an ice cube is freesinf in such a way thag ghe side length s,in inches, is s(t)=1/2t+2 where t is in hours. The surface area of the ice cube is the function A(s)=6s^2. Part A: Write an equstion that gives the volume at t hours after freezing begins. Part B: Find the surface area as the function kf time, using composition, and determjne its range.Part C: After how many hours will the surface area equak 216 squRs inches? Show all neccesady calculations.

Answer: can you translate this in English?

Step-by-step explanation: I don’t understand Spanish yet, I apologize.

Answer:

1 Stage: 280 Meters

2 Stages: 220 Meters

4 Stages: 100 Meters

It will take about 5 2/3 stages to reach the surface level.

Answer:

The marginal​ profit is \(\frac{1000(100-x^{2})}{(x^{2}+100)^{2}}\).

Step-by-step explanation:

The profit function p (x) is the difference between the revenue and cost function.

The profit function is given as follows:

\(p (x) = \frac{1000x}{100+x^{2}}\)

Determine the marginal profit function as follows:

\(\text{Marginal Profit}=\frac{\text{d}}{\text{dx}} p (x)\)

                        \(={\tfrac{\mathrm{d}}{\mathrm{d}x}\left[\dfrac{1000x}{x^2+100}\right]}}\\\\={1000\cdot{\tfrac{\mathrm{d}}{\mathrm{d}x}\left[\dfrac{x}{x^2+100}\right]}}}}\\\\\)

                        \(=1000\cdot\frac{\frac{\text{d}}{\text{dx}}(x)\cdot (x^{2}+100)+x\cdot \frac{\text{d}}{\text{dx}} (x^{2}+100)}{ (x^{2}+100)^{2}}\\\\=\frac{1000(x^{2}-2x^{2}+100)}{(x^{2}+100)^{2}}\\\\=\frac{1000(100-x^{2})}{(x^{2}+100)^{2}}\)

Thus, the marginal​ profit is \(\frac{1000(100-x^{2})}{(x^{2}+100)^{2}}\).

Put 1

\(\\ \rm\Rrightarrow \left(\dfrac{3^{1+1}}{3(1)+1}\right)\)

\(\\ \rm\Rrightarrow 3^2/4=9/4=2.2\)

Put 2

\(\\ \rm\Rrightarrow \left(\dfrac{3^{2+1}}{3(2)+1}\right)=3^3/7=27/7=3.8\)

R is

Its greater than 1 .

Answer:

\(r=\dfrac{12}{7}\)

series diverges

Step-by-step explanation:

To find the common ratio (r) of a geometric series, divide the (n+1)th term by the nth term.

When n = 1:

\(a_1=\dfrac{3^{1+1}}{3(1)+1}=\dfrac{3^2}{4}=\dfrac94\)

When n =2:

\(a_2=\dfrac{3^{2+1}}{3(2)+1}=\dfrac{3^3}{7}=\dfrac{27}{7}\)

Therefore,

\(r=\dfrac{a_2}{a_1}=\dfrac{\frac{27}{7}}{\frac{9}{4}}=\dfrac{12}{7}\)

A series that converges has a finite limit.  If |r| < 1, then the series will converge.

A series that diverges means either the partial sums have no limit or approach infinity.  If |r| > 1 then the series diverges.

Therefore, as the limit of the series approaches infinity and it's r value is greater than 1, the series diverges.

Answer:

101.6cm²

Step-by-step explanation:

1 inch = 2.54cm

that means:

40in² × 2.54 = 101.6cm²

Answer: \(35x < 4-5x+3x^2\) is \(x < \frac{1}{3}\) or \(x > \frac{4}{3}\)

Step-by-step explanation:

A) To generate the table of values, we can substitute different values of x into the equation and solve for y.

x             y

-2        26

-1        12

0         4

1         2

2        10

To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.

c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.

To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.

To determine the range of values of x for which 35x​<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.

When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.

When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.

Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer:

1. Send me the chart and ill get you the answer.

2. unit cost is $0.30

Step-by-step explanation:

Answer: 59.96 meters

Step-by-step explanation:

Let's use the formula for the area of a rectangle to find the width:

Area = length x width

224.7 = 15 x width

width = 224.7 / 15

width ≈ 14.98 m

Now that we know the length and width of the rectangle, we can use the formula for the perimeter of a rectangle to find the perimeter:

Perimeter = 2 x (length + width)

Perimeter = 2 x (15 + 14.98)

Perimeter ≈ 59.96 m

Therefore, the perimeter of the rectangle is approximately 59.96 meters.

Step-by-step explanation:

If you check by inspection there are two sides which are equal. The triangle is considered an Isosceles Triangles where two sides amd angles are equal.

The two base angles are equal=x°

38°+x°+x°=180°

2(x°)=180°-38°

2x°=142°

x=71°

The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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This problem would equal 80

Answer:

Doesn't look like a geometric sequence.

Step-by-step explanation:

If 1, -4, 16 keeps repeating then the answer is 16.

Answer:

\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)

\(7 = - \frac{8}{3} ( - 3) + b\)

\(7 = 8 + b\)

\(b = - 1\)

\(y = - \frac{8}{3} x - 1\)

The y-intercept is -1.

Part A)

As for branch A, notice the following pattern

Therefore, the equation that models branch A is

Whereas, as for branch B

which is a linear equation.

Thus, the answer to part A is

Branch A is an exponential function; Branch B is a linear equation, option 2.

coefficient of 5r² is 5

hope it helps...!!!

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.

Answer:

3x

Step-by-step explanation:

If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.

Answer:

c

Step-by-step explanation:

(-1)x5= -5

-5+6=1

Answer:

The answer is C.

Step-by-step explanation:

Answer:

(1,4)

Step-by-step explanation:

Hope it is helpful...

Answer:

12 ÷ 3 = 24 ÷ 6

Step-by-step explanation:

12/3 = 4 and 24/6 = 4

So 4 = 4

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

The product of z and w is 76(cos(3pi/16)+isin(5pi/16)). This can also be written in rectangular form as 71.02 + 39.47i, where the magnitude is approximately 81.34 and the angle is approximately 29.3 degrees.

To find the product of z and w, we simply multiply the two complex numbers. We start by multiplying the real parts and imaginary parts separately, then combine them.

(zw) = 38(cos(pi/8)+isin(pi/8)) * 2(cos(pi/16)+isin(pi/16))
= 76(cos(pi/8+pi/16)+isin(pi/8+pi/16))
= 76(cos(3pi/16)+isin(5pi/16))

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Answer:

132 square feet

Step-by-step explanation:

The formula for the area of a triangle is 1/2 * b * h. B stands for base and h stands for height. 1/2 multiplied by the base, 10, is 5. We then multiply 5 by 12 which is 60. Let's look at the rectangle now. The area of a rectangle is length by width. The length is 12ft and the width is 6ft. 12 * 6 = 72. 72+60=132 square feet.

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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Answer:

Step-by-step explanation:

The problem bothers on the dimension of a scaled drawing/prototype

The indications on the blueprint actually represent the scale

 that is 1 inch: 3.5 feet

Given that a wall is 6 inches on the blueprint, now, in reality, the  actual    

 length will be 3.5*6= 21 feet

Usually, the scale is given as a ratio. A drawing, which has been reduced or enlarged or a drawing whose dimensions have been changed to a particular size other than its previous or initial size is a scaled drawing.

Answer:

\(20x+240y/y\)

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.

Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.

The slope formula exists \($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\), or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize \($x_{1}\)and \($y_{1}\). The coordinates of the second points exist \($x_{2} , y_{2} .\)

The slope of the line exists the ratio of the rise to the run, or rise separated by the run.

\($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\)

The Line, AB contains points A (8, −4) and B (1, −5).

Substitute the value of points in the equation then we get

\($m = (y_{2} -y_{1})/(x_{2} - x_{1} )\)

m = (-5-(-4))/(1 - 8)

Simplifying the above equation, we get

m = (-5+4)/(1 - 8)

m = (-1)/(-7)

m = 1/7

Therefore, the slope of line AB exists 1/7.

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Answer: D

I believe :0

The table which represents a linear function is table 4.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

The tables in the question

Now,

The table that represents a linear function is:

X   Y

1   3

2   7

3   11

4   15

The reason this is a linear function is that for each increase in the input value of X by 1, the output value of Y increases by a constant amount of 4. In other words, the rate of change of Y with respect to X is constant at 4, indicating a linear relationship between the two variables.

Therefore, the answer of the function will be table 4.

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