a circle had a sector with area 33pi and central angle of 11/6pi radians
what is the area of the circle?

Answer:

Its value in 2006 would be $99, 183, 639, 920

Step-by-step explanation:

Use the compounding interest formula for this one, which looks like this in its standard form:

[tex]A(t)=P(1+r)^t[/tex]

Our P is the initial amount of $24, the r in decimal form is .06, and the time between 2006 and 1626 in years is 380.  Fitting this into our formula we get:

[tex]A(t)=24(1+.06)^{380}[/tex] or

[tex]A(t)=24(1.06)^{380}[/tex]

First raise the 1.06 to the power of 380 on your calculator and then multiply in 24.

As for the second part of the question, I'm not quite sure how it's supposed to be answered. But maybe you can figure that out according to what the unit normally asks you to do.

Answer:

342.24 units²

Step-by-step explanation:

The area of one of the 8 triangular sections of the octagon is ...

A = (1/2)r²·sin(θ) . . . . . where θ is the central angle of the section

The area of the octagon is 8 times that, so is ...

A = 8·(1/2)·11²·sin(360°/8) = 242√2

A ≈ 342.24 units²

The area of the octagon should be 342.24 units²

Since the area of 1 of the 8 triangular sections of the octagon should be.

[tex]A = (1\div 2)r^2.sin(\theta)[/tex]

Here θ represent the central angle of the section

Since

The area of the octagon is 8 times

So,

[tex]A = 8.(1/2).11^2.sin(360\div 8) \\\\= 242\sqrt2[/tex]

A ≈ 342.24 units²

learn more about the area here: https://brainly.com/question/20822399

Answer:

Option B, two line perpendicular to the same line are parallel.

Step-by-step explanation:

Since DA and CB are perpendicular to AB, they are considered parallel. This is like a transversal line.

Answer:

Definition of right angles.

Step-by-step explanation:

A rectangle is a parallelogram whose opposite sides are parallel to each other. Also, these opposite sides measure the same and all four sides create right angles. In this sense the reason would complete the proof in lines 3 and 5 is the "Definition of right angles". This is because by definition the rectangle is a parallelogram with a right angle, since it is a parallelogram, its opposite is also a right angle. The other angles, which are supplementary to the previous two, add up to 180º. And since they are opposite, they are the same, therefore each of the four is a right angle.

[tex]\angle ABC = \angle BCD = \angle CDA = \angle DAB=90^{\circ}[/tex]

Answer:

option b 5√2  

option a 20

option c 4

option d 3/4

option b 3

Step-by-step explanation:

To solve all these questions we will use trigonometry identity which says that

sinΔ = opposite / hypotenuse

1)

sin45 = 5 / KL

Kl = [tex]\frac{5}{\frac{\sqrt{2}}{2} }[/tex]

KL = 5√2  

2)

TanФ = opp / adj

Ф = Tan^-1(5/14)

Ф = 19.65

   ≈ 20

3)

sin(30) = rq / 8

rq = sin(30)(8)

rq = 4

4)

tan(Ф) = 6/8

5)

angle 3

Answer:

  x = 24

Step-by-step explanation:

The segments on either side of an angle bisector are proportional:

  (x +4)/44.8 = 35/56

  x +4 = 44.8·(35/56) = 28 . . . . multiply by 44.8

  x = 24 . . . . . subtract 4

Answer:

The value of x is 24.

Step-by-step explanation:

Given information: In ΔGHE, ED is angle bisector, EG=44.8 millimeters, GD=(x+4) millimeters, DH=35 millimeters, and EH=56 millimeters.

According to the angle bisector theorem, an angle bisector divide the opposite side into two segments that are proportional to the other two sides of the triangle.

In ΔGHE, ED is angle bisector, By using angle bisector theorem, we get

[tex]\frac{GD}{DH}=\frac{EG}{EH}[/tex]

[tex]\frac{x+4}{35}=\frac{44.8}{56}[/tex]

Multiply both the sides by 35.

[tex]x+4=\frac{44.8}{56}\times 35[/tex]

[tex]x+4=28[/tex]

Subtract 4 from both the sides.

[tex]x=28-4[/tex]

[tex]x=24[/tex]

Therefore the value of x is 24.

Answer:

11.4 million

Step-by-step explanation:

Let's define the variables i and i' to represent the number of infected bacteria initially and after 1 hour, and the variables n and n' to represent the number of non-infected bacteria initially and after 1 hour. The biologist's theory predicts ...

0.50i +0.20n = i'

0.50i +0.80n = n'

In matrix form, the equation looks like ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right] \left[\begin{array}{c}i&n\end{array}\right]=\left[\begin{array}{c}i'&n'\end{array}\right][/tex]

If i''' and n''' indicate the numbers after 3 hours, then (in millions), the numbers are ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right]^3 \left[\begin{array}{c}11&5.2\end{array}\right]=\left[\begin{array}{c}i'''&n'''\end{array}\right][/tex]

Carrying out the math, we find i''' = 4.8006 (million) and n''' = 11.3994 (million).

The population of non-infected bacteria is expected to be about 11.4 million after 3 hours.

Answer:

C

Step-by-step explanation:

When you have the radius of a circle, you find the circumference by multiplying the radius by 2PI.

The answer is C.

Answer:

AE = 3

Step-by-step explanation:

Answer:

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  slope AB = (1 -4)/(6 -p) = 3/(p -6)

The slope of BC is ...

  slope BC = (q -1)/(9 -6) = (q -1)/3

The product of these is -1, so we have ...

  (slope AB)·(slope BC) = -1 = (3/(p -6))·((q -1)/3)

Multiplying by q -1 gives ...

  -(q -1) = p -6 . . . . . . the factors of 3 in numerator and denominator cancel

  1 = p + q -6 . . . . . . add q

  7 = p + q . . . . . . . . add 6 . . . . matches choice D

Answer:

D. p + q = 7

Step-by-step explanation:

Just did this quiz on edmentum :P

Answer:

  y = 90°

Step-by-step explanation:

The angle y subtends an arc of 180°, so its measure is 180°/2 = 90°. (We know the arc is 180° because the end points of it are on a diameter, so it is half a circle.)

Answer: [tex]cos(\pi-x)=-cos(x)[/tex]

Step-by-step explanation:

We need to apply the following identity:

[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]

Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:

[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]

We need to remember that:

[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]

Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].

Then, you get:

[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]

[tex]cos(\pi-x)=-1cos(x)+0[/tex]

[tex]cos(\pi-x)=-cos(x)[/tex]

The vertex form of the equation of a parabola is

                     f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that      (h,k) = (5,0). Hence,

                     f(x) = a( x − 5)^2 + 0

                           =a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

                        a( 7 − 5)^2 = -2

                           a(2)^2 = -2

                              4a = -2

                               a = -1/2

Thus, the given parabola has equation

                      f(x) = -1/2(x − 5)^2

Answer:

Option A. (6,2)

Step-by-step explanation:

We have the following inequality:

[tex]y- x <-3[/tex]

Solving for y we have:

[tex]y<x-3[/tex]

The line that limits the region of inequality is

[tex]y = x-3[/tex]

Then the region of inequality are all values of y that are less than [tex]f (x) = x-3[/tex]

In other words, the points belonging to the inequality are all those that lie below the line.

To find out which point belongs to this region substitute inequality and observe if it is satisfied

A. (6,2)

[tex]2<6-3[/tex]

[tex]2<3[/tex]   is satisfied

B. (2, 6)

[tex]6<2-3[/tex]

[tex]6<-1[/tex]   it is not satisfied

C. (2, -1)

[tex]-1<2-3[/tex]

[tex]-1<-1[/tex] it is not satisfied

The answer is the option A

The slope is 3

I am not that shure on the y intercept

The assumption of the inductive step is not correct. If [tex]\mathrm{max}(x,y)=2[/tex], for instance, it's entirely possible that [tex]x=1[/tex] and [tex]y=2[/tex].

Answer:

13

Step-by-step explanation:

The longest side must be less than the sum of the shorter sides:

c < a + b

c < 6 + 8

c < 14

So the largest whole number length is 13.

The Lagrangian is

[tex]L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)[/tex]

with partial derivatives (set equal to 0)

[tex]L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0[/tex]

[tex]L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0[/tex]

[tex]L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0[/tex]

[tex]L_\lambda=4x^2+4y^2-z^2=0[/tex]

[tex]L_\mu=2x+4z-2=0\implies x+2z=1[/tex]

Case 1: If [tex]y=0[/tex], then

[tex]4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|[/tex]

Then

[tex]x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23[/tex]

[tex]\implies x=\dfrac15\text{ or }x=-\dfrac13[/tex]

So we have two critical points, [tex]\left(\dfrac15,0,\dfrac25\right)[/tex] and [tex]\left(-\dfrac13,0,\dfrac23\right)[/tex]

Case 2: If [tex]\lambda=-\dfrac14[/tex], then in the first equation we get

[tex]x(1+4\lambda)+\mu=\mu=0[/tex]

and from the third equation,

[tex]z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0[/tex]

Then

[tex]x+2z=1\implies x=1[/tex]

[tex]4x^2+4y^2-z^2=0\implies1+y^2=0[/tex]

but there are no real solutions for [tex]y[/tex], so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

[tex]f\left(\dfrac15,0,\dfrac25\right)=\dfrac15[/tex] (min)

and

[tex]f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59[/tex] (max)

This problem involves using Lagrangian multipliers to optimize a function with two constraints. The maximum and minimum points can be found by solving the Lagrange equations, which are derivatives of the function and constraints. These points can be confirmed by checking the positive or negative value of the second-order derivative.

To find the maximum and minimum values of the function ​f(x,y,z)=x²+y²+z² subject the cone z²=4x²+4y² and the plane 2x+4z=2, we use Lagrange multipliers. We have two constraint functions here, given by the cone and the plane equations.

The first step is to set up the Lagrange equations, with and as Lagrange multipliers. From w=gradientf=gradientg+gradienth, we have three equations: 2x=*8x+2, 2y=*8y+0, 2z=*4. The second step is to solve these three equations, together with the original constraints ​g(x,y,z)=​0 and ​h(x,y,z)=​0.

Solving these equations will give you specific values for x, y, and z that correspond to the maximum and minimum points. To determine if a point is a maximum or minimum, one can compute the second-order partial derivatives and organize them into the Hessian matrix.

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Answer:

0.74 m

Step-by-step explanation:

The distance around a circle on the other hand is called the circumference (c).

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d) .

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula:

C=π⋅d

or

C=2π⋅r

Given r = 119.3 mm

So, C = 2 * 3.14 * 119.3 = 749.2 mm = 0.74 m

Answer:

(1,2) is the only solution to the given linear equation

Step-by-step explanation:

To see whether an ordered pair is a solution to an equation, the easiest thing to do would be to plug the pair into the equation and see if it equals the right hand side.

(1,2):

[tex]4*x+7*y=18\\4*(1)+7*(2)=18\\\therefore (1,2) \text{ is a solution}[/tex]

(8,0):

[tex]4*(8)+7*(0)=32\\\therefore (8,0) \text{ is not a solution}[/tex]

(0, -2):

[tex]4*(0)+7*(-2)=-14\\\therefore (0,-2) \text{ is not a solution}[/tex]

The pair (1,2) is a solution to the linear equation 4x+7y=18. However, the pairs (8,0) and (0,-2) are not solutions because they do not satisfy the equation.

a. To determine if the ordered pair (1, 2) is a solution to the linear equation 4x + 7y = 18, we substitute the values of x and y into the equation: 4(1) + 7(2) = 18. This simplifies to 4 + 14 = 18, which is true. Therefore, (1, 2) is a solution to the given linear equation.

b. To determine if the ordered pair (8, 0) is a solution, we substitute the values of x and y into the equation: 4(8) + 7(0) = 18. This simplifies to 32 + 0 = 18, which is false. Therefore, (8, 0) is not a solution to the given linear equation.

c. To determine if the ordered pair (0, -2) is a solution, we substitute the values of x and y into the equation: 4(0) + 7(-2) = 18. This simplifies to 0 - 14 = 18, which is false. Therefore, (0, -2) is not a solution to the given linear equation.

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The complete question is here:

Determine whether each ordered pair is a solution of the given linear equation.

4 x+7 y=18 ;(1,2),(8,0),(0,-2)

a. Is (1,2) a solution to the given linear equation?

No

Yes

b. Is $(8,0)$ a solution to the given linear equation?

Yes

No

c. Is (0,-2) a solution to the given linear equation?

No

Yes

Answer:

a. $295

Step-by-step explanation:

Add the net pay and the interest. This is the total net income.

Then add all other amounts separately. These are the expenses.

Subtract the expenses from the total net income.

The answer is a. $295

Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.

It is given that:

Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet shown in the picture.

From the spreadsheet:

Add the interest to the net pay. The overall net income is shown here.

= 2300 + 200

= $2320

Next, add each additional sum separately. The costs are as follows.

= 800+120+90+45+95+80+275+520

= $2025

From the entire net income, deduct the costs.

= 2320 - 2025

= $295

Thus, Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

Learn more about the expenses here:

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Answer:

(8,0)

Step-by-step explanation:

The equation that models the path traced by the ball is

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

To find the point at which the ball hit the ground, we must equate the function to zero.

[tex]-8x^2+64x=0[/tex]

Factor;

[tex]-8x(x-8)=0[/tex]

[tex]-8x=0,(x-8)=0[/tex]

This implies that;

x=0,x=8,

At x=0, the ball was not yet kicked.

So we take x=8, to be the time the ball hit the ground.

We substitute x=8 into the function to get;

[tex]h(8)=-8(8)^2+64(8)=0[/tex]

Hence the point at which the ball hit the ground is (8,0)

Answer:

A.  The two triangles.

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In B, they kept the same shape, but not the same side.

In C, you can see the figure has been transformed,.

A bit if not A them it’s C (sorry I tried)

Answer:

A U B = {x|x is an integer}

Step-by-step explanation:

If A={x|x is an odd integer} then:

A = 1, 3, 5, 7, 9, 11, etc.

(Negative odd integers are also included)

and B= {x|x is an even integer}  

A = 2, 4, 6, 8, 10, 12, 14, etc.

(Negative even integers are also included)

We have that a u b is going to be the set of all integer numbers. That is to say:

A U B = {x|x is an integer}

Answer:

  50 cm

Step-by-step explanation:

Consider isosceles triangle AEF in the attachment. Point B is the center of the incircle, and it divides altitude AC into segments having the ratio 12:5.

Triangle ABD is similar to triangle AEC by AA similarity. (Angle A is the same for both right triangles. Then the ratio of hypotenuse to short leg will be the same for each. In triangle ABD, that ratio is 12:5, as given by the problem statement. Since we know AE = 60 cm, also from the problem statement, we know that ...

  AB/BD = AE/EC

  12/5 = 60 cm/EC

so ...

  EC = (60 cm)·(5/12) = 25 cm

Base length EF is twice that, or 50 cm.

Let Hannah = X and Heather = Y.

The sum of their ages is 30, so you would have x + y = 30

Then Hannah's age is 4 less than 2 times Heather's age so X = 2y-4

The equations are :

X + Y = 30 and X = 2y - 4

The answer is C.

We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]h(t)=-16t^2+25t+5[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16})[/tex]

X-term: [tex]-\frac{25}{16}[/tex]

Half of the x term: [tex]-\frac{25}{32}[/tex]

After squaring: [tex](-\frac{25}{32})^2=\frac{625}{1024}[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16}+\frac{625}{1024}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{5}{16}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{945}{1024}) \\ \\[/tex]

[tex]h(t)=-16[(t-\frac{25}{32})^2-\frac{945}{1024}] \\ \\ \boxed{h(t)=-16(t-\frac{25}{32})^2-\frac{945}{64}}[/tex]

Finally, the vertex of this function is:

[tex](\frac{25}{32},\frac{945}{64})[/tex]

So in this vertex we can find the answer to this problem:

The ball will reach its maximum height at [tex]t=\frac{25}{32}s=0.78s[/tex]

The ball maximum height is [tex]H=\frac{945}{64}=14.76ft[/tex]

Also we will use completing squares. We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]R(p)=-5p^2+1230p[/tex]

[tex]R(p)=-5(p^2-246p)[/tex]

X-term: [tex]-246[/tex]

Half of the x term: [tex]-123[/tex]

After squaring: [tex](-123)^2=15129[/tex]

[tex]R(p)=-5(p^2-246p+15129-15129)[/tex]

[tex]R(p)=-5[(x-123p)^2-15129] \\ \\ R(p)=-5(x-123p)^2+75645[/tex]

Finally, the vertex of this function is:

[tex](123,75645)[/tex]

So in this vertex we can find the answer to this problem:

The price will maximize the revenue is [tex]p=123 \ dollars[/tex]

The maximum revenue is [tex]R=75645[/tex]

Answer:

Answer: Nolan took 97.75 Seconds

Step-by-step explanation:

85 x .15 = 12.75  

85 + 12.75 = 97.75

Answer:

c ≈ 4.105

Step-by-step explanation:

You want to find c in ...

cos(13°) = 4/c

Multiply the equation by c/cos(13°) and evaluate.

c = 4/cos(13°) ≈ 4.105

Answer:

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.

Step-by-step explanation:

These are the sample answers, use how you would like :)

Answer:

A.  

x + y = 28

1.68x + 2.44y = 54.64

Step-by-step explanation:

Let x = paperback books and y = hardback books

x+y =28

We know that paperbacks cost 1.68 and hardback cost 2.44

1.68x + 2.44y = 54.64

We have 2 equations and 2 unknowns

x+y =28

1.68x + 2.44y = 54.64

6.

Intersecting chords:

RT x ST = PT x TQ

2 x 6 = 3 x TQ

12 = 3TQ

TQ = 12/3

TQ = 4

7.

AD = 90 -BE = 90-18 = 72

ADE = 180. DE = 180 - AD = 180-72 = 108

AE = 180.  AB = 180-18 = 162

DE = 108

BD = BE +DE = 18 + 108 = 126

DAB = 72 +   162 = 234

ADE = 90 degrees

8.

AB^2 = BC* (BC +x)

8^2 = 2 * (2 +x)

64 = 4 + 2x

60 = 2x

X = 60/2

X = 30