The diagram shows a model for the roof of a toy building. The roof is in the form of a solid triangular prism ABCDEF. The base ACFD of the roof is a horizontal rectangle, and the cross-
section ABC of the roof is an isosceles triangle with AB = BC.
The lengths of AC and CF are 2x cm and ycm respectively, and the height of BE above the base of
the roof is rcm.
The total surface area of the five faces of the roof is 600 cm and the volume of the roof is V cm.
(a) Show that v = kx(300 - x?), where k = Va+b and a and b are integers to be determined. [6]
(b) Use differentiation to determine the value of x for which the volume of the roof is a maximum.
(c) Find the maximum volume of the roof. Give your answer in cm', correct to the nearest integer.
[1]
(d) Explain why, for this roof, x must be less than a certain value, which you should state.
[2]​

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

hi there!

the answer is: 2 and -2

step-by-step explanation:

case 1: an absolute value of positive number will still be a positive number

so absolute value of 2 is 2

case 2: an absolute value of negative number will be positive number so absolute value of -2 is 2