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3 years ago

Find the circumference of a circle with a radius of 2 inches. Give an exact answer.

Mathematics

1 answer:

pychu [463]3 years ago

4 0

Answer:C=2πr=2·π·2≈12.56637in

Step-by-step explanation:

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How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

erastovalidia [21]

Find total number of integers.

$a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51$

Find how many integers is divisible by 2.

$a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26$

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

$a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8$

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>

6 0

3 years ago

A person earns $187.42 before deductions for 3 days' work. What is the rate of pay per hour assuming 8 hours of work per day?

gavmur [86]

8 hours = 1 day

24 hours = 3 days

187.42/24

Round it up and it will give you $7.80/hour

8 0

3 years ago

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$

Now, we differentiate the profit function to get the marginal profit function (P'):

$P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530$

This is the marginal profit function , P'.

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

$P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194$

and

$P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268$

6 0

3 years ago

Question 3

mamaluj [8]

Question 4: a ray is formed by an endpoint and a line starting at the endpoint and going on forever in one direction
We cannot see angle MBW to be able to classify it

8 0

3 years ago

Find the slope of line. y= -3x-1

Paladinen [302]

Answer:

<em>*****Slope: M = -3*****</em>

6 0

3 years ago

Read 2 more answers