Im confused. Its not equal to any of the choices
Unless C is the cube root of 32^5.
[t3] \sqrt[n]{x} [32^5]
So 8x3 = 24
24 + 12x
the common factor is 12
so you divide everything by 12
24 ÷ 12 = 2
12x ÷ 12 = x
final answer: 12 (2+x)
Answer:
7. r = -5
8. x = -1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
r + 2 - 8r = -3 - 8r
<u>Step 2: Solve for </u><em><u>r</u></em>
- Combine like terms: -7r + 2 = -3 - 8r
- Add 8r to both sides: r + 2 = -3
- Subtract 2 on both sides: r = -5
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: -5 + 2 - 8(-5) = -3 - 8(-5)
- Multiply: -5 + 2 + 40 = -3 + 40
- Add: -3 + 40 = -3 + 40
- Add: 37 = 37
Here we see that 37 does indeed equal 37.
∴ r = -5 is a solution of the equation.
<u>Step 4: Define equation</u>
-4x = x + 5
<u>Step 5: Solve for </u><em><u>x</u></em>
- Subtract <em>x</em> on both sides: -5x = 5
- Divide -5 on both sides: x = -1
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: -4(-1) = -1 + 5
- Multiply: 4 = -1 + 5
- Add: 4 = 4
Here we see that 4 does indeed equal 4.
∴ x = -1 is a solution of the equation.
Answer:
The rate of change of the volume of the cylinder at that instant = 
Step-by-step explanation:
Given:
Rate of increase of base of radius of base of cylinder = 7 mm/hr
Height of cylinder = 1.5 mm
Radius at a certain instant = 12 mm
To find rate of change of volume of cylinder at that instant.
Solution:
Let 
represent radius of base of cylinder at any instant.
Rate of increase of base of radius of base of cylinder can be given as:
Volume of cylinder is given by:
Finding derivative of the Volume with respect to time.
Plugging in the values given:
Using 
(Answer)
Thus rate of change of the volume of the cylinder at that instant =
(((1/y - 1) + (5/12)) = (-2/3y - 3))
((((1)(12)/12(y - 1) + (5(y + 1)/12(y + 1) = (-2/3y - 3))
((12/12y - 12) + (5y + 5/12y - 12)) = (-2/3y - 3))
((5y + 17/12y - 12) = (-2/3y - 3)
(12y - 12/5 + 17) × (5y + 17/12y - 12) = (-2/3y - 3)(12y - 2/5 + 17)
y = -21y + 4/66y - 66
y = -7/22 - 2/33
y = -25/66
