By equating both quadratic equations, Brian can determine the point of intersection of both equations. Upon graphing he was able to identify that both share the same vertex but of opposite opening. Based on this, he can say that both equations are equations of parabolas with same vertex but open on different directions.
Answer: In 36 minutes both buses will end up at the library.
Step-by-step explanation:
Given: Buses from one route stop at the library every 9 minutes.
Buses from the other route stop at the library every 12 minutes.
The number of minutes in which both buses will end up at the library= LCM(9,12)
Now , 9= 3 x 3
12= 2 x 2 x 3
LCM(9,12) = 2 x 2 x 3 x 3 = 36
Answer:
i)
ii) n = 33
Step-by-step explanation:
For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)
i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi
ii) The Tn values are at x = (n·π - π/2)/4
solving (n·π - π/2)/4 > 25 gives:
n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33
Answer:
Step-by-step explanation:
The straight line passes through (0,1) and (2,-2).
Equation of a straight line passing through two points (x1,y1) and (x2,y2)
is given by:
Everything to the left of the line is shaded.
We have to visualize the graph:the straight line has a positive y-intercept and a negative slope.The graph is given in the attachment below.
From the figure we can see origin lies on the shaded region.Hence (0,0) should satisfy the inequality.
LHS=y=0
RHS=
LHS<RHS as 0<1
Hence , the inequality is:
Between 15 and 20 miles per gallon.