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Y_Kistochka [10]
3 years ago
8

Keith as 11/12 hours to play, he has already played 1/4. which is the best estimate of the fractional part of an hour he has lef

t to play.
is greater than 0 but less than 1/4
is greater than 1/ but less than 1/2
is greater than 1/2 but less than 3/4
is greater than 3/4 but less than 1
Mathematics
1 answer:
____ [38]3 years ago
4 0

Answer:

The best estimate is greater than 1/2 but less than 3/4

Step-by-step explanation:

If you multiply 1/4 by 3/3 (which is also 1), you can change the denominator without changing the value.  So 1/4 is equal to 3/12.

Since keith has 11/12 hours to play, and he has already played 3/12 hours, subtract 3/12 from 11/12 to get 8/12 hours. This is how much time he has left to play.  

If you simplify 8/12 hours, you get 2/3 hours.

So the best estimate would be: greater than 1/2 but less than 3/4.

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Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).
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Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}

Now, differentiate to obtain

\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}

=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}

To obtain the required form, extract a factor in both the numerator and denominator:

\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)

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3 years ago
If the measure of angle 1 is (3x-4) degrees and the measure of angle 2 is (4x+10) degrees, what is the measure of angle 2 in deg
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The sum of two numbers is 51 and the greater number is twice the smaller number. Find the numbers. a) set up the variables Let _
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Answer:

  • 34 and 17

Step-by-step explanation:

a) set up the variables

Let x represent the first number Then  y will represent the second number.

b) What is the equation that represents the above situation?

  • x = 2y
  • x + y = 51

c) Solve the equation.

<u>Substitute x in the second equation and solve for y:</u>

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<u>Then find x</u>

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3 years ago
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Viefleur [7K]

(11)

the equation of a line in point- slope form is

y = mx + c ( m is the slope and c the y-intercept

thus y = 4x + 3 ← in slope-intercept form

the equation of a line in point- slope form is

y - b = m(x - a ) ( m is slope and (a, b ) a point on the line )

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the equation of a line in standard form is

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y = - 2x - 1 ← in slope-intercept form

y + 1 = - 2x ← in point- slope form

2x + y = - 1 ← in standard form




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3 years ago
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