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2 years ago

Write an equation of the line perpendicular to the given line that contains P.

Mathematics

1 answer:

lara31 [8.8K]2 years ago

7 0

Answer:

Step-by-step explanation:

perp. -5

y + 7 = -5(x - 4)

y + 7 = -5x + 20

y = -5x + 13

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In Exercise, find the derivative of the function. y = ln(3 + x2)

erastovalidia [21]

Answer: $\dfrac{2x}{3 + x^2}$

Step-by-step explanation:

We know the property of derivative: $\dfrac{d}{dx}(\log (x))=\dfrac{1}{x}$

Given function : $y=\ln(3 + x^2)$

Differentiate both sides with respect to x , we get

$\dfrac{dy}{dx}=\dfrac{d}{dx}(\ln(3 + x^2))$

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot\dfrac{d}{dx}(3 + x^2)$ [By Chain rule]

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot(0+2x)$

[Since $\dfrac{d}{dx}(a)=0$ , where a is scalar and $\dfrac{d}{dx}(x^n)=n(x)^{n-1}$ ]

$\Rightarrow\ \dfrac{dy}{dx}=\dfrac{2x}{3 + x^2}$

Hence, the derivative of the given function is $\dfrac{2x}{3 + x^2}$ .

5 0

3 years ago

Mark buys a fresh pair of Walmart shoes that cost $35.99 plus 5.5% tax. How much did he pay?

elena55 [62]

Answer:

$37.97

Step-by-step explanation:

The price of the shoes before tax is 100% of the price of the shoes.

Then the tax adds 5.5% of the price of the shoes to the price of the shoes.

He ends up paying 100% + 5.5% of the price of the shoes.

100% + 5.5% = 105.5%

Now we find 105.5% of $35.99.

105.5% of $35.99 = 1.055 × $35.99 = $37.96945

Answer: $37.97

8 0

2 years ago

Read 2 more answers

The table below shows the outputs y for different inputs x:

igor_vitrenko [27]

Part A)
The table doesn't represent y as a function of x.
Why? One reason is that 1 or 3 is the first element in more than one ordered pair.
Part B)
f(x) = 10x + 20
f(120)= 10*120 + 20 = 1200 + 20 = 1220
f(120) represents cost of boating for 120 hours.

3 0

2 years ago

Read 2 more answers

Jennifer earned $1000 babysitting over the summer. She spent $250 of her earnings on new clothes. What percent of her earnings d

emmainna [20.7K]

Answer:

25%

Step-by-step explanation:

she earned $1,000

she spent $250

250/1000 = 0.25

0.25 x 100 = 25%