Answer:
A. Plane B because it was 9.33 miles away
B. 48 units
Step-by-step explanation:
A. Since the airplanes fly at an angle to the runway, their direction forms a triangle with the runway with their height above the ground as the opposite of the angle and their distance from the airport as the hypotenuse.
So for airplane A with 44° angle of departure,
sin44° = y/h where y = height above the ground and h = distance from airport
So h = y/sin44° = 6/sin44° = 8.64 miles
So for airplane B with 40° angle of departure,
sin40° = y/H where y = height above the ground and H = distance from airport
So H = y/sin40° = 6/sin40° = 9.33 miles
Since airplane B is at 9.33 miles away from the airport whereas airplane A is 8.64 miles from the airport, airplane B is farther away.
B. We know that scale factor = new size/original size
Our scale factor = 4 and original size = 12 units. So,
new size = scale factor original size = 4 × 12 = 48 units.
-4 is your answer hope this helps
Problem 7: Correct
Problem 8: Correct
Problem 9: Correct
The steps are below if you are curious
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Problem 7
S = 180*(n-2)
2340 = 180*(n-2)
2340/180 = n-2
13 = n-2
n-2 = 13
n = 13+2
n = 15
I'm using n in place of lowercase s, but the idea is the same. If anything, it is better to use n for the number of sides since S already stands for the sum of the interior angles. I'm not sure why your teacher decided to swap things like that.
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Problem 8
First find y
y+116 = 180
y+116-116 = 180-116
y = 64
which is then used to find x. The quadrilateral angles add up to 180*(n-2) = 180*(4-2) = 360 degrees
Add up the 4 angles, set the sum equal to 360, solve for x
x+y+125+72 = 360
x+64+125+72 = 360 ... substitution (plug in y = 64)
x+261 = 360
x+261-261 = 360-261
x = 99
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Problem 9
With any polygon, the sum of the exterior angles is always 360 degrees
The first two exterior angles add to 264. The missing exterior angle is x
x+264 = 360
x+264-264 = 360-264
x = 96
Answer:
Step-by-step explanation:
Given the center of sphere is: (-2, 2, 3)
Passes through the origin i.e. (0, 0, 0)
To find:
The equation of the sphere ?
Solution:
First of all, let us have a look at the equation of a sphere:
Where (
) are the points on sphere.
is the center of the sphere and
is the radius of the sphere.
Radius of the sphere is nothing but the distance between any point on the sphere and the center.
We are given both the points, so we can use distance formula to find the radius of the given sphere:
Here,
So, Radius is:
Therefore the equation of the sphere is:
There are 4 quarts in a gallon so the amount used can be shown as 4 1/4, or 4.25 so to find out how much gas is left in the tank you simply subtract 4.25 from 20.
20-4.25
=15.75
There is 15.75, or 15 3/4, gallons of gasoline left in the tank.
