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3 years ago

Hello there!

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

7 0

Answer:

4. dy/dx = -2

8. dy/dx = 1/2 x^(-3/2)

10/ dy/dr = 4 pi r^2

Step-by-step explanation:

4. y = -2x+7

dy/dx = -2(1)

dy/dx = -2

8. y = 4 - x^-1/2

dy/dx = - (-1/2x^ (-1/2-1)

dy/dx = 1/2 x^(-3/2)

10. y = 4/3 pi r^3

dy/dr = 4/3 pi (3r^2)

dy/dr = 4 pi r^2

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1. Which is the dependents variable in the following situations?

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3 years ago

If a=2b^3 and b= -1/2c ^-2,express a in terms of c.

ElenaW [278]

Answer:

Part 1) $a=-\frac{1}{4c^6}$

Part 2) $a=-\frac{1}{4c^{-6}}$

Step-by-step explanation:

Part 1) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2}c^{-2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{1}{2}c^{-2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}$

therefore

$a=-\frac{1}{4c^6}$

Part 2) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{c^{2}}{2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})$

simplify

$a=-\frac{c^{6}}{4}$

therefore

$a=-\frac{1}{4c^{-6}}$

6 0

3 years ago

A little help please

DaniilM [7]

Answer:

x = 30

Step-by-step explanation:

by solving ;

18 / x = 6 / 10
1 / x = 6 / ( 18 × 10 )
1 / x = 6 / 180
1 / x = 1 / 30
x = 30

4 0

3 years ago