:

4 0

3 years ago

Will mark brainliest

SVETLANKA909090 [29]

Answer:

I think the answer should be Mat A cause it has more space.

3 0

2 years ago

Find the circumference. use 3.14 for π r=2 cm c=? c=π d help please

Helga [31]

Answer:

C = 12.56m

Step-by-step explanation:

circumference is the distance around the outside of a circle. The r stands for radius, half way across, from the center(thats the little line on the diagram) "d" stands for diameter. That would be double the radius, bc its all the way across the circle through the center. The formula to find the CIRCUMFERENCE is given, C=pi × d

They told you to use 3.14 for pi. And also the radius is 2, so the diameter is 4

C = pi × d

C = 3.14 × 4

C = 12.56 meters

5 0

3 years ago

Pat is painting a stage backdrop for a play. The paint he is using covers 90 square feet per quart. How many quarts of paint sho

Scorpion4ik [409]

A) If you cut off half the peaks (3.5 ft down from the top), they will just fill the valleys making a rectangle 18.5 ft by 30 ft. The area is the product of these dimensions.
A = (18.5 ft)*(30 ft) = 555 ft²

b) To determine the number of quarts of paint required, divide this number by 90 ft². Since you cannot buy a partial quart, if there is any remainder, use the next higher integer number of quarts.
555/90 ≈ 6.2 so Pat should buy 7 quarts of paint.

4 0

3 years ago