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>
Answer:
Two acute angles
Step-by-step explanation:
The right triangle has one 90 degree angle and two acute angles. Since the sum of the angles of a triangle is always 180 degrees... The two sides of the triangle that are by the right angle are called the legs... and the side opposite of the right angle is called the hypotenuse.
Answer:
D) Divsion
hope this helps
I took the test and got it right
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Solve your equation step-by-step.
2(x−3)−17=13−3(x+2)
Simplify both sides of the equation.
2(x−3)−17=13−3(x+2)
Simplify
2x−23=−3x+7
Add 3x to both sides.
2x−23+3x=−3x+7+3x
5x−23=7
Add 23 to both sides.
5x−23+23=7+23
5x=30
Divide both sides by 5.
5x/5 = 30/5
x=6
We have the value -0.000125
Since this is negative value the cube number cannot be positive since it will not give an negative answer
hence the answer should be a negative number
this already eliminates the option A, B and D
now we have
![\sqrt[3]{-0.000125}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B-0.000125%7D%20%20)
![\sqrt[3]{(-0.05).(-0.05).(-0.05)}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%28-0.05%29.%28-0.05%29.%28-0.05%29%7D%20%20)
=-0.05 (option C)
