find the complement and supplement of an angle with the given measure. a.)10° 10' 30" , b.)1° 40' 19"

a)
90°=89° 59' 60"
so...
complement:
89° 59' 60"-10° 10' 30"=
79° 49' 30"
supplement:
169° 49' 30"
b)
complement
89° 59' 60"-1° 40' 19"=
88° 19' 41"
supplement:
178° 19' 41"

Solve: 3(4^2x)+5(4^x)-2=0

u+2 is extraneous, assuming all solutions are to be real



Taking log base 4 of both sides...

find the largest four digit number which is divisible by 5,8,and 9

our number must be a multiple of...
(5)(8)(9)=360
The greatest 4-digit number is 9999, so...
9999/360=27 31/40
so take 27...
360*27=9720

Find the inverse for a quadratic function

y=(x+3)^2

Not invertible unless we restrict the domain



inverse:
 

The length of a football field is 180 feet more than its width. If the perimeter of the field is 1,060 feet, find the length of the field

1)

so

2)

so


adding equations...

Alan participated in a car race in which he had to cover a distance of at least 50 kilometers. He had fuel in his car for a maximum distance of 53 kilometers. If the distance is given by S(t)=3t+47 , where (t) is the time in hours, find the minimum and maximum number of hours for which Alan can drive his car.

so


In general his limits are:

but assuming he wants to stay in the race:


and his limits are:

Find the difference quotient (f(x+h)-f(x))/h , where h is not equal to zero for the function below: f(x)=5x^2 +3x Simplify the answer as much as possible.

so that means


furthermore

AP exam in math has a mean score of 73 with a standard deviation of 7.8. If one student is randomly selected, find the probability that the student's test score is less than 70.

find the smallest square number that is divisible by 6, 18 and 21?

6=2*3
18=2*3^2
21=3*7 

To be a square we need all prime factors squared (at least once in general):
n=((2)(3)(7))^2=1764

B=(a-c)/( d-e) make e the subject of the formula

Solve by substitution: {6x+2y=11, 4x+y=6}.

6x+2(6-4x)=11
6x+12-8x=11
-2x=-1
x=1/2
y=6-4(1/2)=6-2=4
y=4
solution: (1/2, 4)

Find the average rate of change for the function between the given values. f(x) = sqrt 2x ; from 2 to 8

 

A painter can finish painting a house in 6 hours Her assistant takes 8 hours to finish the same job How long would it take for them to complete the job if they were working together?

rates can be added:
1/6+1/8=1/t
4/24+3/24=1/t
1/t=7/24
t=24/7 =3 3/7 hr

What is the solution set of the following equation? -8x + x + 15 = -7x + 12

-8x + x + 15 = -7x + 12
-7x+15=-7x+12
this is a contradiction so there is no solution, i.e. { } is the solution set.

If f(x)= x+ 1/x, show that f(x).f(x+1/x)=f(x^2)+3

LHS:

substituting from the the function...
 
RHS:

they are equal!

Solve: |2a-4|=-2a+4

it means the same as:
2a-4=-2a+4 or 2a-4=-(-2a+4)
4a=8 or 0=0
a=2
but notice that the expressions 2a-4 and -2a+4 have the same value when

so that is our solution

Solve: |2p-3|=17

means the same as:
2p-3=17 or 2p-3=-17
2p=20 or 2p=-14
p=10 or p=-7

solve: -3+|2x+7| > 6

-3+|2x+7| > 6
-3+3+|2x+7| > 6+3
|2x+7| > 9
2x+7 > 9 or 2x+7 < -9
2x > 2 or 2x < -16
x > 1 or x < -8

A=2lw+2lh+2wh solve for w

what is the value of sin 150 in fraction?

sin(150)=
sin(90+60)=
sin(90)cos(60)+cos(90)sin(60)=
1*1/2+0*sqrt(3)/2=
1/2

Two picture frames have the same area of 96 inches squared but different perimeters. What could the perimeters of the two frames be?

Both pictures must satisfy the equation:

So choosing valid values for any suitable pair of the four dimensions will produce different perimeters. For example:
, 
results in


and so on...

log5(12). How would you do it on the calculator?

Use log base conversion...check your textbook for details...
log(12)/log(5)=ln(12)/ln(5)=1.543...

What is the 8th term 3,5/3,1/3 ?

, ,