Given f(x)=-2x-3 and Range={-5,-1,-3} find Domain {1,3,5} {-1,0,1} {2,3,1} {0,-2,3}
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The quadratic regression equation for the stream of water is {parabola}
Given that the water stream produced by fountain is parabola
Vertex of parabola is (6,5) , parbola is facing downward,axis of symmetry of parabola is x=6 and parabola passes through (0,0)
according to symmetry the third point on the parabola is (12,0)
General equation for a parabola⇒ Y=-4a
⇒(y-5)=-4a { as the Vertex of parabola is (6,5) }
⇒(y-5)=-4a()
subtituting (0,0) in the equation to get the value of a
⇒-5=-4a(36)
⇒ a=
equation of parabola⇒(y-5)=-4( )
Therefore,The quadratic regression equation for the stream of water is
Learn more about parabola here:
#SPJ4
Answer:68.3 degrees
Step-by-step explanation:
The diagram of the triangle ABC is shown in the attached photo. We would determine the length of side AB. It is equal to a. We would apply the cosine rule which is expressed as follows
c^2 = a^2 + b^2 - 2abCos C
Looking at the triangle,
b = 75 miles
a = 80 miles.
Angle ACB = 180 - 42 = 138 degrees. Therefore
c^2 = 80^2 + 75^2 - 2 × 80 × 75Cos 138
c^2 = 6400 + 5625 - 12000Cos 138
c^2 = 6400 + 5625 - 12000 × -0.7431
c^2 = 12025 + 8917.2
c = √20942.2 = 144.7
To determine A, we will apply sine rule
a/SinA = b/SinB = c/SinC. Therefore,
80/SinA = 144.7/Sin 138
80Sin 138 = 144.7 SinA
SinA = 53.528/144.7 = 0.3699
A = 21.7 degrees
Therefore, theta = 90 - 21.7
= 68.3 degees
Step-by-step explanation:
Given that,
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,
We know that,
Speed = distance/time
The rate while moving downstream
The rate while moving upstream
The rate of the boat in still water is the average of these:
The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph
Hence, this is the required solution.