All categories

3 years ago

A community center is expanding the size

Mathematics

1 answer:

Katen [24]3 years ago

6 0

So the original area is 300*150 (or 45000 ft^2), but now the new area is (300+3y)(150+3y).

The polynomial in standard form would be 45000+900y+450y+9y^2=45000+1350y+9y^2

But the proper way to write it is 9y^2+1350y+45000

When y=4, we get 9(4^2)+1350(4)+45000=9(16)+54000+45000=144+99000=99144

So the new area would be 99144 ft^2

Hope this helped!

You might be interested in

Find the max and min values of f(x,y,z)=x+y-z on the sphere x^2+y^2+z^2=81

Anton [14]

Using Lagrange multipliers, we have the Lagrangian

$L(x,y,z,\lambda)=x+y-z+\lambda(x^2+y^2+z^2-81)$

with partial derivatives (set equal to 0)

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$
$L_y=1+2\lambda y=0\implies y=-\dfrac1{2\lambda}$
$L_z=-1+2\lambda z=0\implies z=\dfrac1{2\lambda}$
$L_\lambda=x^2+y^2+z^2-81=0\implies x^2+y^2+z^2=81$

Substituting the first three equations into the fourth allows us to solve for $\lambda$ :

$x^2+y^2+z^2=\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}=81\implies\lambda=\pm\dfrac1{6\sqrt3}$

For each possible value of $\lambda$ , we get two corresponding critical points at $(\mp3\sqrt3,\mp3\sqrt3,\pm3\sqrt3)$ .

At these points, respectively, we get a maximum value of $f(3\sqrt3,3\sqrt3,-3\sqrt3)=9\sqrt3$ and a minimum value of $f(-3\sqrt3,-3\sqrt3,3\sqrt3)=-9\sqrt3$ .

5 0

3 years ago

A local hamburger shop sold a combined total of 500 hamburgers and cheeseburgers on Wednesday. There were 50 more cheeseburgers

Komok [63]

500-250=250 so if there were 50 more cheeseburgers it would be 300 cheeseburgers so they would of have to sold 200 hamburgers on Wednesday to have sold 500 burgers in total do the answer is 200 hamburgers

4 0

3 years ago

Can you help? thank you

algol [13]

Answer:

Step-by-step explanation:

To find f(4), find the point in the graph where x = 4 .

And if you look at the point where x = 4 ; y = 1 .

So the answer is : 1

6 0

3 years ago

What is the solution to the inequality? 17 < 9 + x

dezoksy [38]

Answer:

x > 8

Step-by-step explanation:

Given

17 < 9 + x ( subtract 9 from both sides )

8 < x , hence

x > 8

7 0

3 years ago

Pls help on this question

sveticcg [70]

Answer:

178.571429

Step-by-step explanation:

Area of square - 10*10 m = 100m

Area of the semicircle = Diameter = 10m, so the radius = 5m

Area of circle = $\pi r^{2}$

=> Area = 22/7 * 25

=> 78.5714286

Area of figure = 78.5714286 + 100 = 178.571429

Hope it helps :)

6 0

3 years ago

Read 2 more answers