The diagram is a straightedge and compass construction. A is the center of one circle,
1 answer:
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we have that
I. Rewrite the equation by substituting the expression u in for sin x.
II. Factor the quadratic expression. Rewrite the equation with factors instead of the original polynomial.
is equal to
using a graph calculator-----> see the attached figure
III. Use the zero product property to solve the quadratic equation.
(u-3)=0--------------> u=3
(2u+1)=0-------- 2u=-1------> u=-1/2-----> u=-0.5
IV. Rewrite your solutions to Part III by replacing u with sin x.
sin x=3--------> is not the solution (sin x can not be greater than 1)
sin x=-0.50------>is the solution
V. Solve the remaining equations for x, giving all solutions to the equation.
sin x=-0.50
if the sine is negative
then
x belong to the III or IV quadrant
we know that
sin 30°=0.50
so
the solution for the III quadrant is
x=180°+30°-------> x=210°
the solution for the IV quadrant is
x=360°-30°------> x=330°
Answer:
Time taken by Doreen is 6 hours and speed is 10 miles per hour.
Time taken by Sue is 4 hours and speed is 20 miles per hour.
Step-by-step explanation:
Let the speed of Doreen be x
According to the question speed of Sue is = x+10
time taken By Sue to cover 80 miles =
time taken by Doreen to travel 60 miles =
According to question Sue take two hours less than Doreen takes
therefore
-
=2
=2
60(x+10) -80x = 2(x(x+10)
60x+600-80x =
simplifying it ,we get
Dividing both sides by 2 ,we get
solving it for x ,we get
(x+30)(x-10) =0
x =-30 which is not possible
x =10 miles per hour
Speed of Doreen = 10 miles per hour
Speed of Sue = 10+10 = 20 miles per hour
Time taken by Doreen = 60 divided by 10 = 6 hours
Time taken by Sue = 80 divided by 20 = 4 hours