Answer:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Step-by-step explanation:
The area of a sphere is given by the following formula:
In which A is the area, measured in cm², and r is the radius, measured in cm.
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.
This means that 
Determine the rate of change in surface area when r = 20 cm.
This is 
when 
. So
Applying implicit differentiation.
We have two variables, A and r, so:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
<h3>
Answer: Movie A</h3>
Q3, or third quartile, is visually located at the right edge of the box. Movie A shows to have a smaller Q3 value as it is to the left of Q3 for movie B.
Answer:
No
Step-by-step explanation:
Let's check by substituting -5 for y and -5 for x:
y > -2x + 4
-5 > -2 * (-5) + 4
-5 > 10 + 4
-5 > 14
However, we know that -5 is definitely not greater than 4, so we know that (-5, -5) is NOT a solution to the given inequality.
Hope this helps!
Answer:
t(n) = 2n² + n - 3
Step-by-step explanation:
<u>Given sequence: </u>
Find the formula for nth term t(n)
<h3>Solution</h3>
<u>Sequence is neither arithmetic nor geometric, analyzing:</u>
<u>First level difference</u>
<u>Second level difference</u>
<u>As there are two levels, the formula should be in the form of:</u>
<u>Trying the formula with the known terms:</u>
- t(2) = 4a + 2b + c = 7 ⇒ 3a + b = 7
- t(3) = 9a + 3b + c = 18 ⇒ 3(3a+b) + c = 18 ⇒ 21 + c = 18 ⇒ c = -3
<u>Going back to previous equations to find remaining coefficients:</u>
- t(1) ⇒ a+ b = 3 ⇒ t(2) = 2a + (a+b) = 7 ⇒2a + 3 = 7 ⇒ a= 2 ⇒ b = 1
<u>So the formula becomes:</u>
t(n) = 2n² + n - 3
