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Question

1. tamara builds a wooden box to store mementos from a concert she attended. the lenth of the box is twice its heght, and three times its width. if the bx has a volume of 36 cubic inches. what is the length in inches.

2. lynda and maggie are playing a game on a coordinate grid. lynda puts a counter on the point (5,2). maggie responds by placing a counter on (3, -2) what is the eqution of the line made by these two points?

3. the sum of 5 consecutive odd integers is 235. what is the greatest of these integers?

4. when an integer x is divided by seven, the remmainder is 2. when x squared is divided by seven, what will the remainder be?

5. a hiker can choose either of two water bottles to bring on a hike on mount baldy. bottle A has a base with a radius that is twice that a bottle B but bottle B is twice as tall as bottle A. which of the two water ottles has the greater volume, and by how much?

Answer 1

1. FIND L
L = 2 H
L = 3 W
W L H = 36 use substitution W = L/3. H = L/2.
L/3 * L * L/2 = 36
LLL/6 = 36
LLL = 6 * 36 = 6*6*6
L = 6.

Answer 2

1) Volume = length * width * height.
Let us use 6x to show the length.
Then 'the length is twice the height' means that height = 3x;
and 'the length is three times the width': width = 2x.

Volume = 36 cubic inches = 6x * 3x * 3x = 36 x^3
therefore x^3 = 1 cubic inch
from that, we say: x = 1 inch.

length = 6x = 6 inches
etc.

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2) The standard equation for a line has the form:
y = mx + c
where m is the slope (how fast does y increase when x increases by 1)
and c is the intercept (the value of y when x = 0)

When x goes from 3 to 5, y goes from -2 to 2. y increases by 4 when x increases by 2, therefore m = 2

y = 2 x + c

To find c, use one of the points (let us say (5, 2) where x = 5 and y = 2)

2 = 2*5 + c
2 = 10 + c
therefore c = -8

y = 2x - 8

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3) call the five numbers:

(x-2), (x-1), (x), (x+1) and (x+2)
These are five consecutive numbers and x is the middle one.

Adding them all together, the +2 cancels the -2, same for +1 and -1.
You are left with 5x

5x = 235

Take it from there (just remember that x is the MIDDLE number).

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4) The easy answer in modulo calculus is 4. Modulo calculus only deals with the remainder; it couldn't care less about the rest of the number.
But, if you want to do it the long way:

'when x is divided by 7, the remainder is 2'
This means we can rewrite x in this way: x = 7k + 2 (where k is an integer).

Then x^2 = (7k + 2)^2
= 49 k^2 + 28 k + 4
=[ 7(7k^2) + 7(4k) + 4 ]
= 7*(7k^2 + 4k) + 4

If you divide this number by 7, the part that contains k's is obviously divisible by 7 because it is 7 times some integer called (7k^2 + 4k). Only the part containing the 4 is not exactly divisible by 7.

4 divided by 7 has a remainder of... 4.

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5) Volume of cylinder = area of base times height.

Let volume of B = 1

If B was cut in half (to make bottle C), it would have the same height as A. Its volume would become 0.5

If C is then expanded to have twice the radius of B (and the same radius as A), the area of the base would be 4 times bigger (area varies as square of radius: Area = pi * r^2 -- pie are squared).
New volume = 4*0.5 = 2

Answer 3

1) x=lenght h= height w=width *=times
H=2x
W=3x
3x*2x*x=36
6x^3=36
x^3=6
x=about 1.8

2) slope= 2
y-intercept= -8
y=2x+-8

3)235/5=47
47+2=49
answer=49

you can do the rest, i have to do my own homework