final pratice exam help please no calculator

Question

Answer 1

(5)

The function is y = (1/8)x^(3/2) - 8

To find the x - intercept of the function, Substitute y = 0 in the function

(1/8)x^(3/2) - 8 = 0

Add 8 to each side.

(1/8)x^(3/2) = 8

Multiply each side by 8.

x^(3/2) = 64

Square on both sides.

x³ = (64)²

x³ = 4096

Apply cube root on both sides.

x = (4096)^(1/3)

x = 16

Therefore x - intercept of the function is x = 16.

Option (d) is the correct answer.

Answer 2

The Cost value of the truck is $32000

Scrap value of the truck after 8 years is $8000

Straight line method,

Depreciation cost = (Cost value - Residual value)/time

Depreciation cost  = (32000 - 8000)/8

Depreciation cost = 3000

Deprecation cost for each year is 3000

Deprecation cost after 2 year is 3000*2 = 6000

The value of the truck after 2 years is 32000 - 6000 = 26000

Therefore the value of the truck after 2 years is 26000.

Option (d) is the correct answer

Answer 3

(7)

The equation of the circle is x²+y²+2x-2y = 0

To find the centre of the circle, first we convert the equation into the general form of circle eqaution.

Add and Subtract 2.

x²+y²+2x-2y + 2 - 2 = 0

x²+y²+2x-2y + 2 = 2

x²+ 2x +1 + y²-2y +1 = 2

(x+1)² + (y-1)² = 2

(x-(-1))² + (y-1)² = 2

This is the form of (x - h)² + (y - k)² = r² where (h,k) are the centre of the circle.

Therefore the centre of the circle is (-1,1).

Option (b) is the correct answer.

Comments

why did you add 2 and -2?

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We need to convert the circle equation into the Standard form (x - h)²+(y - k)² = r².

So to convert the given equation into general form, we add

(half of the x co-efficient)² + (half of the y co-efficient)²

= ((1/2) * 2)²+((1/2) * 2)²

= 1² + 1²

= 2

So we add and subtract with 2.