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3 years ago

What is the equation for the following graph? a. y=-4 b. y=4 c. x=4 d. x=-4

Mathematics

1 answer:

Naddika [18.5K]3 years ago

6 0

Answer:

x=4

Step-by-step explanation:

Consider the coordinate pair (4,y)

We observe that,

y can take any real values to lie on the graph of the equation.

As y really isn't a constant, we exclude it and take the equation as x=4

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A rental car company offers a rental package for a mid-size car.

skelet666 [1.2K]

Answer:

$y=45x+40$

Step-by-step explanation:

Let

x -----> the number of days

y ----> the total cost in dollars,

we know that

The equation of a linear function in slope intercept form is equal to

$y=mx+b$

where

m is the slope o rate of the linear equation

b is the y-coordinate of the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem we have

The slope is equal to the rental cost per day

$m=45\frac{\$}{day}$

When the number of days is equal to zero (x=0) the total cost is equal to $40 (administrative fee for the cleaning and maintenance of the car)

The y-intercept is the point (0,40)

$b=\$40$

substitute the values

$y=45x+40$

8 0

3 years ago

Please help with the questions in the image

algol13

First integral:

Use the rational exponent to represent roots. You have

$\displaystyle \int\sqrt[8]{x^9}\;dx = \int x^{\frac{9}{8}}\;dx$

And from here you can use the rule

$\displaystyle \int x^n\;dx=\dfrac{x^{n+1}}{n+1}+C$

to derive

$\displaystyle \int\sqrt[8]{x^9}\;dx = \dfrac{x^{\frac{17}{8}}}{\frac{17}{8}}=\dfrac{8x^{\frac{17}{8}}}{17}$

Second integral:

Simply split the fraction:

$\dfrac{3+\sqrt{x}+x}{x}=\dfrac{3}{x}+\dfrac{\sqrt{x}}{x}+\dfrac{x}{x}=\dfrac{3}{x}+\dfrac{1}{\sqrt{x}}+1$

So, the integral of the sum becomes the sum of three immediate integrals:

$\displaystyle \int \dfrac{3}{x}\;dx = 3\log(|x|)+C$

$\displaystyle \int \dfrac{1}{\sqrt{x}}\;dx = \int x^{-\frac{1}{2}}\;dx = 2\sqrt{x}+C$

$\displaystyle \int 1\;dx = x+C$

So, the answer is the sum of the three pieces:

$3\log(|x|) + 2\sqrt{x} + x+C$

Third integral:

Again, you can split the integral of the sum in the sum of the integrals. The antiderivative of the cosine is the sine, because $\sin'(x)=\cos(x)$ . So, you have

$\displaystyle \int \left( \cos(x)+\dfrac{1}{7}x\right)\;dx = \int \cos(x)\;dx + \dfrac{1}{7}\int x\;dx = \sin(x)+\frac{1}{14}x^2+C$

7 0

3 years ago