What is the value of 2(x^{3} - y^{2}) + 2(x^{3} + y^{2}) for x = 2 and y = -4?

Solution

Substitute x and y by their values and simplify

2(2^{3} - (-4)^{2}) + 2(2^{3} + (-4)^{2})

= 2(8 - 16) + 2(8 + 16)

= -16 + 48 = 32

If x = 3, what is the value of 6 / x + 4x - 20?

Solution

Substitute x by its value and simplify

6 / x + 4x - 20

= 6/3 + 4(3) - 20

= 2 + 12 - 20 = -6

The surface area A of a cylindrical container is given by the formula

A = 2 pi r^{2} + 2 pi r h

where r is the radius, h is the height of the container and h its height and pi is a constant which can be approximeted by 3.14. Which of the values below is closeset to the area of a container whose radius is 10 cm and its height 5 cm?

A) 628
B) 1256
C) 314
D) 3140
E) 942

Solution

Substitute r, h and pi by their values in the formula for the area.

A = 2(3.14)(10)^{2} + 2(3.14)(10)(5)

= 628 + 314 = 942

If x = - 2 and y = 3, what is the value of - x^{- y}?

Solution

Substitute x and y by their values and simplify

- x^{- y}

= - (-2)^{(-3)}

= - 1 / (-2)^{3}

= - 1 / -8 = 1 / 8

If y = -3, what is the value of (y^{3} - 3) / (- y + 3)?

Solution

Substitute y by its values and simplify

(y^{3} - 3) / (- y + 3)

= ((-3)^{3} - 3) / (- (-3) + 3)

simplify

= (-27 - 3) / (3 + 3)

= -30 / 6 = - 5

What is the value of 3 x^{3} - 2 x^{2} + 2 for x = - 2?

Solution

Substitute x by its values in the given expression

3 x^{3} - 2 x^{2} + 2

= 3 (-2)^{3} - 2 (-2)^{2} + 2

Simplify

= 3(-8) - 2(4) + 2

= -24 -8 + 2 = -30

If x = 2.7, what is the value of x + 0.75(x - 1.5) + 1.2?

Solution

Substitute x by its values in the given expression and simplify

x + 0.75(x - 1.5) + 1.2

= 2.7 + 0.75(2.7 - 1.5) + 1.2

= 4.8

If x = - 0.07 and y = 1.2, what is the value of x y - 0.2 (y - x)?

A) 0.338
B) - 0.338
C) 0.3
D) - 0.3
E) 0.338

At normal resting heart rates, the mean arterial pressure MAP can be approximated by the simple formula

MAP = DP + (1/3)( SP - DP )

where DP is the diastolic pressure and SP systolic pressure. Find the mean arterial pressure MAP, rounded to the nearest unit, for a person with systolic pressure SP of 101 mmHg and a diastolic pressure DP of 72 mmHg.

A) 85
B) 100
C) 90
D) 80
E) 82

What is the value of 3 / (x - 4 y) + 2 / (0.5 x + 8 y) for x = - 2 and y = - 0.25?