Answer:
about 52 feet
Step-by-step explanation:
The figure is omitted--you may draw it to confirm my answer.
sin (38°) = 32/x
x sin (38°) = 32
x = 32 / sin (38°) = about 52 feet
Answer:
11.18 miles
Step-by-step explanation:
The sides of a right triangle a, b, c are related by the equation
a^2 + b^2 = c^2
where c is the longest side of the triangle
Hence given that A connects B and C directly and forms a right angle at A
5^2 + 10^2 = c^2
Where c is the length of the road
25 + 100 = c^2
125 = c^2
c = 125^1/2
= 11.18 miles
Answer:
Should be B
Step-by-step explanation:
NOT MY WORDS TAKEN FROM A SOURCE!
(x^2) <64 => (x^2) -64 < 64-64 => (x^2) - 64 < 0 64= 8^2 so (x^2) - (8^2) < 0 To solve the inequality we first find the roots (values of x that make (x^2) - (8^2) = 0 ) Note that if we can express (x^2) - (y^2) as (x-y)* (x+y) You can work backwards and verify this is true. so let's set (x^2) - (8^2) equal to zero to find the roots: (x^2) - (8^2) = 0 => (x-8)*(x+8) = 0 if x-8 = 0 => x=8 and if x+8 = 0 => x=-8 So x= +/-8 are the roots of x^2) - (8^2)Now you need to pick any x values less than -8 (the smaller root) , one x value between -8 and +8 (the two roots), and one x value greater than 8 (the greater root) and see if the sign is positive or negative. 1) Let's pick -10 (which is smaller than -8). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive
2) Let's pick 0 (which is greater than -8, larger than 8). If x=0, then (x^2) - (8^2) = 0-64 = -64 <0 so it is negative3) Let's pick +10 (which is greater than 10). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive Since we are interested in (x^2) - 64 < 0, then x should be between -8 and positive 8. So -8<x<8 Note: If you choose any number outside this range for x, and square it it will be greater than 64 and so it is not valid.
Hope this helped!
:)
