Answer: the population be after 10 years is 289145
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^t
Where
y represents the population after t years.
t represents the number of years.
b represents the initial population.
r represents rate of growth.
From the information given,
b = 210000
r = 3.25% = 3.25/100 = 0.0325
t = 10 years
Therefore,
y = 210000(1 + 0.0325)^10
y = 210000(1.0325)^10
y = 289145
Answer:
Therefore the greatest number of cookies she can put each bag is 14.
Step-by-step explanation:
Given that Anna has made 30 chocolate chip cookies and 54 sugar cookies.
First we have to find out the number of fried or the number of bags.
So to find the number of bags, We need to find out the G.C.D of 30 and 54.
30=5×3×2
54=3×3×3×2
The common divisor of 30 and 54 is = 3×2 = 6
∴The G.C.D of 30 and 54 is 6.
The number of bags is 6.
The number of chocolate cookies each bags is
=(The number of chocolate cookies÷ 6)
=30÷6
=5
The number of sugar cookies each bags is
=(The number of sugar cookies÷ 6)
=54÷6
=9
Therefore the greatest number of cookies she can put each bag is (5+9)=14.
If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer:
r = 10.72 cm
Step-by-step explanation:
h = 6 cm
Volume of cone = 722 cubic cm
note that the zeroes should be x = 1 and x = - 2 not x = - 1 and x = 2
the factors are then ( x - 1 ) and (x + 2)
and x³ - 4x² - 7x + 10 = (x - 1 )(x + 2) = x² + x - 2
thus x² + x - 2 is a factor
dividing x³ - 4x² - 7x + 10 by x² + x - 2 gives x - 5
the third zero is x = 5
check : (5)³ -4(5)² - 7(5) + 10 = 125 - 100 - 35 + 10 = 0
