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>
The additive inverse property states that when you add a number and its opposite (rational numbers), the result is zero. The reason is that the inverse of a number is the opposite, so if you have a number and when do the opposite with it (add the opposite), the result will be zero. This applies to adding!!!
Hope This Helped =3
Answer:
The student took 28 classes
Step-by-step explanation:
What I did was minus $15 from the $687 total, cause $15 is only a one time registration fee, then 687-15=672, so then I divided 672 by the cost per class, so $24, 672 divided by 24 equals to 28, so the student took 28 classes.
Answer:
The first blank which is in the first row would be 9
The second blank under the 5 is 100
The third blank below the 8 is 160
And the last blank is 240
Step-by-step explanation:
It you do 60 divided by 3, it would be 20, meaning each sweater costs $20.
Answer:
40 meters
Step-by-step explanation:
