Hello,
Use the factoration
a^2 - b^2 = (a - b)(a + b)
Then,
x^2 - 81 = x^2 - 9^2
x^2 - 9^2 = ( x - 9).(x + 9)
Then,
Lim (x^2- 81) /(x+9)
= Lim (x -9)(x+9)/(x+9)
Simplity x + 9
Lim (x -9)
Now replace x = -9
Lim ( -9 -9)
Lim -18 = -18
_______________
The second method without using factorization would be to calculate the limit by the hospital rule.
Lim f(x)/g(x) = lim f(x)'/g(x)'
Where,
f(x)' and g(x)' are the derivates.
Let f(x) = x^2 -81
f(x)' = 2x + 0
f(x)' = 2x
Let g(x) = x +9
g(x)' = 1 + 0
g(x)' = 1
Then the Lim stay:
Lim (x^2 -81)/(x+9) = Lim 2x /1
Now replace x = -9
Lim 2×-9 = Lim -18
= -18
The answer is 36 pls mark me brainliest:)
Answer:
The portion of the volume of the cup that is filled with water is 
Step-by-step explanation:
step 1
Find the volume of the paper water cup
The volume of the cone is equal to
we have
substitute
step 2
If the cup is filled with water to half its height, find out what portion of the volume of the cup is filled with water
Remember that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
In this problem the similar cone has half the height of the complete cone
so
The scale factor is equal to 1/2
therefore
The volume of the cup that is filled with water is equal to the volume of the complete cup by the scale factor elevated to the cube
therefore
The portion of the volume of the cup that is filled with water is
Match the mean, median, mode, and range for the data set below. 2, 7, 8, 4, 8, 2, 5, 5, 7, 2
dusya [7]
Answer:
Mean - 5
Median - 5
Mode - 2
Range - 6
Step-by-step explanation:
Mean-
If you add 2 + 7 + 8 + 4 + 8 + 2+ 5+ 5+ 7 +2= 50
50 divided by 10 (the amount of numbers in the equation) = 5 for the mean
Median-
Put the numbers in order which is
2,2,2,4,5,5,7,7,8,8 and the number is the middle is 5
Mode-
The number that repeats the most is 2
Range-
The largest number is 8 and the smallest number is 2 so 8-2=6
52/2= 26
12/2= 6
26-6= 20
26+6= 32
20+32=52
Ans: 20 and 32
