State the horizontal asymptote of the rational function.<br> f(x) = x^2 + 9x-9/x-9

(07.09) Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car i

atroni [7]

Answer:

Answer: f[c(p)] = 0.9265p

Step-by-step explanation:

Given: Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is , where p is the original price of the car.

He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is , where c is the sale price of the car.

Now, the composite function that can be used to calculate the final price of Jonah's car is given by :-

3 0

2 years ago

Read 2 more answers

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

6 0

3 years ago

The balcony of an apartment is 4 feet by 7 feet. On a scale drawing of the apartment, the balcony is 0.8 inch by 1.4 inches, and

-Dominant- [34]

Answer:

The actual dimensions of the kitchen are $12\ ft$ by $14\ ft$

Step-by-step explanation:

step 1

Find the scale of the drawing

To find the scale , remember that is equal to the ratio of the corresponding dimension in the drawing divided by the corresponding actual dimension

so

$\frac{0.8}{4}\frac{in}{ft}=0.2\frac{in}{ft}$

step 2

To find the actual dimensions of the kitchen, divide the dimension in the drawing by the scale

so

$2.4\ in=2.4/0.2=12\ ft$

$2.8\ in=2.8/0.2=14\ ft$

6 0

2 years ago

Solve for x check your solution

abruzzese [7]

Area for a triangle is (1/2) bh or bh/2
So using this info, b = 1.5 m and h = x and A = 1.5 m^2

A = bh/2
1.5 = 1.5x/2
Multiply both sides by 2 to get rid of fraction ... 3 = 1.5x
Divide both sides by 1.5 ... 2 = x so x= 1.5 m

8 0

3 years ago

12x+5y3z, where x=12, y = 6, and z = 3

mestny [16]

Answer:

12×x+5y×3z

12×12+5×6×3×3

144+30×9

174×9

1,566.

that's what I found out.

8 0

2 years ago

State the horizontal asymptote of the rational function. f(x) = x^2 + 9x-9/x-9