Use the steps to solve the Carbon Dating Problem.

Explain why each of the following integrals is improper. (a) 4 x x − 3 dx 3 Since the integral has an infinite interval of integ

erma4kov [3.2K]

Answer:

a

Since the integral has an infinite discontinuity, it is a Type 2 improper integral

b

Since the integral has an infinite interval of integration, it is a Type 1 improper integral

c

Since the integral has an infinite interval of integration, it is a Type 1 improper integral

d

Since the integral has an infinite discontinuity, it is a Type 2 improper integral

Step-by-step explanation:

Considering a

$\int\limits^4_3 {\frac{x}{x- 3} } \, dx$

Looking at this we that at x = 3 this integral will be infinitely discontinuous

Considering b

$\int\limits^{\infty}_0 {\frac{1}{1 + x^3} } \, dx$

Looking at this integral we see that the interval is between $0 \ and \ \infty$ which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral

Considering c

$\int\limits^{\infty}_{- \infty} {x^2 e^{-x^2}} \, dx$

Looking at this integral we see that the interval is between $-\infty \ and \ \infty$ which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral

Considering d

$\int\limits^{\frac{\pi}{4} }_0 {cot (x)} \, dx$

Looking at the integral we see that at x = 0 cot (0) will be infinity hence the integral has an infinite discontinuity , so it is a Type 2 improper integral

7 0

3 years ago

A company sells its printers to customers in order to make a profit of 25% calculate the price the company paid for a printer wh

ioda

The company paid $2000 for the printer

Step-by-step explanation:

Let x be the price of the printer for which the company bought it.

If x is the price of printer, then 25% of x will be the profit made by the company.

That is:

0.25x

According to the statement,

The cost and profit earned by company are equal to 2500

So,

$x+0.25x = 2500\\1.25x = 2500$

Dividing both sides by 1.25

$\frac{1.25x}{1.25} = \frac{2500}{1.25}\\x = 2000$

Hence,

The company paid $2000 for the printer

Keywords: Percentage, Profit

Learn more about percentage at:

#LearnwithBrainly

7 0

3 years ago

Write a complete two-column proof for the following information given

rosijanka [135]

Statement Reason

1. AB = x + 16 1. Given

BC = 4x + 11

AC = 77

2. AB + BC = AC 2. Segment Addition Postulate

3. x + 16 + 4x + 11 = 77 3. Substitution Property

4. 5x + 27 = 77 4. Simplification (added like terms)

5. 5x = 50 5. Subtraction Property of Equality

6. x = 10 6. Division Property of Equality

7. AB = 10 + 16 7. Substitution Property

8. AB = 26 8. Simplification (added like terms)

5 0

4 years ago

Place the steps for finding f'(X) in the correct order. Plz help Thank you!

SashulF [63]

Answer:

See below

Step-by-step explanation:

Given function is ,

=> f(x) = 4x + 7.

Replace f(x) with y ,

=> y = 4x + 7

For finding the inverse , interchange x and y ,

=> x = 4y + 7

Now solve for y ,

=> 4y = x - 7

=> y = x-7/4

Replace y with f-¹(x) ,

=> f-¹(x) = (x-7)/4

These are the required steps .

8 0

3 years ago

When my mother buys washing powder she pays R45,65 for a 3kg bag hkw much does she pay for 1kg

V125BC [204]

To solve this divide 4565 by 3.

7 0

3 years ago

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