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2 years ago

If anyone knows the anwser pls tell me

Mathematics

1 answer:

Fudgin [204]2 years ago

5 0

Answer:

z = 156

Step-by-step explanation:

y² = 65²-25² = 4225 - 625 = 3600

(x+25)²-65² = z²

x²+50x+625-4225 = z²

x²+50x-3600 = z² ....(1)

x²+60² = z²

x²+3600 = z² ....(2)

(1)-(2): 50x - 7200 = 0

50x = 7200

x = 144

check: x² + y² = z² 144² + 60² = 24336 = z² z = 156

(25+144)²-65² = z² = 28561 - 4225 = 24336 z = 156

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$\large\boxed{B)\ 2\frac{1}{2},\ -1}$

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3 years ago

Which of the following is an improper integral?

guapka [62]

Answer:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

General Formulas and Concepts:

Calculus

Discontinuities

Removable (Hole)
Jump
Infinite (Asymptote)

Integration

Integrals
Definite Integrals
Integration Constant C
Improper Integrals

Step-by-step explanation:

Let's define our answer choices:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

B) $\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx$

C) $\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx$

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

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