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The rate of change of volume with respect to time at t=2 minutes is 240π cm³/min.

At t=0, the radius of the sphere is r=1. At t=2 minutes, the radius will be r=2. The volume of a sphere is V=4/3πr³, so the volume of the sphere at t=2 minutes will be V=4/3π(2)³=33.5π.

The rate of change of volume with respect to time (dV/dt) can be calculated by taking the derivative of the volume equation with respect to time.

dV/dt = 4πr²dr/dt

At t=2 minutes, r=2 and dr/dt=30 cm/min.

dV/dt = 4π(2)²(30 cm/min)

    = 240π cm³/min

Therefore, the rate of change of volume with respect to time at t=2 minutes is 240π cm³/min.

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Answer:

150

Step-by-step explanation:

srry if incorrect but thats what i got

Answer:

Step-by-step explanation:

For the midpoint of AB

\(x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{1+3}{2} ,y=\frac{4+0}{2} \\\\x=2,y=2\)

Hence, co-ordinate of D is D(2,2)

For the midpoint of AC

\(x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{1-3}{2} ,y=\frac{4-2}{2} \\\\x=-1,y=2\)

Hence coordinate of E is E(-1,2)

Now find the slope of DE and BC if they are equal they are parallel.

Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Choice D is correct

Every point on circle is equidistant from the point at its centre and that fixed distance = radius of that circle.

Answer:

[-0.2  0.4]

[0.8   -0.6]

Answer:

B

Step-by-step explanation:

There are several ways to find the vertex of function such as formula, completing the square or differential.

I will use the formula to find the vertex.

We are given the function:

\( \displaystyle \large{f(x) = - {x}^{2} + 4x - 3}\)

Vertex Formula

Let (h,k) = vertex

\( \displaystyle \large{ \begin{cases} h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} \end{cases}}\)

From the function, compare the coefficients:

\( \displaystyle \large{a {x}^{2} + bx + c = - {x}^{2} + 4x - 3}\)

Therefore:-

\( \displaystyle \large{ \begin{cases} h = - \frac{4}{2( - 1)} \\ k = \frac{4( - 1)( - 3)- {4}^{2} }{4( - 1)} \end{cases}}\)

Then evaluate for h-value and k-value.

\( \displaystyle \large{ \begin{cases} h = - \frac{4}{ - 2} \\ k = \frac{4( 3)- 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{12 - 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{ - 4}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2\\ k = 1\end{cases}}\)

Therefore the vertex is (h,k) = (2,1)

Answer:

B (2.1)

Step-by-step explanation:

it was on a test i got it right

The required value of the F in the matrix is given as -8. Option B is correct.

Given that,
A system of equations is given, convert the equation into matrix form, and determine the corresponding value of the F.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
-2x + 5y -3z = -25
-4x - 3y - 8z = -39
6x + 8y - 5z = 14

Converting the above system of equations in the matrix form,
\(\left[\begin{array}{ccc}-2&5&-3\\-4&-3&-8\\6&8&-5\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-25\\-39\\14\end{array}\right]\)
Now compare the above matrix with the given matrix, where F = -8

Thus, the required value of the F in the matrix is given as -8. Option B is correct.

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The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings

Number of servings = Total tofu Stephen has ÷ Tofu per serving

= 1/10 ÷ 2/25

= 1/10 × 25/2

= (1×25) / (10 × 2)

= 25/20

= 5/4 servings

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The answer: 8221 - 2974 = 5274

Answer:

3.5x larger

Step-by-step explanation:

All you do is 7 divided by 2 for an easy answer.

Answer:

\(a \: is \: 3.5times \: larger \: than \: b.....\)

Answer: Width of rectangle = 7 meters

Length of rectangle 7-1=6 meters

Step-by-step explanation: Let w (meters) be the width of the rectangle, then (w-1) (meters ) will be its length.

Now, we know that the area of rectangle is given by :-

Therefore, for the given rectangle , the area of rectangle will be

L = W -1

L * W = 42

L = 42 / W

substituting this into A

42 / W = W -1

Multiplying both sides by "W"

42 = W^2 -W

W^2 -W - 42 = 0

W = 7

Length = 6

Hence, the width of rectangle = 7 meters

Length of rectangle 7-1=6 meters

Answer:

Length : 5 meters
Width : 6 meters

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Answer:

geometric, with a common ratio of 1/2

Step-by-step explanation:

The sequence is geometric because you get successive trems by multiplying the previous term by a certain constant, the 'common ratio'. (If you got each successive term by adding or subtracting  the same constant number each time, that would be an arithmetic sequence.)

In this case, it looks like you get each successive term when you multiply the previous term by 1/2.

Thus, the common ratio is 1/2.

The expression that is not rational is the first one:

\(f(x) = \frac{6x}{4}\)

A rational expression is something of the form:

\(f(x) = \frac{q(x)}{p(x)}\)

Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.

This means that we need to have the variable "x" on the denominator.

Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:

\(f(x) = \frac{6x}{4}\)

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Answer: B

Step-by-step explanation:

I took the test and this was the correct answer

Part (a)

Answers:

A' = (0, 2)

B' = (-1, -2)

C' = (-3, -2)

D' = (-4, -1)

Explanation:

Multiply each coordinate by 1/3.

For instance,

\(B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)\)

====================================================

Part (b)

Answers:

A' = (-5, 5)

B' = (-8, -7)

C' = (-14, -7)

D' = (-17, -4)

Explanation:

Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.

I'll show an example using point C.

\((\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\\)

Therefore, C(-9,-6) moves to C ' (-14,-7)

Answer:GIVE A BETTER DETAILED QUESTION sorry for caps

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

You change the signs to positive and then you put 15 as numerator and then 6 as denominator which gives you 15/6. But you can also simplify it which gives you 5/2. Hope this helps!

Answer:

14

Step-by-step explanation:

so it means the opposite of negative 14 which is postive 14

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

C - 13*

Step-by-step explanation:

Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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The line PQ is altitude of the triangle. This can be obtained by understanding what an altitude is.

Properties of altitude of a triangle:

In the given triangle,

it is clear that angle Q is 90° and therefore PQ is a perpendicular line from the point P.

Since the perpendicular line, which is PQ, is drawn from the vertex, which is P  of the triangle to the opposite side, which is SR.

Thus PQ is the altitude of the triangle.

Hence in the given figure, the line PQ is the altitude of the triangle.

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Answer: The correct answer is x=-10

Step-by-step explanation:

Just took the test and saw the other persons comment<3

Answer:

Step-by-step explanation:

-25/4(x)= -25/8

x= -(25/8) X (4/-25)= 1/2

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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