Thanks for helping me out

Answer:

The rate of change of the area of the circle when the radius is 4 meters = 2 meters²/minute ⇒ answer 4

Step-by-step explanation:

* Lets revise the chain rule in the derivative

- If dy/da = m and dx/da = n, and you want to find dy/dx

∴ dy/dx = dy/da ÷ dx/da = m ÷ n = m/n

* In our problem we have

- The rate of increasing of the circumference dC/dt = 0.5 meters/minute

- We need the find the rate of change of the area of the circle

 when the radius is 4 meters

- The common element between the circumference and the area

 of the circle is the radius of the circle

* We must to find dC/dr and dA/dr and use the chain rule to

 find dA/dr

- Find the rate of change of the radius dr/dt

∵ C = 2πr

- Find the derivative of C with respect to r

∴ dC/dr = 2π ⇒ (1)

∵ dC/dt = 0.5 meters/minute ⇒ (2)

- Divide (1) by (2) to get dr/dt by using chain rule

∵ dC/dt ÷ dC/dr = 0.5 ÷ 2π

∴ dC/dt × dr/dC = 0.5 × 1/2π ⇒ cancel dC together and change

   0.5 to 1/2

∴ dr/dt = 1/2 × 1/2π = 1/4π ⇒ (3)

- Find the rate of change of the area dA/dt

∵ A = πr²

- Find the derivative of A with respect to r

∴ dA/dr = 2πr

∵ r = 4

∴ dA/dr = 2π(4) = 8π ⇒ (4)

- Multiply (4) by (3) to get dA/dt by using chain rule

∵ dA/dr × dr/dt = 8π × 1/4π ⇒ divide 8 by 4 and cancel π

∴ dA/dt = 2 meters²/minute

* The rate of change of the area of the circle when the radius is

  4 meters = 2 meters²/minute

The rate of change of the area of the circle when the radius is 4 meters is 2m²/min

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

where:

r is the radius of the circle

The rate of change of circumference is expressed as:

[tex]\frac{dC}{dt} = \frac{dC}{dr} \times \frac{dr}{dt} \\0.5=2 \pi \times \frac{dr}{dt}\\ \frac{dr}{dt} = \frac{0.5}{2\pi} \\ \frac{dr}{dt} = 0.0796 m/min[/tex]

The change in area of the circle is expressed as:

[tex]\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}\\ \frac{dA}{dt} =2 \pi r\times 0.0796\\ \frac{dA}{dt} = 2(3.14)(4)\times 0.0796\\ \frac{dA}{dt} = 2m^2/min\\[/tex]

Hence the rate of change of the area of the circle when the radius is 4 meters is 2m²/min

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Answer:

[tex]y=\frac{1}{12}(x+5)^2+2[/tex]

Step-by-step explanation:

We start with the standard form of a parabola which is

[tex](x-h)^2=4p(y-k)[/tex]

We know h and k from the vertex, we just need to solve for p and then simplify the equation.  P, by definition, is the distance between the directrix and the vertex.  That is 3 units.  So p = 3.  Fitting that into our equation along with h and k gives us:

[tex](x+5)^2=4(3)(y-2)[/tex]

Divide both sides by 12, then add the 2 to both sides and we have our parabola!

Answer:

The parent function for a concave up parabola with its vertex at the origin is

y=a(x-h)^2+k.

+a points the parabola concave up

-a points the parabola concave down

h moves the vertex along the x axis that many times

k moves the vertex along the y axis that many times.

if you need more clarification comment on this question.

Answer:

The required functions are [tex]f(x)=x^2+3[/tex], [tex]g(x)=2x^2-3[/tex], [tex]h(x)=x^2-3[/tex] and [tex]j(x)=-2x^2-3[/tex].

Step-by-step explanation:

The vertex from of a parabola is

[tex]y=a(x-h)^2+k[/tex]

Where, (h,k) is the vertex of parabola is a is the vertical stretch factor.

If a is negative, then it is downward parabola and if a is positive then it is an upward parabola.

If |a|<1, then it is compressed vertical and if |a|>1, then it is stretched vertically.

The graph of f(x) has vertex at (0,3) and it is not stretch vertically so the value of a is 1. So, the function f(x) is defined as

[tex]f(x)=1(x-0)^2+3[/tex]

[tex]f(x)=x^2+3[/tex]

The graph of g(x) has vertex at (0,-3) and it is stretch vertically by factor 2 so the value of a is 2. So, the function g(x) is defined as

[tex]g(x)=2(x-0)^2-3[/tex]

[tex]g(x)=2x^2-3[/tex]

The graph of h(x) has vertex at (0,-3) and it is not stretch vertically so the value of a is 1. So, the function h(x) is defined as

[tex]h(x)=1(x-0)^2-3[/tex]

[tex]h(x)=x^2-3[/tex]

The graph of j(x) has vertex at (0,-3) and it is stretch vertically by factor 2 and it is downward so the value of a is -2. So, the function j(x) is defined as

[tex]j(x)=-2(x-0)^2-3[/tex]

[tex]j(x)=-2x^2-3[/tex]

Therefore the required functions are [tex]f(x)=x^2+3[/tex], [tex]g(x)=2x^2-3[/tex], [tex]h(x)=x^2-3[/tex] and [tex]j(x)=-2x^2-3[/tex].

Answer:

B. 3¹²

Step-by-step explanation:

To solve this we need to apply the following laws of exponents:

1. [tex](a^n)^m=a^{n*m}[/tex]

2. [tex]a^{-n}=\frac{1}{a^n}[/tex]

Let's apply the first law to the numerator of our fraction and the second law to the denominator. For the numerator, [tex](3^5)^2[/tex], [tex]a=3[/tex], [tex]n=5[/tex], and [tex]m=2[/tex]. For the denominator [tex]3^{-2}[/tex], [tex]a=3[/tex] and [tex]n=-2[/tex]

Replacing values

[tex]\frac{(3^5)^2}{3^{-2}} =\frac{3^{5*2}}{\frac{1}{3^2} } =\frac{3^{10}}{\frac{1}{3^2} }[/tex]

Now, remember that to divide fractions we just need to invert the order of the second fraction and multiply:

[tex]\frac{3^{10}}{\frac{1}{3^2} }=3^{10}*\frac{3^2}{1} =3^{10}*3^2[/tex]

Finally, we can use the law of exponents for multiplication to get our answer:

[tex]a^n*a^m=a^{n+m}[/tex]

[tex]3^{10}*3^2=3^{10+2}=3^{12}[/tex]

We can conclude that the correct answer is B. 3¹²

Answer:

A. 45°

Step-by-step explanation:

The smallest interior angle measure of any regular polygon is that of an equilateral triangle: 60°.

___

The corresponding exterior angle measure for interior angle x will be its supplement: 180° -x. This value must be a divisor of 360° 360° is not evenly divisible by 180°-45°=135°.

Answer:

Given the details of the study carried

out on Hospitals to study the possibility that carpers might be more likely to harbor

germs, in which air from rooms with carpet and those without carpet was pumped over a

dish of agar, and the number of bacteria colonies were counted after incubating

the dish for a fixed period of time. The response in this study is number of bacteria colonies in a dish.

Answer:

No solution

If you multiply the 1st by 4 and the second by -5

The result is

20x +40y= 20

-20x-40y= -20

When you add both equations the result is  0=0

Step-by-step explanation:

There is no solution for 5x + 10y = 5; 4x + 8y = 5 as they are parallel lines.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The given pair of equation is :

5x + 10y = 5

4x + 8y = 5

[tex]a_1[/tex] =5, [tex]b_1[/tex]=10, [tex]c_1[/tex]=5

[tex]a_2[/tex]= 4, [tex]b_2[/tex]= 8, [tex]c_2[/tex]= 5

Now, checking the different condition on two pair of equations

So, we have the satisfied condition as

[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

= [tex]\frac{5}{4} =\frac{10}{8}\neq \frac{5}{5}[/tex]

which is condition for parallel.

Thus, There is no solution

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Answer:

  -∞ ; x = 3

Step-by-step explanation:

The graph tends toward -∞ as x approaches 3 from the left. Thus there is a vertical asymptote at x=3, the value of x that makes the denominator zero.

Answer:

44.444%, (B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)

Step-by-step explanation:

We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set.  There is a 50/50 chance of having a girl or a boy, and there are three children.  For now we'll use B to represent a boy and G for a girl.  It goes as follows:

(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)

I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)

Count the total number of combinations (9).  Next, count the number that include exactly 2 girls (4).  With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy.  4/9 is in simplest form, so all you have to do is find the percentage (44.444%)

Answer:

C or .375

Step-by-step explanation:

Answer:

What i got was -1 .

Step-by-step explanation:

Answer:

B. The sum function is linear but the volume function is not

Step-by-step explanation:

We are given that f(x) and g(x) are linear. Due to this, the sum function S(x) is linear.

And we know the shape of our figure, so we just need to multiply the dimensions for V(x) but the product of three linear functions results in a cubic function, and we conclude V(x) is not linear.

Glad to answer.

Answer:

(a) y = ±(√x)/2

Step-by-step explanation:

You want to find y such that ...

x = f(y)

x = 4y^2 . . . . . . . put in the expression for f(y)

x/4 = y^2 . . . . . . .divide by 4

±√(x/4) = y . . . . . take the square root

y = ±(√y)/2 . . . . . simplify

Answer:

db / dt = kb  

this becomes b(t) = Ce^(kt)  

C = 100, the initial population  

P(1) = 420 = 100 e^(1k)  

4.2 = e^k  

ln 4.2 = k  

a) thus, b(t) = 100 e^(t ln 4.2)  

b) b(3) = 100 e^(3 ln 4.2)  

c) growth constant will still be ln 4.2 (constant percentage of populatioin)  

d) 10000 = 100 e^(t ln 4.2)  

100 = e^(t ln 4.2)  

ln 100 = t ln 4.2  

t = ln 100 / ln 4.2

Step-by-step explanation:

Answer:-

Central angle , Ф/2π , A = Ф/2 r²

The ratio is 1/3 , V = 1/3 Bh

The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Step-by-step explanation:

* Lets revise the rules of the area of the sector of a circle

- The area of the sector which has a central angle Ф° is

  (Ф°/360°) × πr², where 360° is the measure of the circle and r is

  the radius of the circle

- The area of the sector which has a central angle Ф radians is

  (1/2) r²Ф

* Lets complete the missing in the 1st picture

- The ratio of the sector's area A to the circle's area is equal to the

  ratio of the central angle to the measure of a full rotation of the circle

- A full rotation of a circle is 2π. This proportion can written as

 A/πr² = Ф/2π

- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure

 of the central angle and r is the radius of the circle

* Lets revise the rules of the volume of the prism and the volume

 of the pyramid, where they have the same base and height

- The volume of the prism = area of the base × its height

- The volume of the pyramid = 1/3 × area of the base × its height

- From them the ratio of the volume of the pyramid to the volume

 of the prism is 1/3

- The formula of the volume of the prism is V = Bh, where B is the

  area of the base and h is the height, the formula of the volume

  of the pyramid is V = 1/3 Bh

* Lets revise the standard form of the equation of a circle with

 center (h , k) and radius r

- The equation is: (x - h)² + (y - k)² = r²

∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0

∵ x² - 8x + y² - 2y - 8 = 0

- Lets equate the two equation

∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0

∵ -2h = -8 ⇒ ÷ -2

∴ h = 4

∵ -2k = -2 ⇒ ÷ -2

∴ k = 1

∵ h² + k² - r² = -8

∴ (4)² + (1)² - r² = -8

∴ 16 + 1 - r² = -8

∴ 17 - r² = -8 ⇒ subtract 17 from both sides

∴ -r² = -15 × -1

∴ r² = 25

* Substitute the values of h , k , r in the equation of the standard

 form of the circle

∴ (x - 4)² + (k - 1)² = 25

* The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Answer:

  A. Step 1: Multiply 1 × 5.

  Step 2: Multiply 2 × 3.

  Step 3: Add the two products.

Step-by-step explanation:

The total number of miles hiked will be the sum of the numbers of miles hiked each day. Each day, the number of miles hiked can be computed by multiplying time by speed:

  distance = speed × time

So, the total number of miles hiked is ...

  total miles = miles on day 1 + miles on day 2 . . . . . (sum, not a difference—eliminates choice B)

  total miles = (speed on day 1)×(time on day 1) + (speed on day 2)×(time on day 2) . . . . . (sum of products—eliminates choices C and D)

Choice A correctly describes the computation.

Answer:

Table 4

Step-by-step explanation:

Just imagine the data tables are graphs, just presented in a different form.

How do you calculate the slope in a graph?  You divide the variation of Y by the variation of X.  That's the same thing here.  Let's look at each table, and calculate the slope based on the first 2 rows of each table:

Table 1:

S = (1 - -1)/(2-6)= 2/-4 = -2, not the one we want.

Table 2:

S = (8 - 4) / (0 - 2) = 4 / -2 = -2, not the one we want.

Table 3:

S = (4 - 5)/(-4 - -2) = -1 / -2 = 1/2, not the one we want.

Table 4:

S = (0 - 4)/(-2 - 0) = -4 / -2 = 2. Yes!  That's the one!

Answer:

Table 4

Step-by-step explanation:

Table 4 has a slope of 2.

(12 - 4)/(4 - 0) = 2

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-\frac{1}{50}}{ h},\stackrel{\frac{1}{3}}{ k})\qquad \qquad radius=\stackrel{\frac{1}{2}}{ r} \\\\\\ \left[ x-\left( -\frac{1}{50} \right) \right]^2+\left[ y-\frac{1}{3} \right]^2=\left( \frac{1}{2} \right)^2\implies \left( x+\frac{1}{50} \right)^2+\left( y-\frac{1}{3} \right)^2=\frac{1^2}{2^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( x+\frac{1}{50} \right)^2+\left( y-\frac{1}{3} \right)^2=\frac{1}{4}~\hfill[/tex]

Answer:

  B.  C(x) = 0.02(x - 360)2 + 300

Step-by-step explanation:

The minimum of a quadratic function is found at its vertex. The vertex form of the equation lets you read the coordinates of the vertex directly, so that is the form most helpful for finding minimum cost.

___

Perhaps the next most helpful form is that of option D, sometimes called "intercept form." The vertex is located halfway between the intercepts, so will be halfway between 0 and 720. Of course, the vertex location at 360 is read directly from the vertex form of option B.

Answer:

A

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  x^2 (not x2).

To determine the number of t-shirts that would minimize cost, we'd want to have a quadratic function graph that opens up, and to determine the vertex (which point would also be the minimum cost).

Equation A is the one we want.  Why?  because we can ignore the coefficient 0.02 in determining the minimum cost.  We see immediately that the coefficient of the x^2 term is a = 1 and that of the x term is b = -720.

Recall that the axis of symmetry passes through the vertex / minimum, and has equation

                                                                        720

x = -b / (2a).  With a = 1 and b = -720,   x = - --------- = 360

                                                                           2

Again, A is the correct answer.  The miminim cost occurs at x = 360 (shirts).

The answer is watt. :D

Answer:

[tex]V=43.35\pi[/tex] [tex]m^3[/tex]

Step-by-step explanation:

The equation for the volume of a cylinder is [tex]V=\pi r^2h[/tex]

As we know what h and r are, we can plug them into the equation to get

[tex]V=\pi (1.7)^2(15)[/tex]

This then simplifies to

[tex]V=43.35\pi[/tex] [tex]m^3[/tex]

The volume of the cylinder in terms of pi is 43.35π cm³

From the question, we are to determine the volume of the cylinder

The volume of a cylinder can be calculated by using the formula,

V = πr²h

Where V is the volume of the cylinder

r is the radius

and h is the height

From the given information,

h = 15m

r = 1.7 m

Putting the parameters into the formula, we get

V = π × 1.7² × 15

V = π × 2.89 × 15

V = 43.35π m³

Hence, the volume of the cylinder is 43.35π cm³.

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Answer:

$63.36

Step-by-step explanation:

First we need to determine how many pencils are needed

8 pencils times 96 students

8*96 =768 pencils

A dozen is 12 pencils

Divide the number of pencils needed by 12 to determine how many dozen pencils are needed

768/12 =64

We need 64 dozen pencils

They cost .99 per dozen

64*.99 =63.36

It will cost $63.36 for  the pencils

ANSWER

Option A

EXPLANATION

The graph of g(x) has equation:

[tex]g(x) = \sqrt[3]{ x + 2 } - 4[/tex]

The parent function is

[tex]f(x) = \sqrt[3]{x} [/tex]

To obtain the graph of g(x), we must shift f(x) 2 units to the left and 4 units down.

The graph of this function is shown in the attachment.

The correct choice is option A.

Answer:

21

Step-by-step explanation:

We are to find partial quotients of 231 ÷ 11

In other words the question asks: How many 11s are there in 231

First, there are twenty 11s in 220 i.e 20 × 11 = 220

Then, subtract 220 from 231 to get 11

Finally ask yourself: How many 11s are in eleven? Definitely its only one 11.

So there are 20 + 1 elevens in 231

Or, there are 21 elevens in 231

Answer:

15°

Step-by-step explanation:

If CB is a diameter, the arc BKAC is a semicircle and has a degree measure of 180.  If the measure of angle BCK is 20 and it is an inscribed angle, then the measure of the arc it intercepts is twice that.  So arc BK measures 40 degrees.  That means that arc KA has a measure that is found by subtracting arc AC and arc BK from 180.  180 - 40 - 110 = 30.  If that arc is 30 and the angle that intercepts it is inscribed, then the angle measure is half the measure of the arc. So the angle is 15°

Area of parallelogram(A) = base×hight

=4.7×3.3=15.51 sq. cm

Answer:

[tex]Area=15.51cm^2[/tex]

Step-by-step explanation:

The given figure is a parallelogram.

The area of a parallelogram is calculated using the formula:

[tex]Area=b\times h[/tex]

The base of the 4.7 cm.

The height is 3.3 cm.

We substitute the given values into the formula to obtain;

[tex]Area=4.7\times 3.3[/tex]

We multiply out to obtain;

[tex]Area=15.51cm^2[/tex]

let's say is "x", so "x" is then 100% of the whole bill.

we know 15% is 22.05, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 22.05&15\\ x&100 \end{array}\implies \cfrac{22.05}{x}=\cfrac{15}{100}\implies 2205=15x \\\\\\ \cfrac{2205}{15}=x\implies 147=x[/tex]

Answer:

$147

Step-by-step explanation:

15% over 100 is .15

So you get .15x= 22.05

Get x by itself by dividing .15 by .15

whatever you do to one side you have to do to the other so divide 22.05 by .15 and you get $147

8 squared=(x+12)x

8 squared = x squared + 12x

52 = x squared

So x= the square root of 52

Answer:

  4.9 cm

Step-by-step explanation:

The original can has a volume of ...

  V = πr²h = π(6 cm)²(10 cm) = 360π cm³

The new can will have the same volume, but a different height:

  360π cm³ = πr²(15 cm)

  24 cm² = r² . . . . . divide by 15π cm

  r = √24 cm ≈ 4.9 cm . . . . . take the square root

The new radius must be about 4.9 cm.

Answer:

the anwser is 4.9

Step-by-step explanation:

Answer:

  The 6% simple interest account earns more interest in 2 years.

Step-by-step explanation:

You can compare the multipliers in the interest formulas.

For simple interest, the amount in the account (A) starting with principal P and earning at rate r for t years will be ...

  A = P(1 +rt)

For the values given, r=.06 and t=2, the multiplier is ...

  1 +rt = 1 +.06·2 = 1.12

__

For interest compounded annually, the amount will be ...

  A = P(1 +r)^t

For the given values, the multiplier is ...

  (1+r)^t = (1.04)^2 = 1.0816

__

Since 1.12 > 1.0816, the account earning simple interest will earn more interest.

The line integral you need to compute is

[tex]\displaystyle\int_C\langle2xy^2,4x^3+y\rangle\cdot\mathrm d\vec r[/tex]

By Green's theorem, this is equivalent to the double integral,

[tex]\displaystyle\iint_D\left(\frac{\partial(4x^3+y)}{\partial x}-\frac{\partial(2xy^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_D(12x^2-4xy)\,\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the region with boundary [tex]C[/tex]. This integral is equal to

[tex]\displaystyle\int_0^\pi\int_0^{\sin x}(12x^2-4xy)\,\mathrm dy\,\mathrm dx=\int_0^\pi(12x^2\sin x-2x\sin^2x)\,\mathrm dx=\boxed{\frac{23\pi^2}2-48}[/tex]