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elena-14-01-66 [18.8K]
2 years ago
5

stanley bought 108 feet of fencing to put around his backyard. The Backyard is a square. Write a equation to find the dimensions

of his backyard. Is the area big enough for a pool that is 800ft² explain
Mathematics
1 answer:
Vlad1618 [11]2 years ago
4 0

Answer:

Step-by-step explanation:

If he requires 4 sides (sometimes a building is used as a side) then 108 feet would require each side would be 108/4 = 27 feet in length

Area = 27^2 = 729 square feet. That's less than 800

The pool requires slight downsizing to fit in the back yard.

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Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun
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Required solution (a) f(x,y,z)=xyz+3z^2+C (b) 40.

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Given,

F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k

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F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}

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f_x=yz,f_y=xz,f_z=xy+6z

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f(x,y,z)=xyz+g(y,z)

Differentiate this with respect to y we get,

f_y=xz+g'(y,z)

compairinfg with f_y=xz of the given function we get,

g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)

Then,

f(x,y,z)=xyz+h(z)

Again differentiate with respect to z we get,

f_z=xy+h'(z)=xy+6z

on compairing we get,

h'(z)=6z\implies h(z)=3z^2+C   (By integrating h'(z))  where C is integration constant. Hence,

f(x,y,z)=xyz+3z^2+C

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3 years ago
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