We are given the relation between the height (in feet) and the distance (in miles) as follows:
y = sqrt(1.5x + (x/5280)^2).
We want to know the height (x) that makes the distance (y) = 10 miles
So, we will simply substitute in the above equation with y = 10 and calculate x as follows:
10 = sqrt(1.5x + (x/5280)^2)
we will square both sides to get rid of the root:
100 = 1.5x + (x/5280)^2
1.5x + (x/5280)^2 - 100 = 0
(x-66.11475)(x+7986.1147) = zero
either x = 66.11475 feet (accepted solution)
or x = -7986.1147 feet (rejected solution as no height is in negative)
Answer:
2R^2 + 21R - 36
Explanation:
To answer this question, we will follow these steps:
1- expand the brackets
2- gather like terms
Steps are as follows:
(2R-3)(R+12) = 2R(R) + 2R(12) - 3(R) - 3(12)
= 2R^2 + 24R - 3R - 36
= 2R^2 + 21R - 36
Hope this helps :)
First, write the equation of the line containing the points <span>(2,-5) and (-3,2).
We can use 2 point form, or point-slope form.
Let's use </span>point-slope form.
the slope m is

, then use any of the points to write the equation. (ex, pick (2, -5))
y-(-5)=(-7/5)(x-2)
y+5=(-7/5)x+14/5
y= (-7/5)x+14/5 - 5 =(-7/5)x+14/5 - 25/5 =(-7/5)x-11/5
Thus, the lines are
i) y=-ax+4 and ii) y=(-7/5)x-11/5
the slopes are the coefficients of x: -a and (-7/5),
the product of the slopes of 2 perpendicular lines is -1,
so
(-a)(-7/5)=-1
7/5a=-1
a=-1/(7/5)=-5/7
Answer: -5/7