The Anderson family is on a road trip. They're looking at a map (shown below) trying to figure out where to go next. Their car i
1 answer:
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g(x) = or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x =
.
<u>Step-by-step explanation:</u>
We have a function f(x) = and another function , g(x) =
. In the graph of y =
, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
Graphing y = (x - h)2 + k , where h = 0 & k = 0
Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) = or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.
Answer:
Speed of the biker is 13 mph and that of wind is 1 mph.
Step-by-step explanation:
Given:
Time taken by the biker to cover a distance is 7 hrs when he was travelling against the speed of the wind.
Time taken to cover same distance is 6 hours when he was travelling with the speed of the wind.
We have to find the speed of the biker and that of the wind.
Let the speed of the biker is "b" mph
And the speed of the wind is "w" mph
As we know:
Distance = Product of speed and time
Re-arranging the above situation in terms of equation.
⇒ ⇒
⇒ ...(i) ⇒
...(ii)
Multiplying equation (i) with 6 and equation (ii) with 7 so that we can eliminate one variable that is "w" after adding both the equation.
⇒ equation (iii)
⇒ equation (iv)
⇒ Adding both the equations.
⇒
⇒
⇒ mph.
Speed of the biker is 13 mph.
⇒ Plugging b=13 in equation (ii),we have:
⇒
⇒
⇒
⇒
⇒
⇒
⇒ mph.
Speed of the biker is 13 mph and the speed of the wind is 1 mph whenever the biker is with the speed of the wind the biker's speed increases by 1 mph and subsequently decreases when he is against the speed of the wind.