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4 years ago

Suppose you have 40 meters of fencing what is the greatest rectangular area that you can enclose

1 answer:

8 0

It'd help if you could sketch this situation. Note that the area of a rectangle is equal to the product of its width and length: A = L W.

Consider the perimeter of this rectangular area. It's P = 2 L + 2 W. Note that P = 40 meters in this problem.

Thus, if we choose to use W as our independent variable, then P = 40 meters = 2 L + 2 W. Let's express L in terms of W. Divide both sides of the following equation by 2: 40 = 2 L + 2 W. We get 20 = L + W. Thus, L = 20 - w.

Then the area of the rectangle is A = ( 20 - W)*W.

Multiply this out. Your result will be a quadratic equation. Graph this quadratic equation (in other words, graph the function that represents the area of the rectangle). For which W value is the area at its maximum?

Alternatively, find the vertex of this graph: remember that the x- (or W-) coordinate of the vertex is given by

W = -b/(2a), where a is the coefficient of W^2 an b is the coefficient of W in your quadratic equation.

Finally, substitute this value of W into your quadratic equation, to calculate the maximum area.

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26. Law of sines, please give a step by step explanation

Stels [109]

Answer:

174.6 ft

Step-by-step explanation:

It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)

We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...

180° -30° -112° = 38°

Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.

c/sin(C) = a/sin(A)

c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft

The height of the tree is about 174.6 feet.

5 0

3 years ago

Solve for x to the nearest 10th. 410 = 1080(0.915)^x

Hunter-Best [27]

Answer:

410/1080=(0.915)^x

0.379=(0.915)^x

ln0. 379/ln0.915=x

X=10.903

4 0

3 years ago

10+5-7=3y -10x+5x+5=-15 3x+2x-4x+10 pre algebra 8th grade math

jasenka [17]

Answer:

1) y=8/3=2 2/3 2) x=4 3) x+10

Step-by-step explanation:

1) 10+5-7=3y

Calculate the sum or difference.

8=3y

Swap the sides of the equation.

3y=8

Divide both sides by 3.

y=8/3=2 2/3

2) -10x+5x+5=-15

Collect like terms.

-5x+5=-15

Move the constant to the right-hand side and change the sign.

-5x=-15-5

Calculate the difference.

-5x=-20

Divide both sides by -5.

x=4

3) 3x+2x-4x+10

Collect like terms.

(3+2-4)x+10

Calculate the sum or difference.

1x+10

When the term has a coefficient of 1, it doesn't have to be written.

x+10

Hope this helps :)

5 0

3 years ago

Please help me I don't understand!

Kobotan [32]

#3) since angle ABC is 115 degrees, to find EBC you simply have to subtract 115 from 90 and the answer is 25 degrees.
#4)DGJ would be 30 degrees because you take 70 minus 40.
#5) a 90 degree angle.

6 0

4 years ago

Read 2 more answers

two buildings stand 90 ft apart at their closest points, the angle of depression from the top of the taller building to the top

noname [10]

A new kind of temporary pavilion support for a square roof uses just two poles set at the diagonal corners of a square. The allowable distance between the poles is 18 feet. Find the area of the roof. The sides will have lengths of 18/sqrt(2). Since they are perpendicular, the area of the square will be (18^2)/2 = 81*4/2 = 162 square feet.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

8 0

3 years ago