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labwork [276]
3 years ago
6

For the differential equation s′′+bs′+6s=0, find all the values of b that make the general solution overdamped, those that make

it underdamped, and those that make it critically damped. (For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range 2

Mathematics
1 answer:
djyliett [7]3 years ago
6 0

Answer:

<em><u>note:</u></em>

<em><u>solution is attached</u></em>

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The approximate length of each highway in kilometers is 200.
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A cup of coffee has approximately 310 mg of caffeine. Each hour, the caffeine in your system decreases by about 35%. How much ca
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Answer:

∴35.97 mg caffeine would be left in the system after 5 hours.

Step-by-step explanation:

Given that,

A cup of coffee has approximately 310 mg of caffeine.

Caffeine decrease at a rate 35% per hour.

Exponential Function:

y(t)=y_0(1-r)^t

y(t)= Amount caffeine after t hours

y_0= Initial amount of caffeine

r= rate of decrease

t = Time in hour.

Here y(t)=?, y_0 = 310 mg, r=35%=0.35, t= 5 hours

y(t)=310(1-0.35)^5

      =35.97 mg

∴35.97 mg caffeine would be left in the system after 5 hours.

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3 years ago
A school requires an entrance exam score that is in the top 3% of the population in order to be accepted.
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A. 485 is %3 of 500, but the deviation sets it slightly lower than that
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A rectangle on a coordinate plane has vertices (-1.1), R(6, 1). S(6.-8), and T(-1,-8). What are the dimensions of the
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Answer:

b. the base is 9 and the height is 6

Step-by-step explanation:

6 0
2 years ago
Can somebody help me, please?
Sveta_85 [38]

Answer:

a.x=10 \textdegree

b.

m\angle L=39\textdegree\\\\m\angle M=51\textdegree\\\\m\angle K=90\textdegree

Step-by-step explanation:

a. We know that angles in a triangle add up to 180°.

-The right angle triangle in the right triangle has a measure of 90°.

We can therefore equate our angles to 180° and solve for x;

180=\perp\angle+(2x+19)+(3x+21)\\\\180=90+(2x+19)+(3x+21)\\\\90=5x+40\\\\5x=50\\\\x=10\textdegree

Hence, the angle measure is x=10°

b. Having calculated the value of x from a above as x=10°, we can substitute to find the measures of the two acute angles:

m\angle L=(2x+19)\textdegree\\\\=(2\times 10+19)\textdegree\\\\=39\textdegree\\\\m\angle M=(3x+21)\textdegree\\\\=(3\times 10+21)\textdegree\\\\=51\textdegree

Since, the m∠K is a right angle, it measures 90°

8 0
3 years ago
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