Download Question 1 Top of Form State the domain for the following: The

Question 1
State the domain for the following:
The bottom can’t be 0, so:
4X^3 not equal to 0
X not equal to 0
Question 2
State the domain for the following:
The bottom can’t be 0:
X^2 – 36 = 0
(x+6)(x-6) = 0
X not equal to -6 or 6
Question 3
State the domain for the following:
The bottom can’t be 0:
X^2 + 36 = 0
That never happens, so:
The domain is all real numbers
Question 4
Simplify and reduce to lowest terms:
Numbers: 4/2 = 2
X: x^3/x^2 = x
Y: y/y = 1
The whole thing is:
2x
Question 5
Simplify and reduce to lowest terms:
Multiply the second one by x/x:
1/x + 4x/x
Add:
(1+4x)/x
Question 6
Simplify and reduce to lowest terms:
Common denom:
(x-5y)/CD – 5(x+5y)/CD + 3/CD
Combine numerators:
x-5y – 5x – 25y + 3
(-4x-30y+3) / (x^2 – 25y^2)
Question 7
Simplify and reduce to lowest terms:
CD: 90:
2w/90 + 3(3w+2)/90
Add numerators:
(2w + 9w + 6)/90
(11w + 6)/90
Question 8
Solve:
Cross multiply:
3x = 10
X = 10/3
Question 9
Solve:
Multiply by a^2-4:
a-2 = a^2-4
Move to one side:
a^2 – a – 2 = 0
(a+1)(a-2) = 0
A = -1 or 2
BUT 2 is a false solution, since the bottom becomes undefined
A = -1
Question 10
Solve:
Cross multiply:
2x(3x-6) = 3x(2x-4)
Distribute:
6x^2 – 12x = 6x^2 – 12x
They are the same…
All x, except x = 0
Question 11
Solve for s:
Multiply through by s:
s/r = 1 + s/t
Subtract s/t:
s/r - s/t = 1
Factor:
S(1/r - 1/t) = 1
Divide:
S = 1/(1/r - 1/t)
Question 12
Solve for t:
Multiply by t:
tW = a^2
Divide by W:
t = a^2/W
Question 13
Simplify:
Multiply the tops to get a common denom:
c^2c^2/d^3c^2 + dd^3/d^3c^2 / (c^4 + d^4)
c^4/CD + d^4/CD / (c^4+d^4)
(c^4 + d^4)/CD / (c^4 + d^4)
Cancel:
1/CD
Which is:
1/(c^2d^3)
Question 14
Simplify:
Flip the second one and multiply:
a^-2b^2/ac * b^-2c^3/ab
Do the fractions:
a^-3b^2c^-1 * b^-3c^3a^-1
Multiply:
a^-4 b^-1c^2
Or:
c^2/(a^4b)
Question 15
Solve:
The number of fish Jim catches is dependent upon the lures he uses. He also loses lots of
these expensive lures. Here in South Dakota each fisherman can use two poles at one time
so Jim can use two different lures. If L1 represents the number of fish caught per hour for the
lure on the pole that holds and L2 represents the number of fish caught per hour for the lure
on the pole that he puts in the "dummy" holder, then the formula below represents the
relation between the two lures used and the total number of lures lost per hour using the two
poles. (C is the rate of lures lost per hour using both poles.) If the combined loss rate and
the rate for fish on lure 2 are known, write a function for the rate of fish on the first lure (i.e.
solve the equation below for L1.)
Multiply through by L1:
L1/C = 1 + L1L2
Subtract L1L2:
L1/C – L1L2 = 1
Factor:
L1(1/C – L2) = 1
Divide:
L1 = 1/(1/C – L2)
Question 16
Solve:
The greenhouse cools down (after the sun sets) according to the following formula below
where n is the number of hours after the sun stops hitting the building. In December the
average number of hours that the sun does not hit the greenhouse is 16.25. How cool
should we expect the greenhouse to get by sunrise of an average day in December?
Plug in n = 16.25
T = 85 – (16.25^2 – 1)/(16.25+1)
69.75
Question 17
Simplify (all exponents should be positive):
(x3 + 7x2 + 7x - 15) / (x + 3)
Factor the top:
(x-1)(x+5)(x+3)/(x+3)
Cancel:
(x-1)(x+5)
Question 18
Write the quotient:
(4x3 + 4x2 - 4) / (x - 2)
Here is my long division:
4x^2 + 12x + 24 + 44/(x-2)
Question 19
Write the quotient:
(2x3 + x2 - x + 4) / (2x - 5)
Here is the long division:
x^2 + 3x + 7 + 39/(2x-5)