I believe you meant "at the rate of 4.3% per year." The general formula for exponential growth is:
P(t) = P0·(1+rate)t/p
P(t) = population at year t
P0 = starting population = 108
rate = growth rate expressed as a decimal = 0.043
t = years = 5
p = period...
Two ways to do it.
First, multiply the RHS out then differentiate using the Sum and Power rules:
g(x) = x2(1-8x)
g(x) = x2 - 8x3
g'(x) = d(x2)/dx - d(8x3)/dx
Mass = Density × Volume
The problem gives you the density and volume, so just plug them in and compute the answer.
Let x be the unknown number. Its reciprocal is 1/x.
x + 1/x = 29/10
Multiply both sides by 10x to get rid of the denominators:
10x2 + 10 = 29x
10x2 - 29x + 10 = 0
Solve for x by factoring (it does factor) or by using...
Here's one method. It's how I add in my head:
9.73 + 21.6
= 9 + 0.73 + 21 + 0.60 (separate the decimals from the whole numbers)
= 9 + 21 + 0.73 + 0.60 (group the whole numbers and the decimals)
y= 3x - 1
It's easy. Pick any value of x, say x=1, and plug that value into the equation and compute the y value:
y = 3x + 1
y = 3·1 + 1 (plugged in 1 for x)
y = 3 + 1
P(no heads) = (1/2)6
P(at least one heads) = 1 - (1/2)6
Divide 486.52 by 2:
_2_4 3 . 2 6
2 ) 4 8 6 . 5 2
General Burnside replaced General McClellan as the commander of the Army of the Potomac on November 5, 1862. Burnside was not "sent" to replace McCellan as Burnside was already a corps commander in the Army of the Potomac and was present with the army.
Let x = the amount of time needed to fill the tank:
1/6 - 1/9 = 1/x
Solve for x.
Two more (+2) than a number (x) is less than (<) 13:
x + 2 < 13
The formula for the area of a trapezoid is:
A = h·(B1+B2)/2
Solving for B1:
A = h·(B1+B2)/2
2A/h = B1 + B2
2A/h - B2 = B1
B1 = 2·60/6 - 12
B1 = _____?
A(t) = P [1+(r/n)]nt
A(t) = value of investment at year t
P = initial value of the investment = $940
r = rate as a decimal = 6% = 0.06
n = number of compoundings per year = annual = 1
t = years = 6
Plug in the numbers and use your calculator to get the answer...
To graph a parabola, you need to know:
Does the parabola open up or down
The position of the vertex
The axis of symmetry
The x-intercepts (if any)
The general factored form is y = a(x-p)(x-q) where p and q are the x-intercepts and a is a constant...
The general standard form for a hyperbola with a vertical major (transverse) axis is:
(y-k)2/a2 - (x-h)2/b2 = 1
k = y-coordinate of center = 5
h = x-coordinate of center = -7
a = semi-major (transverse) axis = 18/2 = 9
b = semi-minor (conjugate) axis = 8/2 = 4
Set up a proportional relationship of oranges/cost:
6/(0.99) = 10/x
Solve for x.
f'(c) = (f(b)-f(a))/(b-a)
-4e-4c = (e-4·2 - e-4·0)/(2-0)
-4e-4c = (e-8 - e0)/2
-4e-4c = (e-8 - 1)/2
e-4c = (1 - e-8)/8
-4c = ln((1-e-8)/8)
c = -(1/4)ln((1-e-8)/8)
Use your calculator to compute...
I'm guessing you meant (3/2)pi (=3pi/2) and not 3/(2pi). First, compute the total number of radians that the hoop turns through in one minute (60 seconds):
(3pi/2 radians/sec)(60 sec) = 90pi radians
There are 2pi radians in one full revolution, so the number of...
f(x) = x2 + 1
g(x) = x - 5
f(g(x)) = g(x)2 + 1 = (x-5)2 + 1
Can you finish it from here?
f(g(x)) = x2 - 10x + 26
g(f(x)) = f(x) - 5 = x2 + 1 - 5 = x2 - 4
f(g(x)) = f(g(x))
x2 - 10x + 26 = x2 - 4
Solve for x...
Test the discriminant, b2 - 4ac where a=7, b=8, and c = -6.
If the discriminant is > 0, the graph will cross the x-axis twice
If the discriminant is = 0, the graph will touch the x-axis once but not cross it
If the discriminant is < 0, the graph will not cross the x-axis...