Loss: 3 (spaceships) * 20 (points per spaceship)
Gain: 250 (points)
Total: -(3*20) + 250 = +190
Answer:
y = -2.5x +100
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
We need to solve for y
25x+ 10y =1000
Subtract 25x from each side
25x-25x+10y = -25x +1000
10y = -25x+1000
Divide each side by 10
10y/10 = -25x/10 +1000/10
y = -2.5x +100
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 correct expressions are
-8.8
11(-2)
-6.7
