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azamat
3 years ago
8

two buses leave towns 604 mi apart at the same time and travel toward eachother. One bus travels 9 mi/h faster than the other on

e. If they meet in 4 hours, what is the rate of each bus?
Mathematics
1 answer:
muminat3 years ago
3 0

Answer:

s = 71 mph, and s+9 = f = 80 mph

Step-by-step explanation:

The distances the two busses travel add up to 604 mi.

Letting f be the faster speed and s the slower.  Then f = s + 9 (mph).

Then (s + 9)(mph)(4 hr) + (s)(mph)(4 hr) = 604 mi.  Solve this for s:

4s + 36 + 4s = 604 mi, or 8s = 568.  Finally, s = 71 mph, and s+9 = f = 80 mph.


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This is a linear function y=mx + b

If x = 0 then y=b, if A is the point where y intercepts y-axis, the coordinates of
A(0,b)
If you want to shift the graph up by 2 units, then you have to add 2 units to b
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3 years ago
A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the
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(a) Using Newton's Law of Cooling, \dfrac{dT}{dt} = k(T - T_s), we have \dfrac{dT}{dt} = k(T - 75) where T is temperature after T minutes.
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Since T(0) = 185, we solve for C:
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So we get \ln|T - 75| = kt + \ln 110. Use T(30) = 150 to solve for k:
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So

\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t}  \Rightarrow \\
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But choose Positive because T > 75. Temp of turkey can't go under.

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
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100 = 75 + 110(15/22)^{t/30}   \\
25 = 110(15/22)^{t/30}  
\frac{25}{110} = (15/22)^{t/30}   \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22)  \approx 116\ \mathrm{min}

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Football team had scores of 23, 15, 11, 29, and 17 in the last five games the team played. Which score is NOT a prime number?
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Given that u =&lt; 2,12 &gt;, and z =&lt; -7,5 &gt;
swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

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… = √(4•37 + 2•46 + 74)

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