A flower garden is the shape of a circle. The circumference of the garden is 20 meters. What is the area of the garden. Use 3.14 for pie and round your answer to the nearest whole number.

Answer:

Shorter side: 210

Longer side: 420

area: 88200

Step-by-step explanation:

work below

If you haven't learned derivatives yet just use the vertex formula

Answer:

-30+10b=-22

32-22=10b

10b=10

-32+10=-22

hope it helps

Answer:

a) 12989 Ib

b) 2756.3 Ib

Step-by-step explanation:

Density of milk = 64.6 Ib/ft^3

Diameter of tank = 8 ft

radius = 4 ft

a) Calculate force exerted by milk on one end of tank when Tank is full

pressure on strip ≈ 64.6 ( 4 - yi ) i.e. surface of milk = 4

Total force = 129.2 *  [tex]\int\limits^4_4 {4-y} \sqrt{16-y^2} \, dx[/tex]

∴Force exerted  = 129.2 * Area of semicircle( radius =4 ) * radius

                        = 129.2* 8π * 4 ≈  12989 Ib

b) Force exerted when Tank is half full

pressure on strip ≈ 64.6 ( 0 - yi )  i.e. surface of milk = 0

Total force = 129.2 * [tex]\int\limits^0_4 {0-y} \sqrt{16-y^2} \, dx[/tex]

∴ Force exerted ≈ 2756.3 Ib

Hi there! g(0) means the value of g(x) at x = 0. Look at x = 0 and see which y-point makes x = 0.

See that y = 4 makes x = 0 for the graph. Thus, g(0) = 4.

Next is to find the domain and range. Domain is the set of all x-values while Range is the set of all y-values.

For domain, look at the horizontal x-axis plane and the graph. Notice how the graph infinitely goes up for both negative and positive. Since the graph is in negative and positive as well. That means the domain is all real numbers

For range, look at the vertical y-axis and the graph. Notice how when y < -2, there are no points that are part of the graph. The graph goes infinitely for range as well but there're no y-values less than -2 for the graph.

Therefore, range is y >= -2.

Answer

Answer:

[tex]h = 3.5[/tex]

[tex]w = 7[/tex]

[tex]l = 7[/tex]

Step-by-step explanation:

Given

[tex]Volume = 171.5ft^3[/tex]

Required

The dimension that requires least material

The volume is:

[tex]Volume = lwh[/tex]

Where:

[tex]l \to length[/tex]

[tex]w \to width[/tex]

[tex]h \to height[/tex]

So, we have:

[tex]171.5 = lwh[/tex]

Make l the subject

[tex]l = \frac{171.5}{wh}[/tex]

The surface area (A) of an open-top rectangular tank is:

[tex]A = lw + 2lh + 2wh[/tex]

Substitute: [tex]l = \frac{171.5}{wh}[/tex]

[tex]A = \frac{171.5}{wh} * w + 2*\frac{171.5}{wh}*h + 2wh[/tex]

[tex]A = \frac{171.5}{h} + 2*\frac{171.5}{w} + 2wh[/tex]

[tex]A = \frac{171.5}{h} + \frac{343}{w} + 2wh[/tex]

Rewrite as:

[tex]A = 171.5h^{-1} + 343w^{-1} + 2wh[/tex]

Differentiate with respect to h and w

[tex]A_h = -171.5h^{-2} +2w[/tex]

[tex]A_w = -343w^{-2} +2h[/tex]

Equate both to 0

[tex]-171.5h^{-2} +2w=0[/tex]

Make w the subject

[tex]2w = 171.5h^{-2}[/tex]

Divide by 2

[tex]w = 85.75h^{-2}[/tex]

[tex]-343w^{-2} +2h = 0[/tex]

Make h the subject

[tex]2h = 343w^{-2}[/tex]

Divide by 2

[tex]h = 171.5w^{-2}[/tex]

[tex]h = \frac{171.5}{w^2}[/tex]

Substitute [tex]w = 85.75h^{-2}[/tex] in [tex]h = \frac{171.5}{w^2}[/tex]

[tex]h = \frac{171.5}{(85.75h^{-2})^2}[/tex]

[tex]h = \frac{171.5}{85.75^2*h^{-4}}[/tex]

[tex]h = \frac{2}{85.75*h^{-4}}[/tex]

Multiply both sides by [tex]h^{-4}[/tex]

[tex]h^{-4} * h = \frac{1}{85.75*h^{-4}} * h^{-4}[/tex]

[tex]h^{-3} = \frac{2}{85.75}[/tex]

Rewrite as:

[tex]\frac{1}{h^3} = \frac{2}{85.75}[/tex]

Inverse both sides

[tex]h^3 = 85.75/2[/tex]

[tex]h^3 = 42.875[/tex]

Take cube roots

[tex]h = 3.5[/tex] ---- height

Recall that: [tex]w = 85.75h^{-2}[/tex]

[tex]w = 85.75 * 3.5^{-2}[/tex]

[tex]w = 7[/tex] --- width

Recall that: [tex]l = \frac{171.5}{wh}[/tex]

[tex]l = \frac{171.5}{3.5 * 7}[/tex]

[tex]l = 7[/tex] --- length

Answer:

5t + 3 < 30

Step-by-step explanation:

Five times a number t is 5t.

Three more just means add 3 more to your first term (in this case it's 5t).

Less than thirty means not less than or equal to 30 but just less then 30.

Answer:

See in bold

1 x 1 = 1

1 x 2 = 2

1 x 3 = 2

1 x 4 = 4

1 x 5 = 5

2 x 1  = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

2 x 5 = 10

3 x 1 = 3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12     Total 70

3 x 5 = 15

4 x 1 = 4

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16   total 125

4 x 5 = 20

5 x 1 = 5

5 x 2  = 10

5 x 3  = 15  total 175

5 x 4 = 20

5 x 5 = 25  total 220

Total = 220

Algorithm Finding 142  =  220  - 78  = 142

-78 = 6 x 13 therefore 142six = 13

Algarithm Finding X 230six = X diagonal

X diagonal list on table shows;

1 x 1 = 1

2 x2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

Total = 91

230/91 = 2.52747253  if diagonal algorithm

or 230 taken from the last 5 x 5 algorithm total = 220

1 x 6 = 6   220 + 6 = 226   x = 4+  then 1 x 6

2 x 6 = 12  = 18    220 + 18 = 38  x = 8 - then 2 x 6

as X230 = 8- 230 = 2 x 6

or X230 = 4+ 230 = 1 x 6  

Answer:

Pretty sure it's H

Step-by-step explanation:

The two parabolas intersect at (-1,0) and (0,-1)

Answer:

arc KLJ = 205°

Step-by-step explanation:

Recall: measure of arc equals measure of central angle

Therefore:

measure of arc LJ = 56°

measure of arc KL = 149°

arc LJ + arc KL = arc KLJ

Substitute

56° + 149° = arc KLJ

205 = arc KLJ

arc KLJ = 205°

Answer:

402 cm

Step-by-step explanation:

Given :

Radius = 4 cm

The Circumference of a circle :

C = 2πr

C = 2 * π * 4 = 8π

Spool is spun 16 times :

Circumference * 16

8π * 16

8 * 3.14 * 16

= 401.92

= 402 cm

Answer:

402 cm

Step-by-step explanation:

Answer:

Yellow will have the best chance because it’s more red will have the second best chance because it is the second biggest and blue you probably will never get it

Step-by-step explanation:

all the lenses inside the circle ar equal and the two chords are also equal distance from the center point so arc x would equal arc CD

X = 50 degrees

Answer:

a. Photographer A by $10

b. Photographer B by $25

Answer:

4.87 ft

Step-by-step explanation:

The height of the skylight =

The height of the blue △ - the height of the red △

Let b ft be the height of the blue △.

sin 60° = [tex]\frac{b}{25} [/tex]

b = 25 sin 60°

Let r ft be the height of the red △.

tan 40° = [tex] \frac{r}{20} [/tex]

r = 20 tan 40°

The height of the skylight

= 25 sin 60° - 20 tan 40°

= 4.87 ft (rounded to the nearest hundredth)

5d - 6 + 8 - 3d = 12

Combine like terms:

2d + 2 = 12

Subtract 2 from both sides

2d = 10

Divide both sides by 2

D = 5

Answer:

d = 5

Step-by-step explanation:

5d - 6 + 8 -3d = 12

Regroup

5d - 3d - 6 + 8 = 12

Combine like terms

2d + 2= 12

Subtract 2 from both sides

2d = 10

Divide both sides by 2

d = 5

Answer:

4x + 17 + x + 23 = 180 ( being straight line )

5x + 40 = 180

5x = 180 - 40

5x = 140

X = 140 / 5

X = 28 (answer)

Answer:

[tex]P(A|B) = 1[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}[/tex]

[tex]A = \{2,4,6,8,10,12,14\}[/tex]

[tex]P(A) = 7/15[/tex]

[tex]B = \{4,8,12\}[/tex]

[tex]P(B) = 3/15[/tex]

Required

[tex]P(A|B)[/tex]

This is calculated as:

[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

Where

[tex]A\ n\ B = \{4,8,12\}[/tex]

[tex]P(A\ n\ B) = 3/15[/tex]

So, we have:

[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

[tex]P(A|B) = \frac{3/15}{3/15}[/tex]

[tex]P(A|B) = 1[/tex]

Answer:

Mean = 18 and Mode = 10

Step-by-step explanation:

The given data is :

10,10, 18, 24,28

We can find the mean of the data,

[tex]Mean=\dfrac{\text{sum of observations}}{\text{total no of observations}}[/tex]

[tex]M=\dfrac{10+10+18+24+28}{5}\\\\=18[/tex]

Mode is the repetition of data.

Here, 10 repeats 2 times.

So, the mode is 10.

Answer:

the answer is the first one

I hope this is help full to you

Answer:

3

Step-by-step explanation:

because this is the formula of Pythagorean theorem a^2 + b^2 = c^2 so all I did was 5^2 = 25 - 4^2 = 25-16 = 9 and square root of 9 = 3 i hope this helps. :D please give brainliest

Answer:

It would be 7p, 4p + 3p, and 5p + 2p

Step-by-step explanation:

Overall there is 7 p's

4 + 3 = 7 and 5 + 2 = 7

Unless there is more information, those are the answers.

Answer:

Step-by-step explanation:

[tex]3x^2 - 2x + 4 = 0[/tex]

a = 3, b = -2, c = 4

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{2 \pm \sqrt{2^2 - (4 \times3 \times 4} )}{2 \times 3}\\\\x = \frac{2 \pm \sqrt{4 - 48} }{6}\\\\x = \frac{2 \pm \sqrt{-44} }{6}\\\\x =\frac{2 \pm 2i \sqrt{11} }{6}\\\\x =\frac{1 + i \sqrt{11} }{3}\ , x =\frac{1 - i \sqrt{11} }{3}\\\\\\\\[/tex]

r = 44

12 = r -(34-2)

12 = r -(32)

12 = r-32

r = 32+12

r = 44

Answer:

Step-by-step explanation:

(0,-3.5)

Answer:

(0, -3.5)

Step-by-step explanation:

The x coordinate is first

We stay on the y axis so the x coordinate is 0

The y coordinate is second

We go down 3 1/2 units so the y coordinate is -3 1/2

(0, -3.5)

Answer:

The answer to 12 is 40 cubic units

Step-by-step explanation: