<h3>
Answer: 2x^2 + 6x - 4</h3>
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Work Shown:
f(x) - g(x) = [ f(x) ] - [ g(x) ]
f(x) - g(x) = ( 3x^2+x-3) - ( x^2-5x+1 )
f(x) - g(x) = 3x^2+x-3 - x^2+5x-1
f(x) - g(x) = (3x^2-x^2) + (x+5x) + (-3-1)
f(x) - g(x) = 2x^2 + 6x - 4
For the perimeter you have to consider the EXTERNAL SHAPE ONLY:
a) the perimeter of half a circle WITHOUT ITS DIAMETER is:
π.R - 2R → 3.14x1.5 - 2x1.5 → 1.71 cm
b) the perimeter of the rectangle WITHOUT THE UPPER SIDE is:
2.5+3+2.5 = 8 cm
Hence the perimeter of the figure is 1.71 + 8 = 9.71 cm
2) Area of the figure:
Area of half circle is π.R²/2 →3.14 x (1.5)²/2 → Area half circle = 3.5325 cm²
Area of rectangle = 2.5 x 3 = 7.5 cm²
Total area = 3.5325 + 7.5 = 11.0325 ≈ 11 cm²
The rate of change in temperature is −17°F/min
<h3>Rate of change of a function</h3>
The formula for calculating the rate of change of a function is expressed as:
Rate of change = rise/run
This is also known as the slope of the function
Given the following parameters
Temperature = −25.5°F
Cooling time = 1.5mins
Determine the rate of change
Rate = −25.5°F/1.5min
Rate = −17°F/min
Hence the rate of change in temperature is −17°F/min
Learn more on rate of change here: brainly.com/question/8728504
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Let's look at work rates per minute.
Together they can paint the wall in x minutes.
Working together, in 1 minute, they do 1/x of the job.
The student who paints the wall in 16 minutes does 1/16 of the job in 1 minute.
The student who paints the wall in 24 minutes does 1/24 of the job in 1 minute.
Together, they do 1/16 + 1/24 of the job in 1 minute, but from above, we see that together, they do 1/x of the job in 1 minute, so 1/16 + 1/24 must equal 1/x. That gives us our equation.
1/16 + 1/24 = 1/x
1/16 * 3/3 + 1/24 * 2/2 = 1/x
3/48 + 2/48 = 1/x
5/48 = 1/x
x = 48/5 = 9.6
Answer: It takes them 9.6 minutes, or about 10 minutes to do the job together.
