Math Hates Me (5.6 - 6.4)
62
Cambridge Slim ate 33 sausages in the first 16 minutes of a high-stakes eating contest. Assuming that he continued at the same pace, how many sausages would he have eaten by the end of the 30-minute contest?
W = V b/d
Solve W/V = b/d for W.
m = 7r/x + z
Solve r = (x+z)m/7 for m.
12
The speed of a stream is 2 mph. A boat travels 10 miles upstream in the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?
5^5/14
Use the laws of exponents to simplify. (5^5/4)^2/7
(-∞, 9]
f(x) = √9 - x (Interval notation)
-6/5
Find -√36/25
v = Dn/n - d
Solve 1/D = 1/n + 1/v for v.
r = t/t - 1
Solve 1/r + 1/t = 1 for r.
x = jN/D - j
Solve D/j = N + x/x for x
24√x^3y^8z^4
Use rational exponents to write x^1/8 * y^1/4 * z^1/6 as a single radical expression.
5.1
A moving sidewalk at an airport moves at a rate of 1.7 ft/sec. Walking on the moving sidewalk, a person travels 106 ft forward in the time it takes to travel 53 ft in the opposite direction. How fast would a person be walking on a non-moving sidewalk?
61, 75
A steamboat travels 14 km/h faster than a freighter. The steamboat travels 225 km in the same time the freighter travels 183 km. Find the speed of each boat.
10 44/45
A swimming pool can be filled in 19 hours if water enters through a pipe alone, or in 26 hours if water enters through a hose alone. If water is entering through both the pipe and the hose, how long will it take to fill the pool?
104
A pitcher's earned-run average E varies directly as the number R of earned runs allowed and inversely as the number I of innings pitched. A certain pitcher had an earned-run average of 2.92, giving up 85 earned runs in 262 innings. How many earned runs would the pitcher have given up having pitched 320 innings with the same average?
3
Consider the numbers 2, 7, 3, and 9. If the same number is added to each of the numbers, it is found that the ratio of the first new number to the second is the same as the ratio of the third new number to the fourth. What is the number?
{x|x ≥ 5/2}
Determine the domain of the function. (set-builder notation) f(x) = √2x - 5
y = xz/7wp
Find an equation of variation in which y varies jointly as x and z and inversely as the product of w and p, where y = 3/63 when x = 3, z = 21, w = 7, and p = 27.
y = 81x^2
Find an equation of variation where y varies directly as the square of x, and where y = 0.81 when x = 0.1.
y = .004/x^2
Find an equation of variation where y varies inversely as the square of x, and where y = 0.40 when x = 0.1.
y = 2/77 xz^2
Find an equation of variation where y varies jointly as x and the square of z, and where y = 42 when x = 33 and z = 7.
-c^5+7
Find an equivalent expression for the given expression. -c^5 * c^7
|x - 12|
Find the following root. Assume that letters can represent any real number. √x^2 - 24x + 144
-1/5
Find the following root. ∛-1/125
7|c|
Find the following. Assume that c can represent any real number. Use absolute value notation when necessary. √(-7c)^2
|x|
Find the following. Assume x can represent any real number. ∜x^4
9; y = 9x
Find the variation constant and an equation of variation where y varies directly as x and y = 36 when x = 4.
56; y = 56/x
Find the variation constant and an equation of variation where y varies inversely as x and y = 14 when x = 4.
p^2 + 5
Identify the radicand. 6√p^2 + 5
9, 18
John can cut and split a cord of firewood in 9 fewer hr(s) than Dwight can. When they work together, it takes them 6 hr(s). How long would it take each of them to do the job alone?
15, 30
Person A can paint the neighbor's house 2 times as fast as Person B. The year A and B worked together, it took them 10 days. How long would it take each to paint the house?
1/(48xy)^5/8
Rewrite the following expression with positive exponents. (48xy)^-5/8
5a^5/3c^2/5/b^3/4
Rewrite using only positive, rational exponents. 5a^5/3b^-3/4c^2/5
3/x^1/3
Rewrite with a positive rational exponent. 3/∛x
(2x^2y)^9/5
Rewrite with rational exponents. (5√2x^2y)^9
17^1/2
Rewrite with rational exponents. √17
p^9/2
Rewrite with rational exponents. √p^9
9√x
Rewrite without rational exponents, and simplify, if possible. x^1/9
.7(x + 1)
Simplify. ∛.343(x + 1)^3
K^2 = 714.6Y/P
Solve P = 714.6Y/K^2 for K^2
10, 14
The attendants at a parking lot park cars in temporary spaces before the cars are taken to long-term parking stalls. The number N of such spaces needed is approximated by the function N(a) = 2.5√a , where a is the average number of arrivals in peak hours. Find the number of spaces needed when the average number of arrivals is (a) 16 and (b) 31.
7/4
The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 1/7 ampere when the resistance is 33614 ohms. What is the current when the resistance is 2744 ohms?
369,900,000
The number N of aluminum cans used each year varies directly as the number of people P using the cans. If 53 people use 15,900 cans in one year, how many cans are used in a city which has a population of 1,233,000?
112.75
The weight W of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 138 lb. Find her weight when she is 423 mi above the surface of the earth and the spacecraft is not in motion.
180
The weight, W, of an aluminum flatboat varies directly with the length, L, of the boat. If a 14-foot boat weighs 252 pounds, then what is the weight of a 10-foot boat?
201
To determine the number of trout in a lake, a conservationist catches 67 trout, tags them and throws them back into the lake. Later, 33 trout are caught; 11 of them are tagged. How many trout would the conservationist expect to be in the lake?
√3
Use rational exponents to simplify the following expression. Write the answer in radical notation if appropriate. 10√243
(ab)^5
Use rational exponents to simplify. (7√ab)^35
12√5488
Use rational exponents to write ∛2 * ∜7 as a single radical expression.
m^8/3 * n^2
Use the laws of exponents to simplify the following. (m^-1/2 * n^-3/8)^-16/3
2^11/10
Use the laws of exponents to simplify. 2^3/5 * 2^5/10
