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**Outragexl10** · July 21st, 2007, 08:38 AM

Question 1 (Multiple Choice Worth 4 points)
[7.02] Write the equation of the line in standard form that contains the centers of the circles (x – 4)2 + (y + 2)2 = 15 and (x – 7)2 + y2 = 37.
2x – 3y = -14
2x – 3y = 14
2x – 11y = 14
2x – 11y = -14
none of these

Question 2 (Multiple Choice Worth 4 points)
[7.06] In a circle with a radius of 58 units, the center is 42 units away from a chord. Find the length of the chord.
40 units
45 units
56.4 units
80 units

Question 3 (Multiple Choice Worth 4 points)
[7.09] Find the measure of angle JLN.

30
60
42
84

Question 4 (Multiple Choice Worth 4 points)
[7.10] In circle A,

is a tangent. Find AD if CD = 24 and BD = 36.

38
15
30
39

Question 5 (Multiple Choice Worth 4 points)
[7.12] Describe the locus of points in a plane that are 7 cm from point C.
a circle with a radius of 7 cm
a segment 14 cm long
a circle with a radius of 14 cm
a sphere with a radius of 7 cm

Question 6 (Essay Worth 5 points)
[7.10]

is a common external tangent of circle R and circle S. The radius of circle S is 14 feet and the radius of circle R is 4 feet. TU = 8 ft. Find PQ.

Question 7 (Essay Worth 5 points)
[7.12] In a cone with a slant height of 7.5 feet, the slant height forms a 38 degree angle with the radius. Find the surface area and volume of the cone. Show all work.

Question 8 (Essay Worth 5 points)
[7.12] Given a cylinder with a surface area of 140 p units squared and a height of 9 units. Find the volume of the cylinder. Show all work.

Question 9 (Essay Worth 5 points)
[7.02] Write the equation of the circle containing the points J(-3, -3), K(1, -3), and L(1, 1). Show all work to receive credit.

Question 10 (Essay Worth 5 points)
[7.06] A circle is given with an inscribed equilateral triangle and each side of the triangle having a measurement of 24 cm. What is the probability of selecting a point at random inside the circular region, but not inside the triangle, assuming that the point cannot lie outside the circular region. Leave your answer in exact form.

Question 11 (Essay Worth 5 points)
[7.09] ABCD is an inscribed quadrilateral.

a.) Find the values of x and y. Show all work.
b.) Find m

B and m

D.

I'm posting it in here as well... i didn't know if i should only post it here or in the need help fast thread

**Outragexl10** · July 21st, 2007, 08:44 AM

no... i didn't mean to double post i had the wrong thing copied and i pasted the wrong thing with out noticing... I'm fixing it now... sorry

**Jhevon** · July 21st, 2007, 11:57 AM

Originally Posted by Outragexl10

Question 1 (Multiple Choice Worth 4 points)
[7.02] Write the equation of the line in standard form that contains the centers of the circles (x – 4)2 + (y + 2)2 = 15 and (x – 7)2 + y2 = 37.
2x – 3y = -14
2x – 3y = 14
2x – 11y = 14
2x – 11y = -14
none of these

The center of the first circle is (4, -2), the center of the second circle is (7, 0). we want a line passing through both these points.

Let $(x_1, y_1)$ be $(4, -2)$
Let $(x_2,y_2)$ be $(7,0)$
Let $m$ be the slope of the line.

Now $m = \frac {y_2 - y_1}{x_2 - x_1}$

Once you find $m$ you can plug it into the point slope form.

$y - y_1 = m(x - x_1)$

using $m$ as what you found before, and $(x_1, y_1)$ as either of the two original points (I'd use $(7,0)$ )

when done, just get the x's and y's on one side and see which matches the answers given

**Jhevon** · July 21st, 2007, 12:05 PM

Originally Posted by Outragexl10

Question 2 (Multiple Choice Worth 4 points)
[7.06] In a circle with a radius of 58 units, the center is 42 units away from a chord. Find the length of the chord.
40 units
45 units
56.4 units
80 units

See the attached diagram. The center is O. the chord is AC. B is where the line from the center meets the chord (the shortest distance between the two).

Note that we have an isosceles triangle AOC made up of two right-triangles, ABO and BCO. Use Pythagoras' theorem to find BC. Then multiply it by 2 to find AC

**Jhevon** · July 21st, 2007, 12:09 PM

Originally Posted by Outragexl10

Question 3 (Multiple Choice Worth 4 points)
[7.09] Find the measure of angle JLN.

30
60
42
84

Question 4 (Multiple Choice Worth 4 points)
[7.10] In circle A,

is a tangent. Find AD if CD = 24 and BD = 36.

38
15
30
39

Question 5 (Multiple Choice Worth 4 points)
[7.12] Describe the locus of points in a plane that are 7 cm from point C.
a circle with a radius of 7 cm
a segment 14 cm long
a circle with a radius of 14 cm
a sphere with a radius of 7 cm

Question 6 (Essay Worth 5 points)
[7.10]

is a common external tangent of circle R and circle S. The radius of circle S is 14 feet and the radius of circle R is 4 feet. TU = 8 ft. Find PQ.

Question 11 (Essay Worth 5 points)
[7.09] ABCD is an inscribed quadrilateral.

a.) Find the values of x and y. Show all work.
b.) Find m

B and m

D.

These questions are EXTREMELY similar to some of the questions asked in your other thread. In fact, they are the same questions with the numbers changed. See your other thread for the solutions/methods

**Jhevon** · July 21st, 2007, 12:22 PM

Originally Posted by Outragexl10

Question 9 (Essay Worth 5 points)
[7.02] Write the equation of the circle containing the points J(-3, -3), K(1, -3), and L(1, 1). Show all work to receive credit.

recall that the equation of a circle is given by:

$(x - h)^2 + (y - k)^2 = r^2$

where $(h,k)$ is the center and $r$ is the radius
$(-3,-3)$ means when x = -3, y = -3

$(1,-3)$ means when x = 1, y = -3

$(1,1)$ means when x = 1, y = 1

thus when we plug in each of these pair of values for x and y into the form for the equation of a circle, we get three different equations.

$(-3 - h)^2 + (-3 - k)^2 = r^2$ ................(1)
$(1 - h)^2 + (-3 - k)^2 = r^2$ ...................(2)
$(1 - h)^2 + (1 - k)^2 = r^2$ ......................(3)

use the substitution method to help you in solving this system for $h \mbox { , } k \mbox { and } r$ and then plug them back into the form for the equation of the circle to find the desired circle

Now all that's left is Questions 7, 8 and 10

**Jhevon** · July 21st, 2007, 12:41 PM

Originally Posted by Outragexl10

Question 7 (Essay Worth 5 points)
[7.12] In a cone with a slant height of 7.5 feet, the slant height forms a 38 degree angle with the radius. Find the surface area and volume of the cone. Show all work.

Here are the formulas you need to know:

The surface area of a cone is given by: $SA = \pi r \sqrt {r^2 + h^2}$

The volume of a cone is given by: $V = \frac {1}{3} \pi r^2 h$

where $h$ is the height, $r$ is the radius

we are given the slant height, which is s in the diagram below. we are also given $x$ , which is the angle the slant height makes with the radius.

We need to find $h$ and $r$ to answer the question. here's how.

we have a right-triangle with sides $h \mbox { , } r \mbox { and } s$ . as i have mentioned many times before, think of Pythagoras' theorem and trig ratios. we will need both here.

Using the sine trig ratio, we see that:

$\sin x = \frac {h}{s}$

$\Rightarrow h = s \sin x$

Once we have $h$ we can find $r$ using Pythagoras' theorem.

By Pythagoras, $s^2 = h^2 + r^2$

$\Rightarrow r = \sqrt {s^2 - h^2}$

Now that you have $h$ and $r$ , just plug them into the formulas i gave to find the volume and surface area of the cone

Now only questions 8 and 10 are left

**Soroban** · July 21st, 2007, 01:18 PM

Hello, Outragexl10!

Question 10 .(Essay - 5 points)

A circle is given with an inscribed equilateral triangle and with sides 24 cm.
What is the probability of selecting a point at random inside the circular region
and outside the triangle. .Leave your answer in exact form.

The probability is: . $\frac{\text{Area of circle} - \text{Area of triangle}}{\text{Area of circle}}$

The area of an equilateral triangle with side $S$ is: . $A \;=\;\frac{\sqrt{3}}{4}S^2$
We have $S = 24$ , hence: . $A_{\Delta} \;=\;\frac{\sqrt{3}}{4}(24^2) \;=\;144\sqrt{3}$ cm²

Given inscribed equilateral triangle $ABC$ with side 24,
. . $\angle BOC = 120^o$ and $OA = OB = OC = r$

Code:

                A
              * o *
          *     |     *
        *       |       *
       *        |r       *
                |
      *         |         *
      *         *O        *
      *       /   \       *
           r/       \r
       *  /           \  *
      B o - - - - - - - o C
          *    24     *
              * * *

There are many ways to determine the radius.
. . I'll use the Law of Cosines on $\Delta OBC$ .

$r^2 + r^2 - 2\cdot r\cdot r\cos120^o \:=\:24^2$

. . $2r^2 - 2r^2\left(-\frac{1}{2}\right) \:=\:576$

. . $3r^2 \,=\,576\quad\Rightarrow\quad r^2 \,=\,192\quad\Rightarrow\quad r \,= \,8\sqrt{3}$

Hence, the area of the circle is: . $A_{\circ} \;=\;\pi r^2\;=\;\pi(8\sqrt{3})^2\;=\;192\pi$ cm²

The area in the circle but outside the triangle is: . $192\pi - 144\sqrt{3}$

Therefore, the probability is: . $\frac{192\pi - 144\sqrt{3}}{192\pi} \;=\;1 - \frac{3\sqrt{3}}{4\pi}<br />$

**Jhevon** · July 21st, 2007, 01:38 PM

Originally Posted by Outragexl10

Question 8 (Essay Worth 5 points)
[7.12] Given a cylinder with a surface area of 140 p units squared and a height of 9 units. Find the volume of the cylinder. Show all work.

I told you these formulas before, but recall, the surface area, SA, of a cylinder is given by:

$SA = 2 \pi r^2 + 2h \pi r$

where $h$ is the height and $r$ is the radius.

since the surface area is $140 \pi$ and the height is 9, we have:

$140 \pi = 2 \pi r^2 + 18 \pi r$

$\Rightarrow 2 \pi r^2 + 18 \pi r - 140 \pi = 0$

$\Rightarrow r^2 + 9r - 70 = 0$ ............i divided through by $2 \pi$

Solve that quadratic equation to get $r$ . then plug in the values of $r$ and $h$ in the formula for the volume of a cylinder to get the desired volume

Recall, the volume, V, of a cylinder is given by: $V = \pi r^2 h$

where $h$ is the height and $r$ is the radius

And that's all the questions! You're done

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