The equation for continually compounded interest is: A = Pert, where
A = final amount, P = principal invested, r = rate in decimal, and e is the constant.
Since you want to double your investment, let A = 2p.
Thus makes the equation 2P = P e.08t
So:...

So, V = (1/3)πr2h, and h = 14 m., when d = 6.5 m. = 13/2 m., which means r = ½d = 13/4 m.
dV/dt = (-0.008 + k) m3/min (leaking 0.008 and increasing by a constant,m k) at the time when h = 2.5 m. and dh/dt = +.28 m/min.
I would stat by finding...

Since you have the four x intercepts, the equation can be written as:
f(x) = a(x+2)(x+1)(x-1)(x-2).
Use the point given to find the value of a.

let y = -sin(x+5) - 9.
exchange y and x.
x = -sin(y+5) - 9
Solve for y: sin(y+5) = -x - 9.
How do you solve this? Try using the inverse sin of each side.
Good luck.

If sin-1x = π/6, remember what the notation say. It says "the angle whose sine is x, equals π/6."
Therefore, this becomes: sin π/6 = x.
Using the special triangle (30-60-90) says that x = ½.

Sin(A - B) = sinAcosB - cosAsinB
(sinAcosB - cosAsinB)/sinAcosB = sinAcosB/sinAsinB - cosAsinB/sinAsinB.
There is a start. Can you finish?
(hint: Look for common factors)

Remember the double angle formula?
cos(2θ) = cos2θ - sin2θ = 2cos2θ - 1 = 1 - 2sin2θ.
Since your equation has a sin2θ, let's use the last one.
That makes the equation 1 - 2sin2θ + 6sin2θ = 2.
Subtract 1 and combine terms: 4sin2θ...

OK, Irene. I believe your equation is: 2/(w+2) - 3/w + (w+10)/(w2-4).
If this is correct, the LCD (least common denominator) is w(w-2)(w+2).
The first term only has (w+2) and therefore, needs to be multiplied by w(w-2)/(w)(w-2).
The...

Hi, Rachel.
Again, the slopes are the same, i.e. m = -1.
Using the slope, and the y intercept, (0, 6), and the equation: y = mx + b (slope y-intercept form)
we get y = -x + 6. Try this with your 3 points, and you will see they check.
I...

OK, Rachel.
The slopes between any two points of a linear function are the same. Remember that the slope is defined as the change in y, divided by the change in x.
That is: (y2 - y1)/(x2 - x1).
So the slope between the first two points: (-4...

Jasmine,
The ratio is 3:1:2. Let x = mango trees, this makes 2x = orange and 3x = banana.
Since the total is to be 500, 3x + x + 2x = 500
That makes 6x = 500, and therefore, x = 83.33 acres, 2x = 166.67 acres, and 3x = 250 acres.
What...

Molly, let the three integers be x, x+1, and x+2, since consecutive means in order each one unit from the previous.
Translating the problem gives us: -5(x + (x + 2)) = 4(-(x+1)) + 24.
(Remember, the "opposite" means the additive...

6x6x6=63, and (6x6x6)6 means 63x61 = 64.
Now, if you mean (6x6x6)6 then you have (63)6. The rule here says to multiply the exponents: 618.

Factor 5: 5*1
7: 7*1
21: 7*3*1
Therefore, the smallest number divisible by 5, 7, and 21 is 5*7*3 =
105. 105/5 = 21, 105/7 = 15, 105/21 = 5.

I see you have the factors. Great. Not that there is a pair that are equal. If these are divided out, we get:
f(x) = −5(x + 7)
...

Let's use synthetic division. f(x) / (x - c). In dividing by x + 4, to find c, let x + 4 = 0.
This makes x = -4, so c = -4.
Use the c, and the coefficients, 1, 1, and -12. We will...

It means that somewhere between the values x = 2, and x = 3, the graph of f(x) = 0, or crosses the x axis. since the signs of f(x) change from a positive number to a negative number.
In other words, the zero of the function f(x) is between 2 and 3. It appears that it may cross...

Note that this is still a rectangle, and the length of the fencing is still 600 ft.
...

OK. So f(x) = x2-5, and g(x) = √(x+5).
f(4) = 16 - 5 = 11, and g(4) = √9 = 3.
So (f/g)(4) = 11/3.
Since the only restriction on x on the function (f/g)(x) occurs when g(x) ≠0, the domain of this function is x>-5 (since the radical must be...

... or 2(n-3)(n-2)