A sports team is building a new stadium on a lot of land. The lot measures 8x by 12x and the field will be 3x by 6x. how much land will be left for the bleachers, restrooms, and other parts of the stadium?
So would I use the foil method or would I use the distributive. Or would I multiply the 8x and 6x for the area and 3x by the 6x then subtract the 3x and 6x from the product of 8x and 6x (48x^2).
A cylinder has a radius of 4x^2 and a height od 5x+4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V=ðr^2h for the volume of the cylinder.
A sphere has a radius of 2x+5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S=4ðr^2 for the surface area of a sphere.
f(x)=9x^3=2x^2-5x+5 and g(x)=5x^3-7x+4. What is f(x)-g(x)?
Please help me out.
A picture is helpful. Start by drawing the 8 by 12 lot. The field must fit in this lot and is 3 by 6. The area that is not the field is the remaining area.
This is a simple area calculation. Total area of the lot is 8 * 12 minus the area of the field, 3 * 6. The remaining area is 78 square feet.
Oops. Add an x^2 to my previous answer. I wasn't sure why we had random x's in the problem, so I just dropped them.
You're given the radius and the height of the cylinder. Simply stick in the given values into the provided formula and solve, yielding
pi(80x^4 + 64x^4). (You should distribute out the pi, I just can't be bothered to.)
The sphere question is very similar to the cylinder question. Stick the provided value r into the provided surface area equation.
SA = 4pi(2x+5)^2
Here you distribute / foil (2x+5) out when expanding, yielding
4pi(4x^2 + 20x + 25). Again, you should multiply each term by 4pi here, but without symbols that's a bit hard on here.
We want f(x) - g(x) and are given both equations. All you have to do is substitute:
9x^3=2x^2-5x+5 - (5x^3-7x+4)
Be sure to distribute that negative sign!
(I'd give you an answer but I'm not sure what that equals sign is supposed to be?)
Thank you!
F(x)=9x^3+2x^2-5x+4
it was supposed to be a plus sign I was typing to fast.
To determine how much land will be left for the bleachers, restrooms, and other parts of the stadium, we need to calculate the area of the lot and subtract the area of the field.
The lot measures 8x by 12x, so its area can be found by multiplying the length by the width:
Area of the lot = 8x * 12x = 96x^2
The field will be 3x by 6x, so its area can be calculated as:
Area of the field = 3x * 6x = 18x^2
To find the remaining land, we subtract the area of the field from the area of the lot:
Remaining land = Area of the lot - Area of the field
= 96x^2 - 18x^2
= 78x^2
Therefore, the remaining land for the bleachers, restrooms, and other parts of the stadium is 78x^2.
For the second question:
To find the volume of a cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.
Given that the cylinder's radius is 4x^2 and height is 5x+4, we can substitute these values into the formula:
V = π(4x^2)^2(5x+4)
= π(16x^4)(5x+4)
= π * 16x^4 * (5x+4)
= 16πx^4(5x+4)
So, the polynomial in standard form that best describes the total volume of the cylinder is 16πx^4(5x+4).
For the third question:
To find the surface area of a sphere, we use the formula S = 4πr^2, where r is the radius.
Given that the sphere's radius is 2x+5, we substitute this value into the formula:
S = 4π(2x+5)^2
= 4π(4x^2+20x+25)
= 16πx^2+80πx+100π
Therefore, the polynomial in standard form that best describes the total surface area of the sphere is 16πx^2+80πx+100π.
For the fourth question:
To find f(x) - g(x), we subtract the function g(x) from f(x) by subtracting the corresponding coefficients of each term.
f(x) = 9x^3 + 2x^2 - 5x + 5
g(x) = 5x^3 - 7x + 4
f(x) - g(x) = (9x^3 - 5x^3) + (2x^2) - (- 7x) + (5 - 4)
= 4x^3 + 2x^2 + 2x + 1
Therefore, f(x) - g(x) is equal to 4x^3 + 2x^2 + 2x + 1.
I hope this helps! Let me know if you have any further questions.