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2 years ago

Write an equation of the line containing the given point and parallel to the given line.

Mathematics

1 answer:

nadya68 [22]2 years ago

4 0

Answer:

Solution given:

9x-2y=7

making it in a form of y=mx+c

9x-7=2y

y=9/2x -7/2

Comparing above equation with y=mx+c

we get

m=9/2

Since it is passes parallel to (5,-3)

slope will be same

now

Equation of line

y-y1=m(x-x1)

y+3=9/2(x-5)

y=9/2x-5/2-3

y=9/2 x-11/2 is a required equation.

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ipn [44]

Answer:

4 and -5 for the first one

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2 years ago

Read 2 more answers

Find the derivative

zalisa [80]

First use the chain rule; take $y=\dfrac{x+5}{x^2+3}$ . Then

$\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dy}\cdot\dfrac{\mathrm dy}{\mathrm dx}$

By the power rule,

$f(x)=y^2\implies\dfrac{\mathrm df}{\mathrm dy}=2y=\dfrac{2(x+5)}{x^2+3}$

By the quotient rule,

$y=\dfrac{x+5}{x^2+3}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)\frac{\mathrm d(x+5)}{\mathrm dx}-(x+5)\frac{\mathrm d(x^2+3)}{\mathrm dx}}{(x^2+3)^2}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)-(x+5)(2x)}{(x^2+3)^2}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3-10x-x^2}{(x^2+3)^2}$

$\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)}{x^2+3}\cdot\dfrac{3-10x-x^2}{(x^2+3)^2}$

$\implies\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)(3-10x-x^2)}{(x^2+3)^3}$

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3 years ago

20. What is the volume, in terms of r, for a cylindrical

inysia [295]

Step-by-step explanation:

Volume of cylindrical container

$= \pi {r}^{2} h \\ \\ = 3.14 \times ( {3.25)}^{2} \times 10 \\ \\ = 3.14 \times 10.5625 \times 10 \\ \\ = 331.6625 {cm}^{3} \\ \\ \approx \: 331.66 \: {cm}^{3}$