Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty perso
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The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment
<h3>How to determine the true statement?</h3>The complete question is in the attached image
From the image, we have:
PS = 8 units
This means that:
P'S' = 1/2 * PS
So, we have:
P'S' = 1/2 * 8
Evaluate
P'S' = 4
Also, the segment PS and P'S' do not lie on the same segment
Hence, the true statement is (c)
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How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.
#3
Let's start with sin here. Therefore, because sin is y/r, r =
and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.
cos =
#4
Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = . Now, to find csc, we have to do r/y.
csc =
The pythagorean identities are
sin^2 + cos^2 = 1,
1 + cot^2 = csc^2,
tan^2 + 1 = sec^2.
#5
Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.
sin^2 + (-3/4)^2 = 1
sin^2 + 9/16 = 1
sin^2 = 7/16
sin = =
Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.
tan^2 + 1 = (-4/3)^2
tan^2 + 1 = 16/9
tan^2 = 7/9
tan = -
#6
Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.
1 + cot^2 =
1 + cot^2 = 6/4
cot^2 = 2/4
cot =
tan =
Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.
+ 1 = sec^2
4/2 + 1 = sec^2
2 + 1 = sec^2
sec^2 = 3
sec = -
cos =
Hope this helps!! :)
Answer:
15
Step-by-step explanation:
The product of the prime factors of 3375 are
3375 = 3³ × 5³, then
=
= ×
= 3 × 5
= 15