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Juli2301 [7.4K]
3 years ago
6

Here are my steps:

Mathematics
1 answer:
eimsori [14]3 years ago
4 0
You have the correct approximate value of k. The part after that is where things get a bit strange.

You don't plug in t = 5 again. We don't know the value of t yet. We're trying to solve for it.

We do know u(t) is 135 as we want the temperature to be 135 degrees. Plug this in and isolate t. 

So 
u(t) = 70+380e^(-0.1004183888t)
135 = 70+380e^(-0.1004183888t)
135-70 = 380e^(-0.1004183888t)
65 = 380e^(-0.1004183888t)
380e^(-0.1004183888t) = 65
e^(-0.1004183888t) = 65/380
e^(-0.1004183888t) = 13/76
-0.1004183888t = ln(13/76)
-0.1004183888t = -1.7657839828248
t = -1.7657839828248/(-0.1004183888)
t = 17.5842692152893

So it takes about 17.58 minutes for the item to cool to the desired temp

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soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because Lim_{x \to 4}f(x)=f(4)

Step-by-step explanation:

Given the function:

f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right

A function to be continuous  at some value c in its domain if the following condition holds:

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At x=4

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Therefore: Lim_{x \to 4}f(x)=f(4)=2

By the above, the function satisfies the condition for continuity.

The correct option is D.

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4) Alternate angles

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Alternate angles are on the opposite corners of the line of the angle, and 10 and 14 are on opposite corners, so that makes them alternate angles. I hope this helped you!

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