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nevsk [136]
3 years ago
9

The plans for a rectangular deck call for the width to be 10 feet less than the length. Sam wants the deck to have an overall pe

rimeter of 60 feet. What should the length of the deck be?
Mathematics
1 answer:
sergeinik [125]3 years ago
7 0

Length of deck is 40 feet

<h3><u><em>Solution:</em></u></h3>

Sam wants the deck to have an overall perimeter of 60 feet

Perimeter of rectangular deck = 60 feet

Let "L" be the length of rectangle and "W" be the width of rectangle

Given that plans for a rectangular deck call for the width to be 10 feet less than the length

Width = length - 10

W = L - 10  ------ eqn 1

<em><u>The perimeter of rectangle is given as:</u></em>

perimeter of rectangle = 2(length + width)

Substituting the known values we get,

60 = 2(L + L - 10)

60 = 2(2L - 10)

60 = 4L - 20

80 = 4L

L = 20

Thus the length of deck is 20 feet

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olya-2409 [2.1K]
The answer is 10...............
8 0
3 years ago
A fisherman leaves his home port and heads in the direction N 70 ° W. He travels d1 = 40 mi and reaches Egg Island. The next day
Gnesinka [82]

Answer:

A)82.02 mi

B) 18.7° SE

Step-by-step explanation:

From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.

A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;

a² = b² + c² - 2bc Cos A

Thus, let the distance between the home port and forrest island be x.

So,

x² = 40² + 65² - 2(40 × 65)cos 100

x² = 1600 + 4225 - (2 × 2600 × -0.1736)

x² = 6727.72

x = √6727.72

x = 82.02 mi

B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;

A/sinA = b/sinB = c/sinC

82.02/sin 100 = 40/sinθ

Cross multiply to get;

sinθ = (40 × sin 100)/82.02

sin θ = 0.4803

θ = sin^(-1) 0.4803

θ = 28.7°

From the diagram we can see that from parallel angles, 10° is part of the total angle θ.

Thus, the bearing from Forrest Island back to his home port is;

28.7 - 10 = 18.7° SE

4 0
3 years ago
Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

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3 years ago
The scale of a model train is 1 inch to 13.5 feet. One of the cars of the model train is 5 inches long. What is the length, in f
VMariaS [17]
1 inch = 13.5 feet

5 inches = 5 * 13.5 = 67.5 feet
8 0
3 years ago
The length of a rectangle is twice the with. If the perimeter of the rectangle is 60 units, find the area of the garden
Darya [45]

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60    <em>divide both sides by 6</em>

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

<h3>Answer: The area of the garden is equal 200 square units.</h3>
4 0
3 years ago
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