What we should do is create a set of 15 data.
To comply with the mean and median 59, what we will do is make our center point 59, we will add 7 values backwards and 7 values forward, always the same value adding in the case forward or subtracting in the case of backwards the same number so that the mean is not affected
So:
We will add 2.5 in the same proportion, we start with the forward ones:
59 + 2.5 * 1 = 61.5
59 + 2.5 * 2 = 64
59 + 2.5 * 3 = 66.5
59 + 2.5 * 4 = 69
59 + 2.5 * 5 = 71.5
59 + 2.5 * 6 = 74
59 + 2.5 * 7 = 76.5
Backward:
59 - 2.5 * 7 = 41.5
59 - 2.5 * 6 = 44
59 - 2.5 * 5 = 46.5
59 - 2.5 * 4 = 49
59 - 2.5 * 3 = 51.5
59 - 2.5 * 2 = 254
59 - 2.5 * 1 = 56.5
Therefore, the entire data set would be:
41.5, 44, 46.5, 49, 51.5, 54, 56.5, 59, 61.5, 64, 66.5, 69, 71.5, 74, 76.5
We guarantee the mean and median 59.
The standard deviation is equal to 10.8
Now if we change the first value of 41.5 by 1000, we will see what happens:
New dataset:
1000, 44, 46.5, 49, 51.5, 54, 56.5, 59, 61.5, 64, 66.5, 69, 71.5, 74, 76.5
The mean changes to 122.9
And the standard deviation to 234.62
In other words, there is a significant increase in the mean, but in the standard deviation the growth is abysmal.
I attach an excel to check all this data.
I drew it out below (don't you just love my effort? XD)
You're gonna use the sine trig function to find the length of the shadow
sin26 / 1 = 43 / x; now you cross multiply
sin26 x = 43; divide both sides by sin26
x = 43 / sin26
x = 98 which is the shadow
Hope this helps!
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!! :)