Angles A and B together create a 90° angle. ∠A = 4x −10 and ∠B = 2x − 20. Find the angle measures (what will

yarga [219]

<em>The range is 6.25 and the interquartile range is 3.25.</em>

5 0

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

6 0

1 year ago

What is the volume of a pentagonal prism that has a base area of 5.16 cm2 and a height of 9 cm?

strojnjashka [21]

The volume of a pentagonal prism that has a base area of 5.16 cm^2 and a height of 9cm is 46.44cm^3

Have fun!

4 0

3 years ago

Read 2 more answers

1+1+13766969+736837737

never [62]

Ummmm no I can’t tell you LOL

5 0

2 years ago

For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?

lina2011 [118]

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = $\frac{d}{dt}(y)$

y' = $\frac{d}{dt}(sin(kt))\\$

y' = kcos(kt)

Now for y''

y'' = $\frac{d}{dt}(y')$

y'' = $\frac{d}{dt}(kcos(kt))$

y'' = $-k^{2}sin(kt)$

Hence, the equation y'' + 144y = becomes

$-k^{2}sin(kt)$ + $144(sin(kt))$ $= 0$

$(144 - k^{2})(sin(kt)) = 0$

$(144 - k^{2})= 0$

∴ $k^{2} = 144\\$

$k =$ ± $\sqrt{144}\\$

$k =$ ± $12$

∴ $k = +12$ or $-12$

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

7 0

3 years ago