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alexira [117]
3 years ago
10

The base of a triangular prism is a right triangle whose legs are 7 cm and 24 cm. The height of the prism is 30 cm. What is the

lateral area of the prism?
Mathematics
1 answer:
Grace [21]3 years ago
3 0
Ok, base area: triangle sides are 25cm each, or .25m
s=semiperimeter
area=s(sqrt(s-side)^3)
s=75/2
s-side=37.5-25=12.5
area=37.5*12.5*sqrt12.5
let E6 mean 10^6
.075E6m=1/3 (37.5*12.5*(sqrt12.5))h
solve for h
I get:137cm
I hope that helped

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Nuetrik [128]

We have the function

p(t)=550(1-e^{-0.039t})

Therefore we want to determine when we have

p(t_0)=550

It means that the term

e^{-0.039t}

Must go to zero, then let's forget the rest of the function for a sec and focus only on this term

e^{-0.039t}\rightarrow0

But for which value of t? When we have a decreasing exponential, it's interesting to input values that are multiples of the exponential coefficient, if we have 0.039 in the exponential, let's define that

\alpha=\frac{1}{0.039}

The inverse of the number, but why do that? look what happens when we do t = α

e^{-0.039t}\Rightarrow e^{-0.039\alpha}\Rightarrow e^{-1}=\frac{1}{e}

And when t = 2α

e^{-0.039t}\Rightarrow e^{-0.039\cdot2\alpha}\Rightarrow e^{-2}=\frac{1}{e^2}

We can write it in terms of e only.

And we can find for which value of α we have a small value that satisfies

e^{-0.039t}\approx0

Only using powers of e

Let's write some inverse powers of e:

\begin{gathered} \frac{1}{e}=0.368 \\  \\ \frac{1}{e^2}=0.135 \\  \\ \frac{1}{e^3}=0.05 \\  \\ \frac{1}{e^4}=0.02 \\  \\ \frac{1}{e^5}=0.006 \end{gathered}

See that at t = 5α we have a small value already, then if we input p(5α) we can get

\begin{gathered} p(5\alpha)=550(1-e^{-0.039\cdot5\alpha}) \\  \\ p(5\alpha)=550(1-0.006) \\  \\ p(5\alpha)=550(1-0.006) \\  \\ p(5\alpha)=550\cdot0.994 \\  \\ p(5\alpha)\approx547 \end{gathered}

That's already very close to 550, if we want a better approximation we can use t = 8α, which will result in 549.81, which is basically 550.

Therefore, we can use t = 5α and say that 3 people are not important for our case, and say that it's basically 550, or use t = 8α and get a very close value.

In both cases, the decimal answers would be

\begin{gathered} 5\alpha=\frac{5}{0.039}=128.2\text{ minutes (good approx)} \\  \\ 8\alpha=\frac{8}{0.039}=205.13\text{ minutes (even better approx)} \end{gathered}

7 0
1 year ago
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