Answer: A: -2x^3 - 6x^2 + 9x
Step-by-step explanation:
f(x) - g(x) is a simple subtraction problem, just like 2 - 1, or 8 - 5. So, treat the functions like normal questions.
> f(x) = 3x^3 - 4x^2 + 6x
> g(x) = 5x^3 + 2x^2 - 3x
> f(x) - g(x)
Substitute these values for f(x) and g(x).
> f(x) - g(x)
> (3x^3 - 4x^2 + 6x) - (5x^3 + 2x^2 - 3x)
Now, we combine like terms*:
> For x^3: (3x^3 - 5x^3) = -2x^3
> For x^2: (-4x^2 - 2x^2) = -6x^2
> For x: (6x + 3x) = 9x
*NOTE: Remember that when there is a subtraction sign in front of a group of numbers, all the numbers inside of the parenthesis are multiplied by -1, and get their signs switched.
Putting all of these values together, we get (-2x^3 - 6x^2 + 9x).
1. 3y to the power of 25-50y
2. (5x-3y) to the power of 10
3. x to the power of 6x-25
4. x to the power of x - 28
There maybe another step here but I think you just simplify them to lowest terms.
Answer: figures C and D.
Explanation:
The question is which two figures have the same volume. Hence, you have to calculate the volumes of each figure until you find the two with the same volume.
1) Figure A. It is a slant cone.
Dimensions:
- slant height, l = 6 cm
- height, h: 5 cm
- base area, b: 20 cm²
The volume of a slant cone is the same as the volume of a regular cone if the height and radius of both cones are the same.
Formula: V = (1/3)(base area)(height) = (1/3)b·h
Calculations:
- V = (1/3)×20cm²×5cm = 100/3 cm³
2. Figure B. It is a right cylinder
Dimensions:
- base area, b: 20 cm²
- height, h: 6 cm
Formula: V = (base area)(height) = b·h
Calculations:
- V = 20 cm²· 6cm = 120 cm³
3. Figure C. It is a slant cylinder.
Dimensions:
- base area, b: 20 cm²
- slant height, l: 6 cm
- height, h: 5 cm
The volume of a slant cylinder is the same as the volume of a regular cylinder if the height and radius of both cylinders are the same.
Formula: V = (base area)(height) = b·h
Calculations:
- V = 20cm² · 5cm = 100 cm³
4. Fiigure D. It is a rectangular pyramid.
Dimensions:
- length, l: 6cm
- base area, b: 20 cm²
- height, h: 5 cm
Formula: V = (base area) (height) = b·h
Calculations:
- V = 20 cm² · 5 cm = 100 cm³
→ Now, you have found the two figures with the same volume: figure C and figure D. ←
Answer:
9 Km/h
Step-by-step explanation:
Walking 3 Km for 20 minutes from the definition of speed, it's distance covered per unit time. Here, the distance covered is expressed per unit hour.
Substituting 3.5 Km for distance and time for 20 minutes
To convert time into hours, we divide the minutes by 60 hence time=20/60=1/3 hours
Therefore, the speed is 9 Km/h
The snowman is made of 3 spheres (balls) of snow. The diameters, from top to bottom, are 12, 16, 18 inches
Therefore, the radii of the 3 spheres are, respectively, 6, 8, and 9 inches.
The volume of a sphere of radius, r, is given by the formula: V = 4/3 π r3
So, the total volume of snow is the sum of the 3 volumes: V = 4/3 π (63 + 83 + 93)
= 4/3 π (1,457)
=6,099.97
Your answer would be D. 6,099.97
I hope this helps!
