Find a formula for a function f(x,y,z) whose level surface f=81 is a sphere of radius 9, centered at the origin.

Mathematics

1 answer:

Mrrafil [7]3 years ago

4 0

$81(9 \times 8 = 72 + 9) = 81$

You might be interested in

What is the horizontal asymptote for y(t) for the differential equation dy dt equals the product of 2 times y and the quantity 1

marta [7]

First, we need to solve the differential equation.
$\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)$
This a separable ODE. We can rewrite it like this:
$-\frac{4}{y^2-8y}{dy}=dt$
Now we integrate both sides.
$\int \:-\frac{4}{y^2-8y}dy=\int \:dt$
We get:
$\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1$
When we solve for y we get our solution:
$y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}$
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
$$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8$
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.

3 0

3 years ago

What is the y=mx+b of this?

pochemuha

I think it’s y=-1x+ -8 or could be written as y=-1x-8

3 0

3 years ago

Melissa estimated the length of a room is her house to be 13 ft . The actual length of the room is 11 ft. Find the absolute erro

Trava [24]

Answer:

Step-by-step explanation:

4 cm

7 0

3 years ago

Albert drew a scale drawing of a county park. The scale he used was 7 inches : 4 yards. The actual width of the picnic area is 6

Elenna [48]

I think its like you divide 64 by 4. This will tell you how many sets of the 4 yards you have which is important to know since each 4 yards equals 7 inches. 64 divided by 4 is 16. Then multiple 16 by 7 since there's 16 sets of 4 and each set is 7 inches. This will come to a total of 112 inches.

I hope this helps, sorry if its wrong I haven't done this in a while, but I'm pretty sure its correct

8 0

3 years ago

Sheets of Stickers

Molodets [167]

4 sheets cost $14
2 sheets cost $7
1 sheet costs $3.5
1/2 sheet costs $1.75

answer:

11 1/2 sheets cost $40.25

7 0

2 years ago