Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
Answer:
2/3,1,3/2,9/4,27/8
Step-by-step explanation:
f(1)=2/3
f(n)=f(n-1)×3/2
f(2)=f(2-1)×3/2=f(1)×3/2=2/3×3/2=1
f(3)=f(3-1)×3/2=f(2)×3/2=1×3/2=3/2
f(4)=f(4-1)×3/2=f(3)×3/2=3/2×3/2=9/4
f(5)=f(5-1)×3/2=f(4)×3/2=9/4×3/2=27/8
Square=a^2
trapezoid: a+b over 2 times height
triangle=bxh divide by 2
parallelogram= bxh
Then
which is a disk of radius 1, hence with area .