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3 years ago

What is the arc length of a semicircle with a radius of 11?

Mathematics

1 answer:

kap26 [50]3 years ago

7 0

Answer:

The arc length of the semicircle is: $11 \pi$ , which is approximately 34.5575

Step-by-step explanation:

Recall that the length of a circumference of radius R is given by:

$length = 2\,\pi \,R$

therefore, the arc length of a semicircle (half of the circle) would be given by half of the previous expression:

$length\,\,of \,\,semicircle= \pi\,R$

So, in our particular case of radius 11, the formula for the arc length of the semicircle becomes:

$length\,\,of \,\,semicircle= \pi\,R\\length\,\,of \,\,semicircle= 11 \pi\\length\,\,of \,\,semicircle= 34.5575$

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Answer:

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Step-by-step explanation:

We assume you want to find (f -g)(x).

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2 years ago

Which of the following exponential functions goes through the points (1, 12) and (2, 36)?

Savatey [412]

Answer:

The function through which given point passes is f(x) = 24 x - 12 .

Step-by-step explanation:

Given as :

The points are

$x_1$ , $y_1$ = 1 , 12

$x_2$ , $y_2$ = 2 , 36

now, slope of the line

Let The slope of line = m = $\frac{y_2-y_1}{x_2-x_1}$

Or, m = $\frac{36 - 12}{2-1}$

Or, m = 24

So The slope of line = m = 24

<u>Now, equation of line in point-slope form</u>

y - $y_1$ = m × (x - $x_1$ )

Or, y - 12 = 24 × (x - 1 )

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or, y = 24 x - 12

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3 years ago

1. Dorothy bought a teddy bear and sold it at a 20% profit to Kim. Kim bought a suit costing $100 and dressed the teddy bear up

makkiz [27]

1. Dorothy paid $200 for the teddy bear

2. y is more than x by $33\frac{1}{3}$ %

Step-by-step explanation:

1. The given is:

Dorothy bought a teddy bear and sold it at a 20% profit to Kim
Kim bought a suit costing $100 and dressed the teddy bear up in the suit
Kim then sold the teddy bear in the suit to Karen for $442
Kim made a profit of 30%

We need to find how much Dorothy paid for the teddy bear

Assume that Dorothy bought a teddy bear for $x

∵ Dorothy bought a teddy bear for $x

∵ She sold it at a profit 20% to Kim

By using the ratio method

→ Buying price : Profit : Selling price

→ 100% : 20% : 120% ⇒ (100% + 20%)

→ x : : ?

By using cross multiplication

∴ 100% × Selling price = x × 120%

- Divide both sides by 100%

∴ Selling price = 1.2x

∴ Dorothy sold the teddy bear for $1.2x to Kim

∵ Kim bought a suit costing $100 and dressed the teddy bear

up in the suit

∴ The cost of the teddy bear = 1.2x + 100

∵ Kim sold the teddy bear in the suit to Karen for $442

∵ Kim made a profit of 30%

By using the ratio method

→ Cost price : Profit : Selling price

→ 100% : 30% : 130% ⇒ (100% + 30%)

→ 1.2x + 100 : : 442

By using cross multiplication

∴ (1.2x + 100) × 130% = 100% × 422

- Divide both sides by 130%

∴ 1.2x + 100 = 340

- Subtract 100 from both sides

∴ 1.2x = 240

- Divide both sides by 1.2

∴ x = 200

∴ Dorothy bought the teddy bear for $200

Dorothy paid $200 for the teddy bear

2. The given is:

x is less than y by 25%
Then y is more than x by how many percent

Assume that y is 100%

∵ y = 100%

∵ x is less than y by 25%

∴ x = 100% - 25%

∴ x = 75%

- The percentage of increasing of y = $\frac{y-x}{x}$ × 100%

∵ The percentage of increasing of y = $\frac{100-75}{75}$ × 100%

∴ The percentage of increasing of y = $\frac{25}{75}$ × 100%

∴ The percentage of increasing of y = $\frac{1}{3}$ × 100%

∴ The percentage of increasing of y = $33\frac{1}{3}$ %

y is more than x by $33\frac{1}{3}$ %

Learn more:

You can learn more about the ratio in brainly.com/question/4713715

#LearnwithBrainly

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Step-by-step explanation:

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2 years ago