Answer:
[tex]\displaystyle f'(16) = \frac{1}{32}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle f(x) = \sqrt[4]{x}[/tex]
f'(16) is x = 16 for the derivative f'(x)
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle f(x) = x^{\frac{1}{4}}[/tex]Basic Power Rule: [tex]\displaystyle f'(x) = \frac{1}{4}x^{\frac{1}{4} - 1}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{1}{4}x^{\frac{-3}{4}}[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle f'(x) = \frac{1}{4x^{\frac{3}{4}}}[/tex]Step 3: Solve
Substitute in x [Derivative]: [tex]\displaystyle f'(16) = \frac{1}{4(16)^{\frac{3}{4}}}[/tex]Evaluate exponents: [tex]\displaystyle f'(16) = \frac{1}{4(8)}[/tex]Multiply: [tex]\displaystyle f'(16) = \frac{1}{32}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
There are two bags of oranges on sale. The prices are shown below: Bag A: $2400 containing 12 oranges Bag B: $3000 containing 20 oranges Which is the better buy?
Answer:
Bag B which is $150 for one orange
Step-by-step explanation:
In ,bag A 12 oranges cost 2400
The price of one orange in bag A is
= 2400/12
= $200
In bag B 20 oranges cost $3000
The cost of one orange in bag B is
= 3000/20
= $150
Hence the better buy is bag B which goes for $150 for one orange
Find the equation of a straight
line passing through the point of
intersection of the lines
y = 2x +3 and x +y = 3 and
parallel to the line y = -5x +7
Answer:
y = -5x + 3.
Step-by-step explanation:
We can find the point of intersection by solving the system:
y = 2x + 3 .... 1
x + y = 3 ...... 2 from this:
y = 3 - x ....... .3
Equating equations 1 and 3:
2x + 3 = 3 - x
3x = 0
x = 0 so y = 2(0) + 3 = 3.
So the point of intersection is (0, 3).
So the required equation has slope -5 and passes through (0, 3) and, using the point-slope form of a straight line, we have:
y - 3 = -5(x - 0)
y - 3 = -5x
y = -5x + 3.
how many cups is 5 1/8 gallons
Answer:
82 Cups
Step-by-step explanation:
Which expressions simplify to a single term?
Answer:
c and d
Step-by-step explanation:
I think this is it sorry if wrong but i tryed really hard i am not good at math dont take this down pls.
The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is What is the value
of b?
-18
-9
9
18
Answer:
B.) -9
Step-by-step explanation:
The value of b if 3/2 is the axis of symmetry for the graph of the function f(x)=3x2+bx+4 is -9
How to calculate the axis of symmetry of a function?The standard equation of a function in vertex form is given as:
f(x) = (a + x)^2 + h
Given the function f(x)=3x^2+bx+4 with an axis of symmetry of 3/2, the vertex is expressed as:
3/2= -b/2a
-b/2(3)=3/2
-b/6=3/2
Cross multiply
-2b = 18
-b=9
Hence the value of b if 3/2 is the axis of symmetry for the graph of the function f(x)=3x2+bx+4 is -9
Learn more on axis of symmetry here: https://brainly.com/question/21191648
PLEASE HELP I ONLY HAVE 10 minutes
In Mr. Forester's science class,
students are given five tests in a
semester. Latoya's scores on the first
four tests are 86%, 82%, 91%, and
98%. If Latoya's score on the final
test is represented by x, then her
class average y can be found using
the equation below.
y =
86% + 82% + 91% + 98% + x
5
Mr. Forester awards an "A" to any
student whose class average falls
within the 90 - 100% range. Which
interval represents the domain of final
test scores that Latoya can get and
still receive an "A"?
F [90%, 100%]
G [87%, 100%]
H [93%, 100%]
[96%, 100%]
Answer:
The answer is "H [93%, 100%]"
Step-by-step explanation:
I'll edit this in a second to show the process, but it may take a minute. Just have the answer for now.
This is a surprisingly useful question hah, I'll bet many will need to do this.
This question is just finding the average. Pretty simple.
y = 86 + 82 + 91 + 98 + x / 5
y = 357 + x / 5
An easy way is to do the lowest question first, then go from lowest to second lowest and so on. Because if you go to the highest one and the answer is one of the lower ones, well, of course it's going to be within the 90-100 range, but that doesn't necessarily mean it's the answer.
y = 357 + (87) / 5
y = 444 / 5
y = 88.8
Okay, so the answer isn't G. Then let's try H.
y = 357 + (93) / 5
y = 450 / 5
y = 90
Yep, the answer is H. This is because it equals 90, which is indicative of the 90-100% range that Latoya needs to get an "A".
If 2y =a and y =3x +12 what is a?
Step-by-step explanation:
2y=a
y=a/2
putting value of y
y=3x+12
a/2=3x+12a=6x+24stay safe healthy and happy ...Bro this is so simple but I don't know. At the party, jorden shared out all the loonies in his present. Altogether there was 47 Lolies and 6 boys. How many lollies were leftover.
Answer:
5 lollies are left over
Step-by-step explanation:
Total lollies Jordan has = 47
Number of boys at the party = 6
If the lollies are shared equally,
Number of lollies each boy gets = Total lollies ÷ number of boys
= 47 ÷ 6
= 7 lollies remainder 5
That is,
6 boys × 7 lollies each = 42 lollies
How many lollies were leftover.
Remaining lolly = Total lollies - shared lollies
= 47 - 42
= 5 lollies are left over
Find the arch length
(Give an exact answer & show work)
Answer:
12.56637
Step-by-step explanation:
[tex]Arc length = 2\pi r(\frac{0}{360}) \\Arc lenght = 2\pi 6(\frac{120}{360} )[/tex]
At the Valero gas station, gas costs $2.55 per
gallon. The RV holds 55 gallons of gas. If the
RV currently has 20 gallons of gas, how much
will it cost to completely fill the RV with gas?
Answer:
140.25$
Step-by-step explanation:hope this helps <3
Answer:
Step-by-step explanation: valero gas station gas cost 2 dollars. 55 per gallon
55 + 20
An equilateral triangle has perimeter P. The length of one side is P/3. Which expression is equivalent to the length on one side
Answer: [tex]3\times \dfrac{P}{3}=P[/tex]
Step-by-step explanation:
Given
The perimeter of one equilateral triangle is P
The lengths of the equilateral triangle are equal
Suppose x is the length of each side
[tex]\therefore 3\times x=P\\\\\Rightarrow x=\dfrac{P}{3}[/tex]
i.e.
[tex]\Rightarrow 3\times \dfrac{P}{3}=P[/tex]
Which two triangles below are similar?
Answer:
Triangle A and B
Step-by-step explanation:
Both triangles have two same angles.
If Triangle A is rotated like Triangle B, they would be the same.
Vice versa, if Triangle B is rotated like Triangle A, it would be the same.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Hey ASAPPP PLS 80 points
Answer:
using pythagoras theorem
a^2+b^2=c^2
8^2+x^2=(x+2)^2
64+x^2=x^2+2*x*2+2^2
64+x^2=x^2+4x+4(here x^2 of left hand side and x^2 of right hand side gets cancel)
64=4x+4
64-4=4x
60/4=x
15=x
Step-by-step explanation:
A group of 7 students was asked, "How many hours did you watch television last week?" Here are their responses.
12, 5, 14, 6, 17, 7, 15
Send data to calculator
Find the mean number of hours for these students.
If necessary, round your answer to the nearest tenth.
Answer:
10.9
Step-by-step explanation:
The "mean" is just school's fancy way of saying "the average". To find the mean of the numbers, you add them all up first. 12 + 5 + 14 + 6 + 17 + 7 + 15 = 76. The next step is to divide 76 by the number of values that were added. 12, 5, 14, 6, 17, 7, and 15 are a total of 7 numbers. So, we will divide 76 by 7.
76/7 = 10.8571428571, which rounds to 10.9 if you are rounding it to the nearest tenth.
Answer:
[tex]\boxed {\boxed {\sf 10.9 \ hours }}[/tex]
Step-by-step explanation:
The mean is also called the average. It is a measure of central tendency and provides information about the center of a data set.
The mean is found by adding up all the values, then dividing by the number of values. Remember, this is the data set we have:
12, 5, 14, 6, 17, 7, 15
1. Add up values
12 + 5+ 14 + 6 + 17 + 7 + 15= 76
2. Divide by the number of values
There are 7 values ( 1 for each student)76/7=10.8571428571
3. Round
We need to round our answer to the nearest tenth. The 5 in the hundredth place tells us to round the 8 up to a 9.10.8571428571 ≈ 10.9
The mean number of hours spent watching television for this group of students is 10.9 hours.
A 7 character computer password is made up of 3 letters followed by 4 numbers. How many different passwords are possible?
Answer:
the answer is 456,976,000
Answer:
✅ C. 456,976,000⬇️ i got it right
One juice and to sandwiches cost $70.00. One juice and four sandwiches cost $130.00.
What is the cost of one sandwich?
Step-by-step explanation:
One juice and to sandwiches cost $70.00. One juice and four sandwiches cost $130.00.
What is the cost of one sandwich?
Answer:
One sandwich costs $30
One juice costs $10
Which is the equation of a parabola with vertex (0, 0), that opens to the left and
has a focal width of 12?
a. y2 = 12x
b. y2 = -12x
c.x = 12y
d. x = -12y
Answer:
Step-by-step explanation:
I'm going to guess that the square exponents are on the top y's only? then answer b) looks good
Answer:
b. y^2 = -12x
Step-by-step explanation:
The general form for the given parabola is y^2 = -4ax where the focus is at (-a, 0). The focal width is 4a which in this case = 12.
how many times can 495 go into 156
Answer:
0
Step-by-step explanation:
Answer:
0.315 times
Step-by-step explanation:
156÷495 ≈ 0.315
Have a good day :)
The type of number that cannot be expressed as a fraction because the fractional part would go on for infinity without ever repeating a sequence is:
PLEASE HELP ME FAST! WILL GIVE BRAINLIEST.
What is the length of the segment joining the points at (−3, 0) and (5, 6)?
Enter your answer in the box.
units
Answer- √ 26
Explanation:
Use the distance formula:
√ ( y 2 − y 1 )² + ( x 2 − x 1 ) ²
Plug in your values:
√ ( − 5− ( − 4 ) )² + ( 2 − ( − 3 ) )²
Simplify:
√ ( − 1 )² + ( 5 )²
Simplify:
√ 1 + 25
Simplify:
√ 26
-----------------------------------------------------
Anyways bye!
solve the equation 5(x-1)=17
Answer:
5(x-1) = 17
5x - 5 = 17 (write equation in simpler terms)
add 5 on each side like this (5x = 17 + 5)
= 5x = 22 which results in 4.4
simplify 2(2x-y)-4(x-y)+3y
please give the answer if you know how to solve it
Answer:
2( 2x - y ) -4( x - y ) +3y
4x - 2y - 4x + 4y + 3y
-2y + 4y + 3y
-2y +7y
5y
I NEED THIS ASAP!!! What is GC?
9514 1404 393
Answer:
D. 14
Step-by-step explanation:
Point G divides each median into parts that have the ratio ...
short : long = 1 : 2
Then ...
GD : GC = 1 : 2 = 7 : 14 . . . . . . . . multiply the ratio by 7
GC = 14
A jar contains 6 red marbles, 3 green marbles, 5 white marbles, and 7 yellow marbles. Find the probability of drawing a green marble. All answers should be given as a fraction in simplest form!
Any help is appreciated! Thanks!
Answer:
simple - 1/21 chance
Step-by-step explanation:
since its asking for the probability of "a" marble, and not all the green marbles, you add everything up and slap what outcome (1 in this case) on top of the 21
here is cat
Answer:
3 is for green marbles
21 is the total of all marbles
Step-by-step explanation:
you only have 1 event so I think we don't need some formula or something
the formula is this if the event A and B has no intersection P( A U B)= P(A)+P(B)
and if it has intersection, the formula is like this P( A ∩ B)=P(A)+P(B)-P( A ∩ B)
Complete the table of values for y = x2 - 2
Answer:
x = -1
Step-by-step explanation:
LOCO LOOOCOOOO LOCO LOOOOCOOO
I have an average of 84 right now but I failed my homework so that would most likely turn to an 82 and my parents will actually kill me I need to get to at least an average of 90 minimum I know report cards will be out soon and I will guess I have a week before marking period three ends could I boost my average up by 6-8% within a week of getting straight hundreds in my homework? Homework’s count a lot.
Answer:
I would say yes. Now I'm not in your type of school grading system, but if you try to get as many 90s and 100s in your homework for the next week, you would probably get there.
Step-by-step explanation:
Good luck! I know you will do great.
Which of these are the coffenent?
4y+1+9x
Answer:
coefficient*
Your coefficients are 4 and 9
Why?
Because the number attached to the variable will always be your coefficient.
The Ace Bicycle Shop charges a flat fee
of $4, plus $1 per hour, for the hire of a
bicycle. The Best Bicycle Shop charges
a flat fee of $8, plus 50 cents per hour.
Connie and her friends hire three bicycles
from Ace, and David and his brother hire
two bicycles from Best. After how many
hours will their hire costs be the same?
Answer:
x = number of hours = 8 hours
Step-by-step explanation:
Let
x = number of hours
There are 3 people who rented bicycle from each shop
Ace bicycle shop:
Total cost = 3(4 + x)
= 12 + 3x
Best bicycle shop:
Total cost = 3(8 + 0.50x)
= 24 + 1.5x
Equate both equations and solve
12 + 3x = 24 + 1.5x
12 - 24 = 1.5x - 3x
-12 = -1.5x
x = -12/-1.5
x = 8 hours
x = number of hours = 8 hours
11 times z=121
(11xz=121
Answer:
z will be11
11z = 121
z = 121/11
z= 11
Answer:
1=121= 11
Step-by-step explanation:
+
Find the missing side to the nearest tenth 23 and 19