Answer:
n = 64
Step-by-step explanation:
We can solve using cross products
10/15 = n/96
10*96 = 15*n
960 = 15n
Divide each side by 15
960/15 =15n/15
64 = n
Draw a cartesian plane, create a graph with the equation x = y^2 - 2
then substitute numbers into the equation so that it is true, to find points on the graph, e.g. substitute y with 1, you get
x = 1^2 - 2
x = 1 - 2 = -1, so when y = 1, x = -1, this point is (-1, 1)
for the next substitute y with 2,
x = 2^2 - 2
x = 4 - 2 = 2, the point is (2, 2)
you might want to try negative values of y
y = -1, x = (-1)^2 - 2
x = -1 the point is (-1,-1)
then plot the points on the graph
Let h = height of triangle
h^2 + 12^2 = 15^2
h^2 + 144 = 225
h^2 = 225 - 144
h^2 = 81
sqrt{h^2} = sqrt{81}
h = 9 cm
For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.
1. First find the lateral area.
LA = perimeter of triangle • height
LA = ph
p = 15 + 15 + 24
p = 30 + 24
p = 54 cm
LA = (54)(9)
LA = 486 cm^2
2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.
A = (1/2)bh
A = (1/2)(24)(9)
A = 108 cm^2
A = 2•108 cm^2
A = 216 cm^2 = our B in the surface area formula.
SA = B + LA
SA = 216 cm^2 + 486 cm^2
SA = 702 cm^2
The amount of cardboard needed is 702 cm^2.
