Change to Rational form
Write the radical in exponential form.
sqrt(19)
19^(1/2)
Write the rational expression in radical form.
8^(1/5)
root(5)(8)
Simplify.
32^(1/5)
2
The inverse of y = 2x + 4.
y = 1/2 x - 2?
f(x) = x4
Even
If y varies inversely as x2 and y = 8 when x = 2,
what is y when x = 4?
y = 32
k = 2 as 8 = (2)2k; 32 = (4)2(2)
Write the radical in exponential form.
root(4)(63)
63^(1/4)
Write the rational expression in radical form.
a^(3/4)
root(4)(a^3)
Simplify.
square root of 50
5 times the square root of 2
The inverse of y = 1/3 x + 2
y = 3x - 6?
f(x) = x3 - x
Odd
(-2)3 - (-2)1 doesn't equal (2)3 - (2)1 due to sign.
-8 + 2 doesn't equal 8 -2
-6 6
Y varies jointly as x2 and z2.
If y = 72 when x = 4 and z = 3,
find y when x = 3 and z = 5.
y = 112.5
k = (1/2) as 72 = (42)(32)(1/2)
so 72 = (22)(62)(1/2)
Write the radical in exponential form.
root(3)(5xy^2)
5^(1/3)x^(1/3)y^(2/3)
Write the rational expression in radical form.
4^(2/7)
root(7)(16)
Simplify.
b^(4/9)*b^(5/9)
b
The inverse of y = 5x2
y = √ 1/5 x
or
y=square root of (x/5)
f(x) = x6 + 1
Even
(-2)6 + 1 equals (2)6+ 1
64 + 1 equals 64 + 1
65 65
A balloon capacity varies directly as the radius cubed (r3).
The capacity of the balloon is 33.5 mL air when its radius is 2 cm. What is the capacity of a balloon with a radius of 4 cm?
268 mL
k = 4.1875
33.5 mL = (23) (4.1875)
268 mL = (43)(4.1875)
Write the radical in exponential form.
root(4)(625x^4)
5x
Write the rational expression in radical form.
(x^3)^(3/2)
sqrt(x^9)
Simplify.
(y^(1/4))^(3/5)
y^(3/20)
The inverse of y = x3 + 2.
y= 3√ (x - 2)
f(x) = (-x)6 + (-x)3
Neither
(- -2)6 + (- -2)3 doesn't equal (- 2)6 + (- 2)3.
64 + 8 doesn't equal 64 - 8
72 56
The momentum of an object varies jointly with mass and speed. If a 6 kg object moving 12 m/s has momentum of 72 newton-seconds (or kgm/s). If the object is 12kg and moving 11 m/s, what is it's momentum?
133 Ns
k = 1
72 Ns = (6 kg) (12 m/s)
133 Ns = (12 kg) (11 m/s)
Write the radical in exponential form.
root(3)(27x^6y^8z)
3x^2y^(8/3)z^(1/3)
Write the rational expression in radical form.
(a^(4/5))/(a^(1/5))
root(5)(a^3)
Simplify.
cube root of (16x7y5)
2x2y cube root of (2xy2)
Two functions that are inverses result in this value when function composition is applied.
x
In order, do the following formulas spell out
EON, NEO, or ONE
when labelled correctly?
1. f(x) = x5 + x2
2. f(x) = x7 - x3
3. f(x) = x10 + x2
1. f(x) = x5 + x2 ODD
2. f(x) = x7 - x3 NEITHER
3. f(x) = x10 + x2 EVEN
The cost of windows varies jointly with the area of the window and the thickness of the window. If a $1,200 window has an area of 10 square feet and is 2 inches thick, how much is a window that is 8 square feet and 2 inches thick?
$960
k = 60
$1200 = (10)(2)(60)
$960 = (8)(2)(60)