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Gem Carnelian
 #1 Posted : Monday, October 17, 2011 3:48:15 AM
Rank: Newbie

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Joined: 10/17/2011
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1. From a 100cm by 100cm and 60cm block of marble, a pyramid with a square base of 100cm and a height of 60cm was carved. What is the volume of the pyramid? What is the volume of marble removed?

2. If three vertices of a parallelogram are A (2,0), B (4,4), C (6,0), find the fourth vertex D if D is in the 4th quadrant.

3. Two vertices of isosceles triangle ABC are A (0,2) and B (2,2)and AB is the base. Find the vertex C if it is on the x-axis.

Thank you for the help extended.

lisa
 #2 Posted : Tuesday, November 08, 2011 4:44:22 PM

Groups: Administration , Administrators, Member, Registered Users

Joined: 3/16/2011
Posts: 33

HI!

I will try to help you as well as I can

1. The volume of a pyramide you will find using the following formula found on this page http://www.mathplanet.co...sms,-cylinders-and-cones

where h is the height (in our case 60 cm)

and B is the base area (in our case the area of a square base of 100 cm)

We begin by getting the value of B

The area of a square is the base times the height i.e.

Now we have a value of h and a value of h and can insert them into the formula of the volume of a pyramid

2. Plot the 2 coordinates in a coordinate plane. In a parallelogram two opposite sides are parallel which means that the slope of the line L1 that intersects vertex B and C is the same as the slope of the line L2 that intersects veritces A and D. This means that if we find the slope of the line L1 we can use that to find the coordinates for D

We call the slope m which gives

The slope-intersect form of a linear function as L1 and L2 is

This means that the function of L2 is

To get the value of b we can insert the coordinates for one point on the line (in this case (2, 0) and solve for b

Which gives us the linear function of L2

Then we can do the same but for lines L3 (intesects A and B) and L4 (intersects C and D)

The coordinates of D you will find where L2 and L4 intersect which gives us the following system of equations

Solve for x

To find the corresponding y-value we insert the value of x in either L2 or L4. We use L4

i.e. the coordinates for vertex D is (4, .4)

3.Begin by plotting the points in a coordinate plane.

In an isosceles triangle the two sides that are not tha base are congruent i.e. of the same length.

This means that the distance between A and C is the same as the distance between B and C and we can use this fact together with the distane formula to solve this problem.

The distance formula

We know that the vertex C is on the x-axis which means it has the y-coordinate 0 i.e. the coordinates (x, 0). We also know tha values of A and B which gives us the following equations

Since we know that

we can form the following system of equations

and solve it for x

This means that the coordinates for vertex C is (1, 0)

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