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2 years ago

Write an equation equivalent to the verbal statement “The sum of three times a number n and 7 is 16.”

Mathematics

1 answer:

Sindrei [870]2 years ago

4 0

3n + 7 = 16 (equation)

3n = 9

n = 3 (answer

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Find the area of the region which is inside the polar curve r=5sin(θ) but outside r=4. Round your answer to four decimal places

natka813 [3]

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.

<h3>What is an area bounded by the curve?</h3>

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be

Then the intersection point will be given as

$\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214$

Then by the integration, we have

$\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\$

$\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\$

On solving, we have

$\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75$

Thus, the area of the region is 3.75 square units.

More about the area bounded by the curve link is given below.

brainly.com/question/24563834

#SPJ4

5 0

2 years ago

A calculator may be used for this question. The energy saving from recycling one glass bottle will power the oven Adam uses to c

anastassius [24]

6 hours=360 minutes
Glass bottles needed to cook for 6 hours=360/7.5
=48
Weight of 48 glass bottles=48x500g
=24000g
=24kg
Price of 24kg of glass=5px24
<span> =120p</span>

7 0

3 years ago

The cost of a pair of jeans was changed from $47 to $42.13. What was the percent change?

zhenek [66]

Answer:

10.36

Step-by-step explanation:

$47 - $42.13 = $4.87
($4.87 ÷ $47) × 100 = 10.36%

6 0

3 years ago

At 3:00 AM, the temperature was 44 degrees. By 7:00 AM, the temperature had risen to 60 degrees. What was the average change in

White raven [17]

60-44=16
16/4hrs= 4deg per hour

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2 years ago

Eli lives 3 3/4 miles from the library. He decided to bike from his home to the library to return some books. Eli biked 1 1/10 m

KIM [24]

Eli traveled a total of 8.6 miles. He went to the library and back. 3.75 + 3.75. and he also added and extra 1 1/10 mile. so, 3.75 x 2 = 7.5, 7.5 + 1 1/10 = 8.6. Hope that helped!

7 0

3 years ago

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