Answer:
20.16 meters
82.77º
Step-by-step explanation:
We have that the ramp would have the shape of a rectangular triangle, where the height and width would be the legs and the slope the hypotenuse.
We can solve it by means of the Pythagorean theorem that tells us:
c ^ 2 = a ^ 2 + b ^ 2
a = 2.5 and b = 20, replacing:
c ^ 2 = 2.5 ^ 2 + 20 ^ 2
c ^ 2 = 406.25
c = 20.16
Therefore the slope would be 20.16 meters.
The angle, we will do it using the function: Sin A ° = opposite / hypotenuse
where the opposite is the height, that is to say 20 and the hypotenuse that is the slope is equal to 20.16, replacing:
Without Aº = 20 / 20.16
Without Aº = 0.992
Aº = arc sin (0.992)
Aº = 82.77
Which means that the angle is of the slope with the horizontal is 82.77º
Dividing by a fraction is the same as multiplying by the reciprocal. so dividing by 1/2 is the same as multiplying by 2/1, or 2. so (3/4)/(1/2) = (3/4)*2 = 6/4 = 1 and 1/2
To find the percent increase, we divide the amount of change by the original number. The amount of change is the difference between the 2 numbers which in this case is 700 - 620 and the original number is 620.
700 - 620 is 80 so we're left with which is 0.129.
Finally, since our problem is asking for a percent, we write 0.129 as a percent by moving the decimal point 2 places to the right to get 12.9%
So when the population of a town changes from 620 to 700, it has increased by 12.9%.
So we have
h=hits
m=miss
h+m=10
gain 5 for every hit and lose 3 for every miss
so 5 times number of hit=points from hit
-3 times number of miss=points deducted from miss
add
5h-3m=18
so we have the equations
h+m=10
5h-3m=18
multiply first equation by 3
3h+3m=30
add to first equatio
3h+3m=30
<u>5h-3m=18 +</u>
8h+0m=48
8h=48
divide by 8
h=6
subsitute
h+m=10
6+m=10
subtract 6
m=4
6 hits
4 miss
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