Find the circumference and area of a circle with a diameter of 22 inches. Leave your answers in terms of pi. (4 points) C = 11π; A = 44π C = 22π; A = 44π C = 11π; A = 121π C = 22π; A = 121π

Answer:

Step-by-step explanation:

Hello,

[tex]x^6-6x^3y+9y^2\\\\=(x^3)^2-2\cdot x^3\cdot 3y+(3y)^2\\\\=(x^3-3y)^2[/tex]

So the correct answer is

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

Do not hesitate if you have any question

Answer:

The answer is given below

Step-by-step explanation:

Let us assume the truck accelerates for 4 seconds.

Given that:

Initial velocity (u) = 0 (starts from rest),

acceleration (a) = 4 m/s²

time (t) = 4 s

Final velocity (v) = ?,

Distance (s) = ?

To calculate the final velocity, we use the formula:

v = u + at

Substituting values gives:

v = 0 + 4(4)

v = 0 + 16

v = 16 m/s

The final velocity is 16 m/s²

To calculate the distance traveled by the truck, we use the equation:

[tex]s=ut+\frac{1}{2}at^2\\ Substituting\ values\ into\ the\ equation:\\s=0(4)+\frac{1}{2}(4)(4)^2\\s=0+2(16)\\s=0+32\\s = 32\ meters[/tex]

The distance traveled by the truck during the time interval is 32 meters

Answer:

1:15 pm

Step-by-step explanation:

It takes 6 hours to reach London from Minneapolis and she reached Minneapolis at 7:15pm so

7:15 - 6 = 1:15

Answer:

x=larger no

y= smaller no

Step-by-step explanation:

x+y=7--------(1)

x=16 + 2y------(2)

(2)--->(1)

16+2y+y = 7

3y + 16 = 7

3y = -9

y = -3//

so x=10

Answer:

x=larger no

y= smaller no

Step-by-step explanation:

x+y=7--------(1)

x=16 + 2y------(2)

(2)--->(1)

16+2y+y = 7

3y + 16 = 7

3y = -9

y = -3//

so x=10

Answer:

64.7%

Step-by-step explanation:

To solve this problem we use compounded interest formula.

[tex]a = p(1 + (r \div n))^{nt} [/tex]

a = amount

p = principle

r = interest rate

n = number of times compounded in a period

t = time period

[tex]a = 1000(1 + (.05 \div 12)^{12 \times 10} [/tex]

a = 1647.01

1647.01-1000 = 647.01

647.01/1000 = 0.64701

0.64701*100% = 64.7%

Answer:

60°

Step-by-step explanation:

30° + 90° = 120°

180° - 120° = 60°

180 is the sum of interior angels

i think it might be linear function

Answer:

[tex]\large \boxed{\sf \ \ \pi r^2 \ \ }[/tex]

Step-by-step explanation:

Hello,

We will follow the instructions and then we need first to find the area of any regular n-gon.

I attached one graph so that it is easier to understand.

The n-gon can be divided in n similar isosceles triangles.

So we can find the area of one of these triangles and then multiply by n to get the total area, right?

Let's focus on the triangle OAB then. OA = OB = r, right?

The area of this triangle is the (altitude * AB ) / 2

The angle AOB is [tex]\dfrac{2\pi}{n}[/tex] by construction of the regular n-gon.

So half this angle is [tex]\dfrac{\pi}{n}[/tex] and we can use cosine rule to come up with the altitude:

   [tex]\boxed{ altitude = r\cdot cos(\dfrac{\pi}{n}) }[/tex]

Using the sine rule we can write that

   [tex]\boxed{ AB=2r\cdot sin{\dfrac{\pi}{n}} }[/tex]

So, the area of the triangle is

   [tex]\dfrac{1}{2}\cdot r\cdot cos(\dfrac{\pi}{n}) } \cdot 2r\cdot sin(\dfrac{\pi}{n})\\\\=r^2\cdot cos(\dfrac{\pi}{n})\cdot sin(\dfrac{\pi}{n})[/tex]

Ok, but wait, we know how to simplify. We can use that

[tex]sin(2\theta)=2cos(\theta)sin(\theta)[/tex]

So it gives that the area of one triangle is:

   [tex]\dfrac{1}{2}r^2sin(\frac{2\pi}{n})[/tex]

Last step, we need to multiply by n.

[tex]\large \boxed{\sf \ \ A(n)=\dfrac{1}{2}nr^2sin(\dfrac{2\pi}{n}) \ \ }[/tex]

Now, let's use a result from Calculus:

[tex]\displaystyle \lim_{x\rightarrow0} \dfrac{sin(x)}{x}=1[/tex]

How to use it here? Just notice that

[tex]\displaystyle \lim_{n\rightarrow +\infty} \dfrac{sin(\dfrac{2\pi}{n})}{\dfrac{2\pi}{n}}=1\\\\\lim_{n\rightarrow +\infty} \dfrac{n}{2\pi}sin(\dfrac{2\pi}{n})=1\\\\\lim_{n\rightarrow +\infty} nsin(\dfrac{2\pi}{n})=2\pi[/tex]

So, finally

[tex]\Large \boxed{\sf \lim_{n\rightarrow +\infty} A(n)=\dfrac{1}{2}r^22\pi=\pi r^2 }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

We khow that Mary invested 12000£ and the account pays 1.5 percent interest per year.

So we should khow what is the value of this 1.5 percent interst .

12000£⇒100 percent

x ⇒ 1.5 percent

so the value after 2 years is : 12000+360=12360

Answer:

56,735 people

Step-by-step explanation:

We can set up an equation to model this:

The equation for exponential decay is y = C(1 - r)^t, where C is the original amount, r is rate of change, and t is time.

We can plug in the corresponding values and solve:

y = 62500(1 - 0.016)^6

y = 62500(0.984)^6

y = (62500)(0.9077)

y = 56,734.94, which we can round to 56,735 people

Answer:

Step-by-step explanation:

Given that:

The demand for number 6 screws is fairly constant and  brother's hardware store sells 500 of these screws each day.

So;

The demand for number 6 screws =  500 screws /day

It takes approximately 8 working days for an order of number 6 screws to arrive once the order has been placed.

Delivery time-frame  = 8 days

Lila believes that she can avoid stockouts completely if she only orders the number 6 screws at the correct time.

i.e Lila would want to have 8 days (delivery time-frame) × 500 screws /day

= 4000 screws

This implies that these 4000 screws will only last for 6 days.

Thus Lila ROP ( reorder point) will be to reorder for another set of  screw the day she receives the current shipment, this implies that after 8 days she would have sold the present 4000 screws and she will be expecting a new re-stock.

In this exercise, we have to use our knowledge of finance to calculate the number that should be replenished in the stock, in this way:

This implies that these 4000 screws will only last for 6 days.

The exercise statement states that:

With this information we can also say that:

Then, performing the calculation, we find:

[tex] 8 * 500 = 4000 screws[/tex]

See more about finances at brainly.com/question/10024737

Answer:

Step-by-step explanation:

Base of triangle  = length of the rectangle

Since, all are identical rectangles,

Length of a rectangle= 36/2 = 18 cm

Base of triangle = 18 cm

Height of triangle = length of the rectangle + width of the rectangle

Width of 6 rectangles = 36

Width of 1 rectangle = 36/ 6 = 6 cm

Height of the triangle = 18 + 6 =  24 cm

Area of the shaded triangle = [tex]\frac{1}{2}base*height[/tex]

                                              = [tex]\frac{1}{2}*18*24[/tex]

                                              = 9 * 24

                                             = 216 cm²

Answer:

(-1,0)

Step-by-step explanation:

Here, our interest lies in finding the coordinates that splits the points (-5,-8) and (2,6) in the ratio 4:3. Let the point that does the splitting be called point P

The section formula is used here and the point we are having would be;

P = (mx2 + nx1)/(m+n) , (my2 + ny1)/(m + n)

From the question;

m = 4 and n = 3

x1 = -5, y1 = -8

x2 = 2 , y2 = 6

Plugging these values in the equation above, we have;

P = [4(2) + 3(-15)](3+4), [4(6) + 3(-8)]/(3+4)

P = (8-15)/7, (24-24)/7

= -7/7, 0/7

= (-1, 0)

The coordinates of point P is (-1,0)

Answer:4.5

Step-by-step explanation:

Answer:

ANSWER A

Step-by-step explanation:

Answer:

it has a horizontal asymptote at y=O

Step-by-step explanation:

answer is A.

because A linear parent function is the equation y = x or f(x) = x.

If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.

Answer:

its c

Step-by-step explanation:

Answer:

mBC = 96°

mB = 55°

mC = 77°

mAB = 154°

Step-by-step explanation:

The angle mB inscribes the arc mAC, so we have:

[tex]mB = mAC / 2[/tex]

[tex]mB = 110 / 2 = 55\°[/tex]

The sum of internal angles of a triangle is 180°, so in the triangle ABC we have:

[tex]mA + mB + mC = 180[/tex]

[tex]48 + 55 + mC = 180[/tex]

[tex]mC = 180 - 48 - 55[/tex]

[tex]mC = 77\°[/tex]

Using again the property of inscribed angles, we have:

[tex]mAB = 2*mC = 154\°[/tex]

[tex]mBC = 2*mA = 96\°[/tex]

Answer:65.6

Step-by-step explanation:

So $0.25 per yard

16.4/$0.25=65.6

Answer:

b = 48°

a = 67°

step by step explanation

b = 48°

a = 67°

Answer:

a = 67°

b = 48°

Step-by-step explanation:

a = 180° - 132° = 48° (angles in a straight line add up to 180°)

     65° + 48° = 113°

     180° - 113° = 67° (sum of angles in a triangle add up to 180°)

b = 180° - 132° = 48° (co-interior angles add up to 180°)

I HOPE THIS HELPED, MARK ME BRAINLIEST PLEASE:)

Answer: [-12, 3, 2, -2]

Step-by-step explanation:

Multiply each corresponding integer by each other.

4 * -3 = -12

3 * 1 = 3

-1 * -2 = 2

-1 * 2 = -2

Answer:

(1)7 (2)9 (3)6

Step-by-step explanation:

[tex]\left|\begin{array}{c|cc}X&f(X)=X^2+7\\--&-----\\2&11\\3&16\\4&23\\5&32\\6&43\end{array}\right|[/tex]

(1)The average rate of change between x=2 and x=5

[tex]\dfrac{dy}{dx} =\dfrac{f(5)-f(2)}{5-2} =\dfrac{32-11}{3} =\dfrac{21}{3} =7[/tex]

(2)The average rate of change between x=3 and x=6

[tex]\dfrac{dy}{dx} =\dfrac{f(6)-f(3)}{6-3} =\dfrac{43-16}{3} =\dfrac{27}{3} =9[/tex]

(3)The average rate of change between x=2 and x=4

[tex]\dfrac{dy}{dx} =\dfrac{f(4)-f(2)}{4-2} =\dfrac{23-11}{2} =\dfrac{12}{2} =6[/tex]

Answer:

2 .   4 .  8 .  

Step-by-step explanation:

increases

Answer:

79

Step-by-step explanation:

Let the original number be x.

x/2 = 39.5

x = 39.5 × 2

x = 79

Answer:

x = 79

Step-by-step explanation:

Let the number be x

Condition:

[tex]\frac{x}{2} = 39.5[/tex]

Multiplying both sides by 2

=> x = 39.5 * 2

=> x = 79

Answer:

in order to use up all the eggs and cream, the number of quarts of each flavor that should be made is;

Creamy vanilla x = 200 quarts

Continental mocha y = 100 quarts

Step-by-step explanation:

Let x and y represent the number of quarts of Creamy Vanilla and Continental Mocha that should be made in order to use up all the eggs and cream respectively.

For Creamy Vanilla go 2 eggs and 3 cups of cream

For Continental Mocha go 1 egg and 3 cups of cream.

Total number of eggs = 500 eggs

Total number of cream cups = 900 cups.

For the eggs;

2 eggs × x + 1 egg × y = 500

2x + y = 500 .......1

For the cream cups;

3 cups × x + 3 cups × y = 900

3x + 3y = 900

Dividing through by 3

x + y = 300 .......2

Solving the simultaneous equation;

Subtracting equation 2 from 1

(2x + y) - (x+y) = 500-300

2x -x = 200

x = 200

Substituting x = 200 into equation 2;

200 + y = 300

y = 300 - 200

y = 100

Therefore, in order to use up all the eggs and cream, the number of quarts of each flavor that should be made is;

Creamy vanilla x = 200 quarts

Continental mocha y = 100 quarts

Answer:

The correct locations are;

Part to part ratio is 3 cats to 5 dogs

Whole to part ratio is 10 pets to 2 rabbits

Part to whole ratio is 5 dogs to 10 pets

Step-by-step explanation:

The given information are;

The number of cats Jim has = 3

The number of dogs Jim has = 5

The number of rabbit Jim has = 2

The total number of pets Jim has = 3 + 5 + 2 = 10 pets

Therefore;

The fraction of the pets that are cats = 3/10

The fraction of the pets that are dogs = 5/10

The fraction of the pets that are rabbits= 2/10

Therefore we have;

Part to part ratio = 3/10 cats to 5/10 dogs = 3 cats to 5 dogs

Whole to part ratio → 10 pets to 2 rabbits

Part to whole ratio → 5 dogs to 10 pets.

⭐Solución de problemas: Cada encomiendo tiene un peso de 2 kilogramos. En fracción esto representa 1/4 de la masa total.

Y

¿por qué? Usted tiene una masa total entre los 4 encomiendos de 8 kilogramos, por lo que en orden

para expresar el peso de cada uno de ellos, tenemos

la siguiente expresión: Masa total de encomiendas (kg)/Número de encomiendas (unidad)Sustituimos:

8 kg/4 s

2 kg por encomiendaOfertamos la fracción que representa cada una en el total:

kg por encomienda/total de kg

2/8 x 1/4

Answer:

The rate of the water current is 4mph

Step-by-step explanation:

Let c= the rate of the current in mph

18+c= the rate of the boat going downstream in mph

18-c= the rate of the boat going upstream in mph

t = time in hrs for both upstream and downstream trips

Going downstream:

33=(18+c)*t (1)

Going upstream

21=(18-c)*t (2)

From (1)

33=(18+c)*t

t=33/1(8+c)

Substitute t=33/(18+c) into (2)

21=(18-c)*t

21=(18-c)*33/(18+c)

Cross product

21(18+c)=33(18-c)

378+21c=594-33c

21c+33c=594-378

54c=216

Divide both sides by 54

54c/54=216/54

c=4

Therefore,

The rate of the water current is 4mph

Answer:

A) 17,000 = 1.7x10^4

B) 26,000,000 = 2.6x10^7

C) 740,000 = 7.4x10^5

Step-by-step explanation:

Answer:

1.7x10

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the table above f(-2) = 3

Hope this helps you

Answer:  x=3

Step-by-step explanation:

5x+9 =24   subtract 9 from both sides

    -9    -9

5x = 15    Divide both sides by 5

x = 3

Answer:

[tex]5x = 24 - 9 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]

Answer:

False

Step-by-step explanation:

A definition produces out of nothing a new mathematical entity. But a theorem utilizes some relation between previously defined mathematical entities.

Usually a theorem must be verified by a proof of its correctness on the basis of generally accepted statements or on the basis of previously established statements which might include other theorems.