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ra1l [238]
3 years ago
5

The volume V of a cube with sides of length x inches is changing with respect to time t (in seconds). When the sides of the cube

are 10 in. long and increasing at the rate of 0.5 in/sec, how fast is the volume of the cube increasing?
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
5 0

Answer:

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

Step-by-step explanation:

Volume V = length l^3

V = x^3

Differentiating both sides;

dV/dt = 3x^2 dv/dt

Given;

x = 10 in

dx/dt = 0.5 in/sec

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

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Jamal has a pair of shoes that have a total mass of 960 grams and four identical books that have a total mass of 2 kilograms. Wh
Andreyy89

Answer: One book has a greater mass.

Step-by-step explanation:

Jamal has a pair of shoes with a total mass of 960 grams. This means that each shoe has a mass of:

960 grams ÷ 2= 480 grams per shoe.

Jamal also has four identical books with a total mass of 2 kilograms. Note that 1000 grams make a kilograms. Therefore 2 kilograms will be (2 × 1000 grams) = 2000 grams.

Each book will have a mass of:

2000 ÷ 4 = 500 grams per book.

One shoe has a mass of 960 divided 2 = 480 grams . One book has a mass of 2000 divided 4 = 500 grams . So one book has a greater mass.

8 0
3 years ago
A 20% apple juice drink is mixed with a 100% apple juice drink. The function f(x)=(2)(1.0)+x(0.2)2+x models the concentration of
luda_lava [24]

Answer:

17.5

Step-by-step explanation:

Given that:

20% apple juice drink is mixed with a 100% apple juice drink.

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

represents the concentration of apple juice in the drink when x gallons of 20% drink are added to 2 gallons of pure juice.

Also, given that 6 gallons of 20% drink are added to the 2 gallons of pure juice.

To find:

The concentration of apple juice in the drink = ?

Solution:

Given the function:

f(x)=\dfrac{(2)(0.1)+x(0.2)}{2+x}

and

x=6\ gallons

f(x)=\dfrac{(2)(0.1)+6(0.2)}{2+6}\\\Rightarrow f(x)=\dfrac{0.2+1.2}{8}\\\Rightarrow f(x)=\dfrac{1.4}{8}\\\Rightarrow f(x)=\bold{0.175}

In percentage, the concentration 17.5.

7 0
3 years ago
Solve for x<br><br> 1/3x=7/6 + 1/9
zimovet [89]

Answer:

x=26/3 because you need to comine like terms as usual

3 0
3 years ago
Based on a​ survey, assume that 43​% of consumers are comfortable having drones deliver their purchases. Suppose we want to find
svlad2 [7]

Answer:

The probability of getting two consumers comfortable with drones is 0.3424.

Step-by-step explanation:

The probability that a consumer is comfortable having drones deliver their purchases is, <em>p</em> = 0.43.

A random sample of <em>n</em> = 5 consumers are selected, and exactly <em>x</em> = 2 of them are comfortable with the drones.

To compute the probability of getting two consumers comfortable with drones followed by three consumers not​ comfortable, we will use the Binomial distribution instead of the multiplication rule to find the probability.

This is because in this case we need to compute the number of possible combinations of two consumers who are comfortable with drones.

So, <em>X</em> = number of consumers comfortable with drones, follows a Binomial distribution with parameters <em>n</em> = 5 and <em>p</em> = 0.43.

Compute the probability of getting two consumers comfortable with drones as follows:

P(X=x)={5\choose x}\ 0.43^{x}\ (1-0.43)^{5-x};\ x=0,1,2,3...

P(X=2)={5\choose 2}\ 0.43^{2}\ (1-0.43)^{5-2}

               =10\times 0.1849\times 0.185193\\=0.342421857\\\approx 0.3424

Thus, the probability of getting two consumers comfortable with drones is 0.3424.

4 0
3 years ago
Suppose the function F(c) represents the earnings of a volleyball team from selling c cupcakes. They are selling each cupcake fo
navik [9.2K]

Answer:

The variable c represents the domain as it is the independent variable.

The domain of the function F(c) is given by c ≥ 0.

So, only positive values for the input make sense.

The upper limit of the domain is +∞ and lower limit is 0.

It is not possible for the team to earn $50.50 as it will be only multiple of 2.

Step-by-step explanation:

If F(c) represents the earning of a volleyball team from selling c cupcakes and each cupcake costs $2 each, then the equation that models the situation is  

F(c) = 2c ..... (1)

The variable c represents the domain as it is the independent variable. (Answer)

The domain of the function F(c) is given by c ≥ 0. (Answer)

So, only positive values for the input make sense. (Answer)

The upper limit of the domain is +∞ and the lower limit is 0. (Answer)

It is not possible for the team to earn $50.50 as it will be only multiple of 2. (Answer)

5 0
3 years ago
Read 2 more answers
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