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3 years ago

Find the area of the shaded regions:

Mathematics

1 answer:

Crank3 years ago

6 0

First, we'll find the area of the large section, including the smaller section that is white.

Area of a circle: pi x r^2

A = pi x 7^2

A = 49pi x 120/360

A = 49/3 pi cm^2

Now, we'll find the area of the small section.

A = pi x 3^2

A = 9 pi x 120/360

A = 3pi cm^2

All that's left to do now is subtract.

49/3 pi - 3 pi

40/3 pi cm^2

(or 13 1/3 = 13.33 cm^2)

Hope this helps!

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Write an equation of a line perpendicular to

Bess [88]

Answer:

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2 years ago

a rectangular box with two sqaure opposite ends is to hold 8000 cubic inches. find the dimensions of the cheapest box if tge rec

AveGali [126]

Answer:

the dimensions of the box that minimizes the cost are 5 in x 40 in x 40 in

Step-by-step explanation:

since the box has a volume V

V= x*y*z = b=8000 in³

since y=z (square face)

V= x*y² = b=8000 in³

and the cost function is

cost = cost of the square faces * area of square faces + cost of top and bottom * top and bottom areas + cost of the rectangular sides * area of the rectangular sides

C = a* 2*y² + a* 2*x*y + 15*a* 2*x*y = 2*a* y² + 32*a*x*y

to find the optimum we can use Lagrange multipliers , then we have 3 simultaneous equations:

x*y*z = b

Cx - λ*Vx = 0 → 32*a*y - λ*y² = 0 → y*( 32*a-λ*y) = 0 → y=32*a/λ

Cy - λ*Vy = 0 → (4*a*y + 32*a*x) - λ*2*x*y = 0

4*a*32/λ + 32*a*x - λ*2*x*32*a/λ = 0

128*a² /λ + 32*a*x - 64*a*x = 0

32*a*x = 128*a² /λ

x = 4*a/λ

x*y² = b

4*a/λ * (32*a/λ)² = b

(a/λ)³ *4096 = 8000 m³

(a/λ) = ∛ ( 8000 m³/4096 ) = 5/4 in

then

x = 4*a/λ = 4*5/4 in = 5 in

y=32*a/λ = 32*5/4 in = 40 in

then the box has dimensions 5 in x 40 in x 40 in

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3 years ago

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2 years ago

Read 2 more answers

A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)

LekaFEV [45]

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

<h3>How to determine the possible outcomes?</h3>

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL