The time, t, it takes a runner to cover a specified distance is inversely proportional to the runner's speed. If Jann Avery runs at an average of 4 miles per her, she will finish a race in 2.4 hours. How long will it take Jackie Donofrio, who runs at 3 miles per hour, to finish the same race.

Q: The quantity a varies directly with d and inversely with b and c when d=12, b=5 and c=8, a = -3.…

A:

Q: The number of gallons of water, W, used when taking a shower varies directly as the time, t, in…

A:

Q: Solve each of the following problems. If y is inversely proportional to x, and y = 1/9 when x = 12,…

A:

Q: The time (T) required to do a job varies inversely with the square of the number of people (P)…

A:

Q: In the electric currect flow, it is found that the resistance (measured in the units called ohms)…

A: Given that resistance offered by a fixed length of wire of a given material varies inversely as the…

Q: If A varies directly as the square of e, and A = 225 when e = 5, find A when e = 10.

A:

Q: Suppose that the amount of time it takes to bulld a highway varies directly with the length of the…

A:

Q: the forces needed to keep a car from skidding on a curve F varies inversely as the radius of the…

A:

Q: The weight, M, of an astronaut on the moon is directly proportional to the weight, E, on Earth. An…

A: Weight on moon will be 12 Kg.

Q: . If S varies inversely as the square root of T andS = 4 when T = 4, what is S when T = 16?

A: Given that, S varies inversely as the square root of T. S α 1TS=kT     k is proportanility constant…

Q: If a is directly proportional to b and if a = 30 when b = 21, what is the value of a when b = 10…

A: Question number 30,Given,          a is directly proportional to b and a=30 whne b=21. Also when…

Q: The volume of gas in a gas shock absorber varies inversely with the pressure and directly with the…

A:

Q: .  If y is inversely proportional to x, and if y = 16 when x = 5, find the constant of variation

A: Given: y is inversely proportional to x y=16 when x= To find the constant of variation

Q: Find a model for the Body Mass Index (BMI) of a person, given that BMI varies directly as a person's…

A:

Q: Solve each of the following problems. If y is inversely proportional to x, and y = 1/35 when x = 14,…

A: Since, it is given that y is inversely proportional to x.Then, y∝1x⇒y=ax-(i), where a is…

Q: The intensity of a light source at a distance is directly proportional to the strength of the source…

A: Given that, the intensity of a light source at a distance is directly proportional to the strength…

Q: varies directly as g and inversely as r?. s jointly proportional to the square of x and the cube of…

A:

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: The rate at which a ceratin disease spreads is proportional to the product of the percentage of the…

A: We have to find the rate R(t) at which disease spreads Constant of  Proportionality = 0.03 Percent…

Q: Suppose the relationship between Y and X is given by: Y = 50 + 3X By how much does Y change if X…

A: Given,   The relationship between Y and X is given by,   Y = 50 + 3X   The objective is to find how…

Q: If f(x) is the slope of a trail at a distance of x miles from the start of the trail, what…

A: Given that f(x) is the slope of a trail at a distance of x miles from the start of the trail.

Q: If y is inversely proportional to the square root of x and y is 2 when x is 9, what is when x is 4?

A:

Q: The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve…

A: Given:A force of 200 pound keeps a car of weigth 3200 pound from skidding on curve of radius400ft at…

Q: If g is proportional to h and the constant of variation is 22, what is the value of g when h=11?

A: Given: g is proportional to h. Constant of variation is 22. The objective is to find the value of…

Q: Solve each of the following problems. If y is directly proportional to x, and y = 42 when x = 28,…

A: Given- If y is directly proportional to x, and y=42, when x=28. To Find- The value of y when x=38.

Q: Given that h is inversely proportional to x and the fact that h = 15 when x = 21, determine the…

A: Given h is inversely proportional to x. So, h∝1x. i.e. h=k1x Where k is constant.

Q: X is inversely proportional to the square root of y and y is inversely proportional to the cube of…

A:

Q: The distance, d, that a rock falls when dropped fro a cliff varies directly as the square of time,…

A:

Q: The number of gallons of water, W, used when taking a shower varies directly as the time, t, in…

A: Given:A Shower  lasting 5 minutes uses 5 gallons of water13 minutes=?

Q: If the constant of variation of h varies directly as k is 11, then what is h when k is 77?

A:

Q: If y is directly proportional to x, and y = 56 ​when x = 6, what is the value of x when y =   84?​

A:

Q: The mass of a spherical solid is inversely proportional as its density and the cube of its…

A:

Q: For a substance C, the time rate of conversion is proportional to the square of the amount of…

A: Given: For substance C, the time rate of conversion is proportional to the square of the amount of…

Q: The value of m varies inversely as N and directly proportional to L, and M= 8 when L = 4 and N = 9,…

A: The value of M varies inversely as N and directly proportional to L. That is, M α LN⇒M=k·LN    →1…

Q: The electrical resistance R of a wire varies inversely with the square of its diameter d. If a wire…

A:

Q: 4. Let c vary directly as d. If c = 210 when d = 35, what is the equation of variation?

A:

Q: The intensity I of light is inversely proportional to the square of the distance d from the light…

A: topic - ratio and proportion

Q: X varies inversely as the square of P. If x is 5 when P is 4, find x when P is 2

A: Given that X varies inversely as the square of P that is

Q: If p varies inversely with q, and p=2 when q=1, find the equation that relates p and q.

A: Given that p varies inversely with q and p=2 when q=1. We have to find the equation that relates p…

Q: he value of A is inversely proportional to the sum of B and C, and A is 4, B is 8 and c is 2, what…

A: Simply fallow the algebraic rule of numbers

Q: . If y is directly proportional to x, and y = 56 when x = 6, what is the value of x when y = 84?

A: Given: y is directly proportional to xy α xy=kxk is a  proportional constant

Q: If y varies indirectly as x and y is 6 when x is 36, find the constant of variation

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A: Given the data

Q: The time t required to drive a fixed distance varies inversely as the speed r. It takes 7hr at a…

A:

Q: (a) If M is inversely proportional to 7√t and M = 161 when t = 16, find an equation to represent…

A: M is inversely proportional to 7√t

Q: If y varies inversely as x, and y=4 when x=12, find the constant of variation k, and then determine…

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: If A varies directly as the square of e, and A=175 when e=5, find A when e=10.

A: Solve the following

Q: If y varies inversely as the square root of x and y=1 and x=25, find y when x=16 Attach Cile

A: Given, y ∝ 1x So , y = kx  ;       (where k is the constant of proportionality)      when  y  =1…

Q: What is the value of d if "d varies inversely with the square of= when k-2, and z-10"?

A: Given that: d varies inversely with the square of z.When k=2, z=10

Q: Suppose  c  is inversely proportional to the square of  d. If  c=8  when  d=2⁢, find the constant of…

A: Given, c is inversely proportional to the square of d.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.