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Lana71 [14]
3 years ago
5

If the population of a country grows at a rate of approximately 5 percent per year, the number of years required for the populat

ion to double is closest to
Mathematics
1 answer:
iogann1982 [59]3 years ago
8 0
THe number of years would be 20 years.
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The measure of one base angle of an isosceles triangle is 35 degrees. What is the measure of the vertex angle?
Elis [28]

Answer:

110 degrees

Step-by-step explanation:

The measures of the two base angles of an isosceles triangle are the same so  180 - 2(35) = 110 which is the vertex angle.

8 0
3 years ago
Convert the 55.68 feet swam by the sea horse to inches
saveliy_v [14]
464 inches. Hope this helped! :)
6 0
3 years ago
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A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the
Naya [18.7K]

Answer:

The area is growing at a rate of \frac{dA}{dt} =226.2 \,\frac{cm^2}{min}

Step-by-step explanation:

<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>

We identify that the info given on the increasing rate of the circle's radius is 3 \frac{cm}{min} and we identify such as the following differential rate:

\frac{dr}{dt} = 3\,\frac{cm}{min}

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find  \frac{dA}{dt}.

So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

A=\pi\,r^2

We now apply the derivative operator with respect to time (\frac{d}{dt}) to this equation, and use chain rule as we find the quadratic form of the radius:

\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}

Now we replace the known values of the rate at which the radius is growing ( \frac{dr}{dt} = 3\,\frac{cm}{min}), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}\\\frac{dA}{dt} =\pi\,*2*(12\,cm)*(3\,\frac{cm}{min}) \\\frac{dA}{dt} =226.19467 \,\frac{cm^2}{min}\\

which we can round to one decimal place as:

\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}

4 0
3 years ago
Question in the photo
ivann1987 [24]

Answer:

  the exponent of x is 4

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

__

  \dfrac{6xy^{-2}}{x^{-3}}=\dfrac{6x^{1-(-3)}}{y^2}=\dfrac{6x^4}{y^2}

6 0
3 years ago
George has $3.71 in pennies,nickels dimes and quarters in his pocket. He has twice as many dimes as nickels, two more nickels th
FromTheMoon [43]
<span>pennies = 0.01 $
 nickels = 0.05 $
 dimes = 0.1 $
 quarters = 0.25 $
 We must write the system of equations that best suits this problem and solve it:
 Let:
 x = pennies
 y = nickels
 z = dimes
 w = quarters
 Writing the equations
 0.01x + 0.05y + 0.1z + 0.25w = 3.71
 I have twice as many dimes as nickels
 z = 2y
 two more nickels than quarters
 y = w + 2
 three fewer pennies than three times the number of nickels
 x = 3y-3.
 Solving the system of equations:
 x = 21
 y = 8
 z = 16
 w = 6
 answer
 He has
 21 pennies
 8 nickels
 16 dimes
 6 quarters
</span>
4 0
3 years ago
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