Yes it is a rational number.
Volume of the tablet is height times pi r squared = .4cm x pi x .5^2 = pi cm^3
So, the tablet has a volume of pi cubic centimeters (cc).
We want the capsule to have the same volume. The two hemispherical ends put together make one sphere. The volume of a sphere is 4/3 pi r^3. And the cylindrical part is the same formula as the first one, but we don't know what r is,
height x pi x r^2.
pi cc = height x pie x r^2 + 4/3 pi r^3 Here, we took the value from the original problem and made it equal to the two ends of the capsule (together were the sphere) PLUS the rest (which is a cylinder.)
Now, divide everything by pi to factor it out of the equation.
cc = height x r^2 + 4/3 r^3 The problem told us that the total length is 5/3 cm, this means the cylinder height + the radius times two = 5/3. (Wish I could draw you a picture) So height in the equation at the beginning of this paragraph is 5/3 - 2r.
Now we have volume in cc = (5/3 - 2r)r^2 + 4/3 r^3 =
5/3r^2 - 2r^3 + 4/3r^3
simplified by combining common terms, and written in standard form,
volume in cc = 2 r^3 + 5/3 r^2 = 1 = r^2 ( r - 5/3) , factoring out the r^2.
this means that r^2 is the reciprocal of r - 5/3, or r^2 = 1/(r - 5/3), and this is a quadratic equation.
r^2 - r + .6 = 0 and r^2 -r + .25 = -.6 + .25 by completing the square
or (r - .25)^2 = -.35. Solve for r: square root of r - .25 = square root of .35 or .59
r = .84 cm
Let's make a table of differences
0 3 8 15 24
3 5 7 9
2 2 2
Constant second difference means a quadratic polynomial,
f(n)=an² + bn +c
f(1)=0, f(2)=3, f(3)=8
0 = a+b+c
3 = 4a + 2b + c
8 = 9a + 3b + c
Subtracting pairs
3 = 3a+b
5 = 5a + b
Subtracting,
2 = 2a
a = 1
b = 5 - 5a = 0
c = -a-b = -1
f(n)=n² -1
Duh, shoulda noticed that at the beginning.
f(17)=17²-1 = 288
a₁ =5
aₙ = aₙ₋₁ - 7
aₙ = a₁ + d(n-1)
aₙ = 5 - 7(n-1)
a₇ = 5 - 7(6) = -37
Answer: -37
Answer:
Most credit card companies also apply a late payment penalty if you owe a balance and do not make a payment. Ignoring that fee, Miriam's balance will increase as:
B(n) = 750(1.018)^n
where B(n) is Miriam's balance after n months. The progression will be:
$750.00
$763.50
$777.24
$791.23
$805.48
Step-by-step explanation:
Answer:
5x- 9 is your expression
Step-by-step explanation:
Decreased means subtraction and the product of any two numbers is multiplication.
Division Keyword: Divided by, or Quotient of.
Multiplication Keyword: Product of, or Multiplied by.
Subtraction Keyword: Subtracted from, or Decreased by.
Addition Keyword: Added to, or Increased by.
If there is no Variable then place the common Variables: X, Y, Z.
