Solving for the polynomial function of least degree with
integral coefficients whose zeros are -5, 3i
We have:
x = -5
Then x + 5 = 0
Therefore one of the factors of the polynomial function is
(x + 5)
Also, we have:
x = 3i
Which can be rewritten as:
x = Sqrt(-9)
Square both sides of the equation:
x^2 = -9
x^2 + 9 = 0
Therefore one of the factors of the polynomial function is (x^2
+ 9)
The polynomial function has factors: (x + 5)(x^2 + 9)
= x(x^2 + 9) + 5(x^2 + 9)
= x^3 + 9x + 5x^2 = 45
Therefore, x^3 + 5x^2 + 9x – 45 = 0
f(x) = x^3 + 5x^2 + 9x – 45
The polynomial function of least degree with integral coefficients
that has the given zeros, -5, 3i is f(x) = x^3 + 5x^2 + 9x – 45
Since vertical angles are congruent, (4x+7)=5(x-4). So simplifying we get 4x+7=5x-20. If we add 20 on both sides we get 4x+27=5x. Now when we subtract x from both sides, we get x=27
Answer:
total volume = (1150/3)pi cm^3
approximate total volume = 1204 cm^3
Step-by-step explanation:
The compound solid looks like it's made up of a cylinder with a base with 10 cm diameter and height of 12 cm and a half sphere with radius 10 cm.
volume of cylinder: (pi)(r^2)h
volume of sphere: (4/3)(pi)r^3
total volume = (pi)(r^2)h + (1/2)(4/3)(pi)r^3
We are given a diameter of 10 cm, so the radius is 5 cm since r = d/2.
total volume = (pi)[(5 cm)^2](12 cm) + (2/3)(pi)(5 cm)^3
total volume = 300pi cm^3 + (250/3)pi cm^3
exact total volume = (1150/3)pi cm^3
approximate total volume = 1204 cm^3
What triangle?
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Answer:
78cm
Step-by-step explanation:
L₁/W₁ = L₂/W₂
22/4 = L₂/6
5.5*6=L₂
L₂=33cm
Perimeter of rectangle = 2L+2W
=2(33)+2(6)
=66+12
=78cm
