A spherical block of ice melts so that its surface area decreases at a constant rate: ds/dt = - 8 pi cm^2/s. calculate how fast the radius is decreasing when the radius is 3cm. (recall that s = 4 pi r^2.)

The unit is converted in new scale as 1 inch is equal to 9 feet.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

For the given situation,

A rectangular sidewalk has a length = 21 feet

Scale factor, 1 inch = 7 feet.

So, 21 feet = [tex]\frac{21}{7}[/tex]

⇒ [tex]3[/tex] inches

The length of the actual side walk changes to 27 feet.

The length of actual side walk in inches = 3 inches.

Now, 1 inch = [tex]\frac{27}{3}[/tex]

⇒ [tex]1 inch = 9 feet[/tex]

Hence we can conclude that the unit is converted in new scale as 1 inch is equal to 9 feet.

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Answer: the first one

Step-by-step explanation:

Answer:

40% of 20

Step-by-step explanation:

Final answer:

To divide 0.4 by 0.02, transform the division problem into 40 divided by 2 by moving the decimal places to the right, resulting in the answer 20.

Explanation:

To solve the division of two decimal numbers, 0.4 divided by 0.02, you can follow these steps:

The division now looks like 40 ÷ 2, which equals 20.

So, 0.4 divided by 0.02 equals 20. This method allows us to divide decimal numbers by converting them into whole numbers, simplifying the calculation.

Answer: The correct option is A.

Explanation:

The given function is,

[tex]f(x)=x^2+8-16x[/tex]

Rewrite the above function.

[tex]f(x)=(x^2-16x)+8[/tex]

To make the perfect square we add and subtract the square of [tex]\frac{b}{2a}[/tex], where b is coefficient of x and a is the coefficient of [tex]x^2[/tex].

Since a=1 and b = -16, So we will add and subtract he square of -8.

[tex]f(x)=(x^2-16x+(-8)^2)+8-(-8)^2[/tex]

[tex]f(x)=(x^2-16x+(8)^2)+8-64[/tex]

Using [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]f(x)=(x-8)^2)-56[/tex]

Therefore, the correct option is A.

Aiko started jumping rope at 7:45, which is calculated by subtracting the 20-minute jump rope activity duration from the time she stopped at 8:05.

To solve this problem, we need to subtract the duration of Aiko's jump rope activity from the time she stopped. We know that Aiko stopped jumping rope at 8:05 and the duration of her jump rope activity was 20 minutes.

Since Aiko's activity lasted 20 minutes and she ended at 8:05, we need to subtract 20 minutes from 8:05 to find out when she started. Thus, Aiko started jumping rope at 7:45.

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Using the equation, 98 hamburgers were sold on Saturday.

An equation is an equality relationship between two expressions written on both sides of the equal to sign.

Let the number of hamburgers sold be h and number of cheeseburgers sold be c.

Then we can formulate an equation

c = 3h

c + h = 392

3h + h = 392

4h = 392

h = 98

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To find the Jacobian of the given transformation, we need to compute the partial derivatives of x and y with respect to u and v. The Jacobian matrix is a matrix that represents these partial derivatives.

To find the Jacobian of the transformation x = u^2 + uv and y = uv^2, we need to compute the partial derivatives of x and y with respect to u and v. Let's start with the partial derivative of x:

∂x/∂u = 2u + v

Now let's find the partial derivative of x with respect to v:

∂x/∂v = u

Using the same process, we can find the partial derivatives of y:

∂y/∂u = v^2

∂y/∂v = 2uv

Putting it all together, the Jacobian matrix is:

J(u, v) = [∂x/∂u, ∂x/∂v; ∂y/∂u, ∂y/∂v]

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The Jacobian of the transformation is [tex]\( uv(4u + v) \)[/tex].

The Jacobian of the transformation given by [tex]\( x = u^2 + uv \) and \( y = uv^2 \)[/tex] is determined by finding the determinant of the matrix of partial derivatives. The matrix of partial derivatives, known as the Jacobian matrix, is given by: [tex]J = \begin{bmatrix} \frac{\partial x}{\partial u} \frac{\partial x}{\partial v} \\ \frac{\partial y}{\partial u} \frac{\partial y}{\partial v} \end{bmatrix}[/tex]

We calculate each of the partial derivatives:

 [tex]\frac{\partial x}{\partial u} = \frac{\partial}{\partial u}(u^2 + uv) = 2u + v[/tex]

[tex]\frac{\partial x}{\partial v} = \frac{\partial}{\partial v}(u^2 + uv) = u[/tex]

[tex]\frac{\partial y}{\partial u} = \frac{\partial}{\partial u}(uv^2) = v^2[/tex]

[tex]\frac{\partial y}{\partial v} = \frac{\partial}{\partial v}(uv^2) = 2uv[/tex]

Now we can construct the Jacobian matrix: [tex]J = \begin{bmatrix} 2u + v u \\ v^2 2uv \end{bmatrix}[/tex]

The determinant of this matrix gives us the Jacobian of the transformation:

[tex]\text{Jacobian} = \text{det}(J) = (2u + v)(2uv) - (u)(v^2)[/tex]

[tex]\text{Jacobian} = 4u^2v + 2uv^2 - uv^2[/tex]

[tex]\text{Jacobian} = 4u^2v + uv^2[/tex]

[tex]\text{Jacobian} = uv(4u + v)[/tex]

Therefore, the Jacobian of the transformation is [tex]\( uv(4u + v) \).[/tex]

Answer:

(A) $1,090

Step-by-step explanation:

We will see that the net income at the comic store is $1,090, so the correct option is a.

The net income will be the difference between how much money enters the store and how much he needs to pay.

We know that each month he gets $3,250.

And he must pay $1,285 for the comics and $875 in expenses, so the net income is:

N = $3,250 - $1,285 - $875 = $1,090

We conclude that the net income is $1,090, so the correct option is a.

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Final answer:

Joyce read 1/6 of her book on Monday, 2/5 on Tuesday, and 1/3 on Wednesday. After converting to a common denominator and adding the fractions, she read 27/30 of her book, which simplifies to 9/10 or 90% of her book in total.

Explanation:

To find out how much of her book Joyce has read over three days, we need to add up the fractions of the book she read each day.

To calculate the total, we can first find a common denominator for the fractions, which in this case is 30. We then convert each fraction and sum them up:

After adding the fractions, we find that Joyce has read 27/30 of her book over the three days, which can be simplified to 9/10 if we divide both the numerator and the denominator by 3.

Therefore, Joyce has read 90% of her book by the end of Wednesday.

Answer:

a). 9 weeks

b). 4 more weeks

Step-by-step explanation:

a). The cost of new bicycle = $155.75

     Amount I have with me   = $30

Therefore remaining amount = 155.75 - 30

                                                 = $ 125.75

Amount I will save in one week = $ 5

Amount my aunt will give me one week  = $ 10

Therefore total amount i will save in one week = 5 + 10

                                                                              = $ 15 in one week

Therefore number of weeks required to collect the remaining amount of $125.75 is  = 125.75 / 15

                   = 8.38 weeks

                  = 9 weeks

Thus 9 weeks are required to save money to buy a bicycle that cost $155.75

b). New cost the bicycle = $ 203.89

    From above at the end of 9 weeks I will have = $ 125.75

    Amount I have with me before = $ 30

   Therefore by the end of 9 weeks I have total amount = 125.75 + 30

                                                                                              = $ 155.75

  Therefore amount less = 203.89 - 155.75

                                         =  $ 48.14

  Number of weeks require to collect the remaining amount of $ 48.14 by saving  $ 15 in one week is = 48.14 / 15

                                             = 3.20 week

                                              = 4 weeks

Thus,  4 more weeks  is required to save money to buy a new bicycle that cost $ 203.89

It will take approximately 9 weeks to save enough money to buy the bicycle. It would take approximately 12 more weeks to save enough money for a bicycle that costs $203.89.

To determine how many weeks it will take to save enough money to buy a bicycle, we can set up an equation:

$30 + ($5 + $10)  imes x = $155.75

Where x represents the number of weeks. Now, we can solve for x:

$30 + $15x = $155.75

$15x = $125.75

x = $125.75 / $15 = 8.38

Since we can't have a fraction of a week, we can round up to the nearest whole number. So, it will take approximately 9 weeks to save enough money.

To determine how many more weeks you would have to save to buy a bicycle that costs $203.89, we can again set up an equation:

$30 + ($5 + $10)  imes x = $203.89

Now, we can solve for x:

$30 + $15x = $203.89

$15x = $173.89

x = $173.89 / $15 = 11.59

Rounding up to the nearest whole number, it would take approximately 12 more weeks to save enough money.

1/2 is twice the sum of -2 and a number is the same as the number decreased by 7/2.

Given that we need to find the sum of -2 and a number is the same as the number decreased by 7/2.

Let's break down the problem and solve it step by step.

The problem states that twice the sum of -2 and a number is the same as the number decreased by 7/2.

Step 1: Assign a variable to the unknown number.

Let's say the unknown number is "x".

Step 2: Write the equation based on the given information.

Twice the sum of -2 and the unknown number is the same as the number decreased by 7/2.

This can be written as:

2(-2 + x) = x - 7/2

Step 3: Simplify the equation.

Multiply 2 by each term inside the parentheses:

-4 + 2x = x - 7/2

Step 4: Isolate the variable on one side of the equation.

To do this, we can subtract x from both sides of the equation:

-4 + 2x - x = x - 7/2 - x

Simplifying:

-4 + x = -7/2

To solve for x, we need to isolate it on one side of the equation.

We can do this by adding 4 to both sides:

-4 + 4 + x = -7/2 + 4

Simplifying:

x = 1/2

Therefore, the unknown number is 1/2.

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The value of all things required to create a good or service are called inputs or factors of production. These include resources such as labor, materials, and machinery. Other related terms include productive efficiency, utility, sunk costs and physical capital per person.

The value of all things needed to create a good or service is referred to as the inputs or factors of production. These include resources like labor, materials, and machinery. For instance, to produce a car, the inputs would include the metal for the body, the labor to assemble the car, and the machinery to manufacture parts. Physical capital per person refers to the machinery and equipment available to help a person produce a good or service. The concept of productive efficiency comes in when it is impossible to produce more of one good without decreasing the quantity produced of another good. Utility represents the satisfaction, usefulness, or value one obtains from consuming goods and services. Sunk costs are costs that have been incurred in the past and cannot be recovered.

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The value of all things needed to create a good or service is referred to as the inputs or factors of production.

These consist of manpower, supplies, and equipment. For example, the inputs needed to construct an automobile would be labor to assemble the vehicle, machinery to make parts, and metal for the body.

The tools and machinery that can be used to assist a person in producing a good or service is referred to as physical capital per person. When it is difficult to generate more of one good without producing less of another good, the idea of productive efficiency enters the picture.

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Answer:

The correct option is B.

Step-by-step explanation:

In the given diagram, we have 6 boxes of -x and 6 box of 1 on the left hand side. It means,

[tex]LHS=6(-x)+6(1)=-6x+6[/tex]

We have 2 boxes of x and 9 box of -1 on the right hand side. It means,

[tex]RHS=2(x)+9(-1)=2x-9[/tex]

So, the equation represented by the given diagram is

[tex]-6x+6=2x-9[/tex]

[tex]-6x-2x=-9-6[/tex]

[tex]-8x=-15[/tex]

Dived both sides by -8.

[tex]x=\frac{-15}{-8}[/tex]

[tex]x=\frac{15}{8}[/tex]

The value of x is [tex]\frac{15}{8}[/tex]

Therefore the correct option is B.

divide:

8/40 = 0.2

0.2 = 20%