Answer: It is simple, if you look at the slope of the 2, if they have the same slope then it means it definitely is not intersecting, and if you look at which points that the equation begins at you can tell if it starts at the same points with the same slope then it is same line, if it starts at different points with same slope then it is parallel lines
the rate of change of a linear function is the same slope
the slope of a linear function is the coefficient that accompanies the variable in this case the variable is x and the slope is -2
so, the rate of change for y is -2
Race track principle says that if two functions are equal at <span>t=0</span>, then the one which has a greater derivative will be greater.
In this case we're comparing <span><span>f′</span>(t)</span> and <span><span>g′</span>(t)</span>. So we make sure that <span>g(0)=<span>f′</span>(0)</span> and that <span><span>f′′</span>(t)≥<span>g′</span>(t)
</span>
<span>g(t)=at+b</span>
Since it is a line.
<span><span>g′</span>(t)=a</span>
<span><span>f′′</span>(t)≥3≥<span>g′</span>(t)⟹3≥a</span>
So let <span>a=3</span>.
<span><span>f′</span>(0)=0=g(0)=3(0)+b⟹b=0
</span>So that means
<span>g(t)=3t
</span>Do something similar for <span>h(t)</span><span> starting with
</span><span>h(t)=a<span>t2</span>+bt+c
</span><span>h(0)=f(0)⟹c=0
</span>
So
<span>h</span><span>(</span><span>t</span><span>)</span><span>=</span><span>a</span><span>t2</span><span>+</span><span>b</span><span>t</span>
Im not sure but i thing its 0.5 or 1/2
cause if you take (3/1)*(1/6) that's what you will get
also you had to make 3 as a fraction so you would put the denominator as 1 so if you divide 1 and 3 you would still get the whole number as 3
The value of x is about 4.7
