100 divided by 7 is 14 r 2, so there are 2 left over
F(x) = 500x-8000
500 times the number of years (x), subtracted by the original price (8000)
Answer:
1.
2. 9.8 m
3. 8.7 m.
Step-by-step explanation:
1. Let the angle be represented by θ, so that:
Cos θ =
=
Cos θ = 0.82192
θ = 0.8219
=
θ =
The angle through which the boy must raise his eyes to see the top of the cross on the tower is .
2. Let the height from the boy's head to the top of the cross be represented by y, so that:
Sin =
y = Sin x 14.6
= 0.5697 x 14.6
y = 8.32 m
The height of the top of the cross from the ground = 1.5 + 8.32
= 9.82 m
The height of the top of the cross from the ground is 9.8 m.
3. Let the height from the boy's head to the top of the building be represented by x, so that:
Tan 31 =
=
x = Tan 31 x 12
= 0.6009 x 12
x = 7.21
The height of the church building = 1.5 + 7.21
= 8.71
The height of the church building is 8.7 m.
The sketch to the question is attached to this answer.
First I will present the polynomial itself: it is
5x^3 - 22x^2 - 3x - 53.
Let's show that when this poly. is divided by (x-5), the quotient is 5x^2 + 3x + 12 and the remainder is 7. Use synthetic division here. Let the divisor be 5 (this comes from the factor (x-5). Then:
__________________
5 / 5 -22 -3 -53
25 15 60
----------------------------
5 3 12 7 where 5 3 12 are the coeff. of the quotient and 7
is the remainder.
Now work backwards. Multiply (x-5) and (5x^2 + 3x + 12) together. We get
5x^3 + 3x^2 + 12 x - 25x^2 - 15x - 60, or
5x^3 - 22x^2 - 3x - 60. Now add the remainder (7) to -60; the result will be -53.
So the poly in question is 5x^3 - 22x^2 - 3x - 53.