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2 years ago

NEED HELP ASAP! Find the area of the shaded region. All angles are right angles.

Mathematics

1 answer:

zhenek [66]2 years ago

6 0

Answer:

166 m^2

Step-by-step explanation:

The enclosing rectangle is 9m by 29m, so is 261 m^2. From that, the white space of 5m by 19m = 95 m^2 must be subtracted. The result is that the shaded area is ...

261 m^2 -95 m^2 = 166 m^2

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poizon [28]

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2 years ago

A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t

frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y

since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

$\mathbf{L = 3x - 2( \dfrac{1000000}{x})}$

$\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}$

$\mathbf{ x^2= \dfrac{2000000}{3} }$

$\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }$

$\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}$

Now, if we replace the value with equation (1), then y will be:

$\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}$

$\mathbf{x =500\sqrt{6}}$

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

$\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}$

$\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}$

$\mathbf{L =2000 \sqrt{6} }$

$\mathbf{L \simeq 4899 \ ft}$

Learn more about the area of a rectangle here:

brainly.com/question/25292087

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1 year ago

If a rectangular prism has a length, width, and height of 3/8 centimeter, 5/8 centimeter, and 7/8 centimeter, respectively , the

sveticcg [70]

Answer:

<h3>The volume of the prism is cubic $\frac{105}{512}$ centimeters.</h3><h3>Step-by-step explanation:</h3><h3>Given that a rectangular prism has the following dimensions:</h3><h3> $length, l=\frac{3}{8}cm \\\\width, w=\frac{5}{8}cm \\\\height, h=\frac{7}{8}$ </h3><h3>We know that a rectangular prism of length 'l', width 'w' and height 'h' is given by</h3><h3> $V=w*h *l.$ </h3><h3>Therefore, the volume of the given prism will be</h3><h3> $V\\\\=w*h*l\\\\=\frac{3}{8}*\frac{5}{8}*\frac{7}{8} \\\\=\frac{105}{512}cm^{3}.$ </h3><h3>Thus, the volume of the prism is $\frac{105}{512}$ cubic centimetres.</h3>

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3 years ago

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2 years ago

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scoundrel [369]

To find V(6), we must plug in the number 6 for r in the equation.

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V(6) = 9*pi*(6)^2

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3 years ago