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pantera1 [17]
4 years ago
10

the length of a rectangular garden is 3 m greater than the width. The area of the garden is 70m squared. find the dimensions of

the garden
Mathematics
1 answer:
Lerok [7]4 years ago
4 0
A = l x w

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = l + 3

you then substitute the second equation into the first to solve for l

70 = l x (l +3)
70 = l^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula 

0 = l^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)
l = -3 +- (square root 9 + 280) / 2
l = -3 +- (square root 289) / 2
l = -3 +- 17 / 2

then you solve for the two seperate roots

l = -3 + 17 /2
l = 14 / 2
l = 7

or 

l = -3 - 17 / 2
l = -20 / 2
l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3
w = 7 + 3
w = 10 

hope this helps! if you did not understand a step or concept please let me know!
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What is the volume of the cone?
Pavlova-9 [17]

Answer:

Volume = 1017.36\ in^3 -- Cone

Volume = 3052.08\ in^3 -- Cylinder

Volume = 3052.08\ in^3 -- Sphere

<em>Best Buy: Sphere Clay</em>

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

<h2>CONE</h2><h3>Calculating Volume</h3>

The volume of a cone is calculated as thus;

Volume = \frac{1}{3}\pi r^2h

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and \pi = 3.14

Substitute these values in the above formula;

Volume = \frac{1}{3} * 3.14 * 9^2 * 12

Volume = \frac{3052.08}{3}

Volume = 1017.36\ in^3

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

Volume:Price  = \frac{Volume}{Total\ Cost}

Where

Volume = 1017.36\ in^3

Total\ Cost = \$12 (Given)

Volume:Price = \frac{1017.36\ in^3}{\$ 12}

Volume:Price = 84.78 in^3/\$

Volume:Price = 84.78 in^3:\$1

<h2>CYLINDER</h2><h3>Calculating Volume</h3>

The volume of a cylinder is calculated as thus;

Volume = \pi r^2h

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and \pi = 3.14

Substitute these values in the above formula;

Volume = 3.14 * 9^2 * 12

Volume = 3052.08\ in^3

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

Volume:Price = \frac{Volume}{Total\ Cost}

Where

Volume = 3052.08\ in^3

Total\ Cost = \$30 (Given)

Volume:Price = \frac{3052.08\ in^3}{\$ 30}

Volume:Price = 101.736\ in^3/\$

Volume:Price = 101.736\ in^3:\$1

<h2>SPHERE</h2><h3>Calculating Volume</h3>

The volume of a sphereis calculated as thus;

Volume = \frac{4}{3}\pi r^3

From the attached diagram

Radius, r = 9 inches; and \pi = 3.14

Substitute these values in the above formula;

Volume = \frac{4}{3} * 3.14 * 9^3

Volume = \frac{9156.24}{3}

Volume = 3052.08\ in^3

<h3>Calculating Volume-Price ratio</h3>

The unit cost of the cone is calculated as thus;

Volume:Price = \frac{Volume}{Total\ Cost}

Where

Volume = 3052.08\ in^3

Total\ Cost = \$28 (Given)

Volume:Price = \frac{3052.08\ in^3}{\$ 28}

Volume:Price = 109.003\ in^3/\$

Volume:Price = 109.003\ in^3:\$1

Comparing the Volume:Price ratio of the three clay;

<em>The best buy is the sphere because it has the highest volume:price ratio.</em>

<em>Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay</em>

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3 years ago
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