you can speed from 0 to 25 m/s in 25 seconds and your friend can speed up from 0 to 6 m/s in 6 seconds. who is faster

Mathematics

1 answer:

aksik [14]2 years ago

7 0

Answer:

Neither; see below

Step-by-step explanation:

Your acceleration: $a=\frac{\Delta v}{\Delta t}=\frac{25-0}{25}=1m/s^2$

Your friend's acceleration: $a=\frac{\Delta v}{\Delta t}=\frac{6-0}{6}=1m/s^2$

Therefore, since both you and your friend accelerate at the same rate, neither is faster.

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In a circle a chord 10 inches long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is t

Lorico [155]

Check the picture below.

keeping in mind that the point of tangency for a radius line and a tangent is alway a right-angle, since the "red" chord is parallel to the "green" tangent line outside, then the chord is cutting the "green" radius there in two equal halves at a right-angle, as you see in the picture.

we know the chord is 10 units long, so 5 + 5, since is perpendicularity with the radius will also cut the chord in two equal halves.

anyhow, all that said, we end up with triangle you see on the right-hand-side, and then we can just use the pythagorean theorem.

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
-------\\
c=2a\\
a=a\\
b=5
\end{cases}\implies (2a)^2=a^2+5^2$

$\bf (2^2a^2)=a^2+25\implies 4a^2=a^2+25\implies 3a^2=25
\\\\\\
a^2=\cfrac{25}{3}\implies a=\sqrt{\cfrac{25}{3}}\implies a=\cfrac{\sqrt{25}}{\sqrt{3}}\implies a=\cfrac{5}{\sqrt{3}}
\\\\\\
\textit{and then we can \underline{rationalize the denominator} }
\\\\\\
a=\cfrac{5}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies a=\cfrac{5\sqrt{3}}{\sqrt{3^2}}\implies a=\cfrac{5\sqrt{3}}{3}$