Answer:
6
Step-by-step explanation:
4+2
The key word “lost” indicates that the football player went back 10 yards. The correct answer is B. -10! :)
Answer:
210 miles
Step-by-step explanation:
Let's represent it mathematically.
Ben drove 65 miles more than half the number of miles Steve drove, so we represent it by
B = 65 + ½S
It is also said that together, they drove 500 miles, we represent it with.
B + S = 500
Now, we solve simultaneously.
Let's eliminate the ½ in Ben's drive. So we multiply the equation by 2.
2B = 130 + S.
Rearranging, we have
S = 2B - 130.
We substitute this value of S, in the second equation. So we have.
B + (2B - 130) = 500, open the brackets
B + 2B - 130 = 500
3B - 130 = 500, collecting the like terms
3B = 500 + 130
3B = 630
B = 630/3
B = 210 miles.
Therefore, Ben drove 210 miles.
Kindly vote Brainliest.
Answer:
Step-by-step explanation:
A = 2π +πrl
A - 2π = πrI subtract by 2π
(A- 2π)/(πr) = I divide by πr to isolate I
(a) It looks like the ODE is
<em>y'</em> = 4<em>x</em> √(1 - <em>y </em>^2)
which is separable:
d<em>y</em>/d<em>x</em> = 4<em>x</em> √(1 - <em>y</em> ^2) => d<em>y</em>/√(1 - <em>y</em> ^2) = 4<em>x</em> d<em>x</em>
Integrate both sides. On the left, substitute <em>y</em> = sin(<em>t </em>) and d<em>y</em> = cos(<em>t</em> ) d<em>t</em> :
∫ d<em>y</em>/√(1 - <em>y</em> ^2) = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / √(1 - sin^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / √(cos^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / |cos(<em>t</em> )| d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
Since we want the substitutiong to be reversible, we implicitly assume that -<em>π</em>/2 ≤ <em>t</em> ≤ <em>π</em>/2, for which cos(<em>t</em> ) > 0, and in turn |cos(<em>t</em> )| = cos(<em>t</em> ). So the left side reduces completely and we get
∫ d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
<em>t</em> = 2<em>x</em> ^2 + <em>C</em>
arcsin(<em>y</em>) = 2<em>x</em> ^2 + <em>C</em>
<em>y</em> = sin(2<em>x</em> ^2 + <em>C </em>)
(b) There is no solution for the initial value <em>y</em> (0) = 4 because sin is bounded between -1 and 1.
