Answer:
Step-by-step explanation:
1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.
2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.
3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.
A radius that meet the chord at center C, and divides it into two equal parts.
So that;
AC = CB = 5 units
Applying Pythagoras theorem to ΔOCB,
OC = d, CB = 5 units and OB = 13 units
=
+ ![d^{2}](https://tex.z-dn.net/?f=d%5E%7B2%7D)
169 = 25 + ![d^{2}](https://tex.z-dn.net/?f=d%5E%7B2%7D)
169 - 25 = ![d^{2}](https://tex.z-dn.net/?f=d%5E%7B2%7D)
144 = ![d^{2}](https://tex.z-dn.net/?f=d%5E%7B2%7D)
⇒ d = ![\sqrt{144}](https://tex.z-dn.net/?f=%5Csqrt%7B144%7D)
= 12 units
Therefore, the chord is at a distance of 12 units to the center of the circle.
-12 + 9 - (-3) - 11
Remember PEMDAS: This is the order of operation.
P-Paragrahp
E-Exponent
M-Multiply
D-Divide
A-Add
S-Subtract
1st step: PEM
-(-3) is actually -1 * -3 = + 3
-12 + 9 + 3 - 11
2nd step: D is not possible, so we do A.
9 + 3 = 12
3rd Step: Subtract
12 - 12 - 11 = 0 - 11 = -11 CHOICE B.
Note that two negatives = one positive
- (-4 1/3) = + 4 1/3
Subtract
-9 + 4 1/3 = -4 2/3
-4 2/3 is your answer
hope this helps
V of large = πr^2 h = π 9^2 (15) = 1215π
V of small= πr^2 h = π 4^2 (15) = 240π
V of non-shade = 1215π - 240π = 975 cm^3
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
the probability is equal to
P=size of the event space/size of the sample space
In this problem
size of the sample size=area of the rectangular dartboard=![648\ cm^{2}](https://tex.z-dn.net/?f=648%5C%20cm%5E%7B2%7D)
size of the event space=area of the triangular part=![162\ cm^{2}](https://tex.z-dn.net/?f=162%5C%20cm%5E%7B2%7D)
![P=\frac{162}{648}=0.25](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B162%7D%7B648%7D%3D0.25)
<u>Convert to percentage</u>
![P=0.25*100=25\%](https://tex.z-dn.net/?f=P%3D0.25%2A100%3D25%5C%25)
therefore
<u>the answer is</u>
![25\%](https://tex.z-dn.net/?f=25%5C%25)