Answer:
(a) The average rate of change is 0
(b) The values of x are: [tex]x =4\ or\ x = -4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 16 - x^2; [-4,4][/tex]
Solving (a): The average rate of change (m)
This is calculated using:
[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]
Where
[tex][a,b] = [-4,4][/tex]
So:
[tex]m = \frac{f(4) - f(-4)}{4 - -4}[/tex]
[tex]m = \frac{f(4) - f(-4)}{8}[/tex]
Solve f(4) and f(-4)
[tex]f(4) = 16 - (4^2) = 16 - 16 = 0[/tex]
[tex]f(-4) = 16 - (-4^2) = 16 - 16 = 0[/tex]
So:
[tex]m = \frac{f(4) - f(-4)}{8}[/tex]
[tex]m = \frac{0 - 0}{8}[/tex]
[tex]m = \frac{0}{8}[/tex]
[tex]m = 0[/tex]
Solving (b): All values of x where [tex]f(x) = m[/tex]
In (a), we have:
[tex]m = 0[/tex]
So:
[tex]f(x) = 0[/tex]
So, we have:
[tex]f(x) = 16 - x^2[/tex]
[tex]16 - x^2=0[/tex]
Express 16 as [tex]4^2[/tex]
[tex]4^2 - x^2=0[/tex]
Apply difference of two squares
[tex](4 - x)(4 + x) = 0[/tex]
Split
[tex]4 - x =0; 4 + x = 0[/tex]
Solve for x
[tex]x =4\ or\ x = -4[/tex]
We will find that the average of the function over the given interval is 0, and the two values of x such that the function is equal to the average are x = -4 and x = 4.
How to find the average of a function over an interval?
To find the average of a function f(x) over an interval [a, b] we need to compute:
[tex]\frac{f(b) - f(a)}{b -a}[/tex]
In this case we have:
f(x) = 16 - x^2
And the interval is:
[-4, 4]
We will get:
[tex]\frac{(16 - (4)^2) - (16 - (-4))^2}{4 - (-4)} = \frac{0}{8} = 0[/tex]
So the function has an average of 0 over that interval.
B) Here we just need to solve:
f(x) = 16 - x^2 = 0
We will get:
16 - x^2 = 0
16 = x^2
±√16 = x
±4 = x
So the solutions are x = 4 and x = -4.
If you want to learn more about averages of functions, you can read:
https://brainly.com/question/16033358
Answer this simple quick question!! Pls :) m
Answer:
Answer is B!
Step-by-step explanation:
58 * 20 = 1160
0+160= 160
160+1000=1160
Answer:
B
Step-by-step explanation:
58 * 20 is 1160 and 0 + 160 + 1000 = 1160
Ignore the answers and please help rn
A cylinder has a volume of 659.4 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder?
(Assume = 3.14)
A.
42 cm
B.
2.1 cm
C.
8.4 cm
D.
21 cm
The height is 8.4.
Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).
HELPPPP!!! On average, a gym claims that 65% of its members renew their memberships each year. If the gym has 440 members, predict how many will renew their members.
Answer:
260 people will renew their memberships
Step-by-step explanation:
Solve for x
Please I need help
Answer:
x=25
Let's solve your equation step-by-step.
3x+18=93
Step 1: Subtract 18 from both sides.
3x+18−18=93−18
3x=75
Step 2: Divide both sides by 3.
3x/ 3 = 75/ 3
x=25
Answer:
x=25
need ko na po this now
please answer this question
thank you po
Answer:
B.
Step-by-step explanation:
80 POINTS
Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Select three options..
A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
ANSWER:
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
Step-by-step explanation:
HOPE IT HELPS
#CARRYONLEARNING
Answer:
1, 3, 5. *please report my answer if it is incorrect.*
Step-by-step explanation:
A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
i need help please help me
Answer: D
Step-by-step explanation:
It shows the bar going left, meaning its going higher, and we only marked 2
Answer:
2 < x
Step-by-step explanation:
There is an open circle at 2, which means it is not equal to
The line goes to the right which means it is greater tha
x> 2
or 2 < x
Find the quotient of 3 2/5 ÷ 4 1/3
Give your answer as a fraction in its simplest form.
Answer:
51/65
Step-by-step explanation:
3 2/5 ÷ 4 1/3 = 51/65
51/65 is in its simplest form.
Hope this helps! :)
The value of the quotient 3 2/5 ÷ 4 1/3 is 51/65
How to evaluate the quotient?The quotient is given as:
3 2/5 ÷ 4 1/3
Convert the fractions to improper fractions
17/5 ÷ 13/3
Express as products
17/5 * 3/13
Multiply
51/65
Hence, the value of the quotient 3 2/5 ÷ 4 1/3 is 51/65
Read more about quotient at:
https://brainly.com/question/629998
#SPJ6
Who is Pemdas Orelse?
Answer:
Pemdas is a lesson in Mathematics.Step-by-step explanation:
What is the meaning of Pemdas?
The operations is rule that tells the correct sequence of steps by step for explanation's math expression.Meaning of each letter in Pemdas?
Pemdas means each letter are Parenthesis, Exponent, Multiplication, Division, Subtraction, and Addition.(ʋ◕ᴥ◕ʋ)
What is the common difference of the arithmetic sequence graphed below?
GO
an
1.
-11
1
2
3
4
5
6
7
8
9
n
-2
-3
4
5
-6
• (1.-3.75)
• (2, -4.5)
(3, -5.25)
• (4, -6)
(5.-6.75)
(6.-7.5)
• (7.-8.25)
• (8, -9)
-7
-8
-9
-10
9514 1404 393
Answer:
-0.75
Step-by-step explanation:
If the difference is common, it is the difference of any pair of adjacent y-values (for sequential x-values).
-4.5 -(-3.75) = -0.75 . . . . . difference between the first two y-values
The common difference is -0.75.
3
Select the correct answer from the drop-down menu.
Find the missing term.
) + (7 - 31) + (5 +91) + 131 = 10 - 51.
Reset
Next
what is 0.598 to the nearest whole number.
The answer is 1.
Answer: 1.
Answer:
1 I'm pretty sure
Step-by-step explanation:
59 is bigger than 50 so Im guessing it would go up to 1
I hope this helps :3
I will give you Brainiest if you are right.
Answer:
C. 3x + 6
Step-by-step explanation:
x + x + x + 1 + 1 + 1 + 1 + 1 + 1 + (-1) + (-1) =
= 3x + 6
Answer: C. 3x + 6
yoo please help me out
Answer:
70
Step-by-step explanation:
Find the measure of each numbered angle or are.
Answer:
<2 = 133degrees
<1 = 135degrees
Step-by-step explanation:
From the diagram, the angle <2 and 47 are supplementary, hence;
<2 + 47 = 180
<2 = 180 - 47
<2 = 133degrees
To get <1;
47 = 1/2(<1 - 41)
47 * 2 = (<1 - 41)
94 = <1 - 41
<1 = 94 + 41
<1 = 135degrees
20 points and brainly ;) You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?
A = p(1+r)^t
1600 = p(1+0.08)¹⁰
P = 1600/2.1589
P= 741.12
741.12 dollar money did you originally deposit into your savings account!
By visual inspection, determine the best fitting regression model for the scatter plot
Answer
Exponential
Step-by-step explanation:
5
Select the correct answer.
A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle?
ОА.
67 inches
B. 7 inches
OC, 24 inches
D.
37 inches
Reset
Next
Answer:
The length of the arc is 6.28 inches
Step-by-step explanation:
Given
[tex]\theta = 60[/tex]
Required
Length of the arc
This is calculated as:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{60}{360} * 2 * \frac{22}{7} * 6[/tex]
[tex]L = \frac{15840}{2520}[/tex]
[tex]L = 6.28in[/tex]
How do we solve for x
Answer:
Use Cross product Or Multiply both sides by 6 to get x alone
x/6 = 4/5
Multiplying 6 on both sides
we have
x=4/5 x 6
x=24/5 = 4.8
8 X 10-3 is how many times as great as 4X 10-6
Answer:
[tex]2X10^{3}[/tex]
Step-by-step explanation:
Find the values of x, y, and z
(Help please !)
Of the total babies born in America, 51.2% are boys. If 3000 babies are born in a certain hospital this year, what is the expected number of boys?
Answer:
1536 boys.
Step-by-step explanation:
Quite simple! 51.2% is 0.512, which we can use to calculate the number.
[tex]3000 * 0.512 = 1536[/tex] boys.
Alternative notation: 3000 * 51.2% = 1536
Find the answer for x
Answer:
I think the answer is 75.
Step-by-step explanation:
because 35 + 70 is equal to 105. So now we will just subtract 105 by 180. which will give us 75.
Whats the area of this thing
Answer:
341 in sq
Step-by-step explanation:
When you are finding the area of trapezoids you have to do b1+b2/2 times height because there are two bases you have to include them both so adding 40 and 22 gives 62 and you have to divide that by 2 because the numbers will be too big and way off so 62/2 = 31 and you multiply that by the height to get 341 in sq. Hope it helps :P
2.25 gal = _______?qt
Ummm I think the answer is 9
the probability that a particular song is played is 76%. What is the probability that this song will be played on exactly 2 days out of 6 days? Round your answer to the near
Answer:
0.0287
Step-by-step explanation:
Using the binomial probability relation :
p = 0.76
q = 1 - p = 1 - 0.76 = 0.24
P(x = x) = nCx * p^x * q^(n-x)
P(x = 2) = 6C2 * 0.76^2 * 0.24^4
P(x = 2) = 15 * 0.76^2 * 0.24^4
P(x = 2) = 0.02874507264
P(x = 2) = 0.0287
If you roll a standard six sided dice, what is the probability you will roll a four?
Answer using a simplified fraction.
Answer:
1/6
Step-by-step explanation:
There are 6 sides on a dice. Every time you roll you you will have one of those sides. So it is a 1 in 6 chance of you getting 4, meaning that the answer to this problem is 1/6
Someone plz help meeeee!!!!
The diagonal of a rectangle is 30 inches and the length of the rectangle is 24 inches.
What is the AREA of the rectangle?
Answer:
area=432
Step-by-step explanation:
use the Pythagoras theory now that you know the width and you'll get the length and the width then you multiply both of them hope it helps you.