Answer:
a) h = 15
b) x = 4
Step-by-step explanation:
a) set up a proportion:
<u> 5 </u> = <u> h </u>
8 24
cross-multiply:
8h = 120
h = 15
b) <u> x + 5</u> = <u> x + 5 + 15</u>
5x + 1 5x + 1 + 35
cross-multiply:
(x + 5)(5x + 36) = (5x + 1)(x + 20)
5
+ 61x + 180 = 5 + 101x + 20
180 = 40x + 20
160 = 40x
x = 4
Answer:
r = 14.998 yd
Step-by-step explanation:
Volume of a cone
V = πr^2h/3
Given:
V = 3,532 yd cubed
π - 3.14
r = h
Since the radius and the height of the cone are equal
So, let r = h = x yd
V = 3.14 * x^2 * x/3
3532 = 3.14x^3/3
3532 = 1.047x^3
Divide both sides by 1.047
3532/1.047 = x^3
3373.45 = x^3
x = 14.998 yd
Since r = h = x
r = h = 14.998yd
r = 14.998yd
Hint: to check if the value of radius and the height are correct, insert the values into the formula
V = πr^2h/3
V = 3.14 * 14.998^2 * 14.998/3
= 3.14 * 224.940 * 4.999
= 3530.852
≈ 3531 yd cubed
Due to approximations
Answer:
Particles are spaced the farthest apart in gas
Step-by-step explanation:
1) We want to find the area of the triangular bases, which means both shown in the net. So, normally we would divide the area by 2 (from the formula), but since we are finding the area of two triangles, that isn't necessary.
A = 8 x 3
2) There are two different sized rectangles here. One that is repeated twice and the other that is on its own. We know that A and C are the same, and if we think about how this net is folded, we can determine that the width of A and C would be 5 cm. For both sized rectangles, the length is 12 cm. For rectangle B, we can see that its width is 8 cm.
A = (8 x 12) + (5 x 12)
3) Now that we have all of the expressions needed to find the surface area, what we need to do is evaluate each of them and add them together to find the total surface area.
Triangles = 8 x 3 = 24
Rectangles = (8 x 12) + (5 x 12) = 96 + 60 = 156
Surface area = 24 + 156 = 180 square centimeters
Hope this helps! :)
The gradient is the same as the slope.
The gradient is always before the x variable or is the coefficient of the x variable when an equation is in the slope intercept form.
The gradient in this equation is 1
