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Osbert12, Master's Degree
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2. The length of a table is 4m greater than the width. The

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2. The length of a table is 4m greater than the width. The area is 77 m^2. Find the dimensions of the table.
3.An aqurium holding African cichlids is 3 inches higher than it is wide. It length is 32 inches, and its vloume is 4260 cubic inches.
4. The product of the page number on two facing pages of a book is 132. Find the page numbers.
5. The product of two consecutive postive integers is 5 more than their sum. Find the integers.
6. A garden has the shape of a right triangle with one leg 2 meters longer than the other. The hypotenuse is 2 meters less than twice the length of the shorter leg. The length of the shorter lleg is?
7. Rosa works due north of home. Her husband Juan works due east. They leave work at the same time. By the time Rosa is 5miles from home, the distance between them is one mile more than Juan's distance from home. How far from home is Juan?
Submitted: 4 years ago.
Category: Pre-Calculus
Expert:  Osbert12 replied 4 years ago.
Thank you for your questions.

 

2. The length of a table is 4m greater than the width. The area is 77 m^2. Find the dimensions of the table.

w(w + 4) = 77

w^2 + 4w - 77 = 0

(w + 77)(w - 7) = 0

width = 7 m

length = 11 m


3.An aqurium holding African cichlids is 3 inches higher than it is wide. It length is 32 inches, and its vloume is 4260 cubic inches.
32(w)(w + 3) = 4260

8w(w + 3) = 1065

8w^2 + 24w - 1065 = 0

w = (-24 ± sqrt(24^2 + 4(8)(1065)))/16 = 10.135

width = 10.135 inches

height = 13.135 inches

(approximately)

 

4. The product of the page number on two facing pages of a book is 132. Find the page numbers.

x(x + 1) = 132

x^2 + x - 132 = 0

(x + 12)(x - 11) = 0

x = 11

Page numbers: 11 and 12


5. The product of two consecutive postive integers is 5 more than their sum. Find the integers.

x(x + 1) = x + (x + 1) + 5

x^2 + x = 2x + 6

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3

Intergers: 3 and 4


6. A garden has the shape of a right triangle with one leg 2 meters longer than the other. The hypotenuse is 2 meters less than twice the length of the shorter leg. The length of the shorter lleg is?

s^2 + (s + 2)^2 = (2s - 2)^2

s^2 + s^2 + 4s + 4 = 4s^2 - 8s + 4

2s^2 - 12s = 0

2s(s - 6) = 0

s = 6

Short leg length = 6 meters


7. Rosa works due north of home. Her husband Juan works due east. They leave work at the same time. By the time Rosa is 5miles from home, the distance between them is one mile more than Juan's distance from home. How far from home is Juan?

5^2 + J^2 = (J + 1)^2

25 + J^2 = J^2 + 2J + 1

2J = 24

J = 12

Juan is 12 miles from home.

 

Osbert

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