Download Can you please check to make sure the answers are

Can you please check to make sure the answers are correct the first four questions the
work has to be shown step -by- step? There are some problems not answer. Can you
please help me! Thanks
Radicals
Hint: Pay attention to the units of measure. You may have to convert from feet to miles
several times in doing these problems. You can use 1 mile = 5, 280 feet for your
conversions.
1. The equation D=1.2 h gives the distance, D, in miles that a person can see to the
horizon from a height, h, in feet.
a. Solve this equation for h
Divide by 1.2:
D/1.2 = h
Square each side:
H = (D/1.2)2 (this can only be positive, since negative h wouldn’t make sense)
b. Long’s Peak in the Rocky Mountains National Park is 14,255 feet in elevation. How
far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne,
Wyoming (about 89 miles away)?
D = 1.2 * 14255
= 143.27 miles
So yes, you can see 89 miles away.
2. According to Einstein’s theory of relativity, time passes more quickly for bodies that
travel very close to the speed of light. The expression
c2  v2
(c is the speed of light,
c2
and v is the speed of the traveling body) gives the aging rate compared to the time spent
on earth. For example, if the aging rate for someone traveling very fast was .5, then one
year for that person would be equal to two years on earth (.5x amount of time on earth =
amount of time for traveler).
a. Suppose that you are traveling at 90% the speed of light. That means that your
velocity, v would be equal to 0.9c. Substitute 0.9c into this expression for v, and
simplify fully. (Hint: your first step should be to use the roots of quotients
a

b
Plug in v = 0.9c:
rule
c 2  (0.9c) 2
c2
a
b
) . What is the aging rate?
=
=
c 2  0.81c 2
c2
0.19c 2
c2
0.19c 2
c2
= 0.19
= 0.4359
=
b. If you travel on a trip that takes 1 year (52 weeks) at this velocity then how much
time will have passed on earth when you return?
X = 1 year/0.4359
X = 2.294 years
3. The space shuttle orbits the Earth at altitudes between 115 and 400 miles. A radar
station at Cape Canaveral locates the shuttle at a distance of 247.5 miles. If the shuttle is
at an altitude of 211.3 miles then how far is it from the station?
This uses the Pythagorean Theorem:
A^2 + b^2 = c^2
(211.3^2) + b^2 = (247.5) ^2
b^2 = 247.5^2 – 211.3^2
b = 247.5^2 - 211.3^2
b = 128.874 miles
4. Many people know that the weight of an object varies on different planets, but did you
know that the weight of an object on earth also varies according to the elevation of the
object? In particular, the weight of an object follows this equation: w=Cr^-2 where C is a
constant and r is the distance that the object is from the center of the earth.
a. Solve the equation w=Cr^-2 for r
Divide by c:
W/c = r^-2
Take the reciprocal:
C/w = r^2
Square root:
R=
C/w – again, this can only be positive
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that
makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
C = w/r^-2 = wr^2
= 100*(3963^2)
= 1570536900
c. Use the value of C you found in the previous question to determine how much the
object would weigh in
I.
Death Valley (282 feet below sea level)
w=Cr^-2
w = 1570536900((3963-(282/5200)) ^-2)
w=100.0027 pounds
ii. The top of Mt McKinley (20,430 feet above sea level)
w=Cr^-2
w = 1570536900((3963+ (20430/5200)) ^-2)
w=99.802 pounds
Radical Expressions and Equations
7
1. Rewrite with rational exponents ( 7mn) =(7mn)7/2
7(1/7) m (1/7) n (1/7)
Alternatively, should the answer be 7mn 1 / 7
2. Multiply. ( 6  1) (7 6  1) =7( 7 )2=7(7)=49
Use FOIL
6 *7 6 + 7 6 + 6 + 1
7*6 + 8 6 + 1
42 + 8 6 + 1
8 6 + 43
3. Multiply. Simplify wherever possible ( 3  6) ( 3  6 )
FOIL:
3 3 + 3 6 – 3 6 – 6 6
3–6
= -3
4. Use rational exponents to write
correct expression
12
4
6  3 5 as a single radical expression choose the
63 * 12 5 4
63 * 54
= 12 135000
=
12
= choice B
a) 12 21870000000
b) 12 135000 c)
1
13500012
d)
12
30
5. Use rational exponents to simplify, Write the answer in radical notation if
possible
6
a4
A (4/6)
= A (2/3)
=
3
a
2
6. The formula r = 2 5 L can be used to approximate the speed r, in miles per hour,
of a car that has left skid marks of length L, in feet. How far will a car skid at 30
mph?
30 = 2 * 5 L
Divide by 2:
15 = 5 L
Square:
225 = 5L
Divide by 5:
L = 45 feet
7. Simplify
3
 27x 3
= 3  27 * 3 x 3
= -3x
8. Multiply and simplify by factoring. Assume that all expressions under radicals
represent non-negative numbers.
3
y 10 3 16 y 11
= 3 16 y 11 y 10
= 3 16 y 21
= y7* 3 16
= 2* 3 2 *y7
9. Subtract. Simplify by collecting like radical terms if possible.
5 3 3  33 3
(5-3) 3 3
=2 3 3
10. Multiply and simplify. Assume that all expressions under the radicals represent
non-negative numbers.
5x 7 15x = 75x8 = 3(25)x8 =5x4 3 Answer: a
Choose correct expression
a) 5x 4 3 b) x 4 75 c) 5x 3 3x d) 5x 4
10. Add. Simplify by collecting like radical terms if possible 3 32  6 72
= 3* 16 * 2 + 6* 36 * 2
= 3*4* 2 + 6*6* 2
= 12 2 + 36 2
= 48 2
11. Divide. Then simplify by taking roots if possible. Assume all expressions under
324xy
radicals represent positive numbers.
3 3
=
=
=
9 * 36 xy
3 3
3 36 xy
3 3
36xy
3
3 *12 xy
=
3
= 12 xy
12. Write and equivalent expression using radical notation.(a 2 b 2 )1 / 7 =(7 ab )2
7/2
ab
13. Solve. x  3  3x  13  2 Should the =2 be outside the radical sign?
The only solution is 4.
14. Find the following. Assume that x can represent any real number. Use absolute
value notation when necessary
x 2  6x  9
Factor the expression:
= ( x  3)( x  3)
= ( x  3) 2
= |x-3|
15. Subtract. Simplify by collecting like radical terms if possible, assuming that all
expressions under radicals represent non-negative numbers
3
54x  3 2 x 4
27 * 2x  3 x 3 * 2x
= 3* 3 2 x  x * 3 2 x
= (3-x) 3 2x
=
3
16. Television sets. What does it mean to refer to a 20-in TV set
Alternatively, a 25-in TV set such units refer to the diagonal of the screen. A 35-in
TV set also has width of 28 inches. What is its height?
Use the Pythagorean Theorem:
A^2 + b^2 = c^2
28^2 + b^2 = 35^2
b^2 = 35^2 – 28^2
b = 35^2 - 28^2
21 inches high
17. Multiply ( 7) (9 7  2) )
= 7 *-9 7 + 2 7
= -9*7 + 2 7
= 2 7 - 63
18. Use the laws of exponents to simplify ( 59 / 4 ) 2 / 5
= 5 (9/4 * 2/5)
= 5(18/20)
= 5(9/10)
19. Find the following. Assume that x can represent any real number. Use absolute
value notation when necessary
9x 2
= 9 * x2
= 3|x|
7
20. Find the following
y 7 Assume that letters can represent any real numbers
Y
21. Simplify by taking roots of the number and denominator
100
121
100
=
121
= 10/11
22. Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers
=
3
27 * 3  t 6 * t 2
= 3t2* 3 3t 2
3
81  t 8 = 27(3)t8