Answers
Answer:
[tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Expanding/FactoringCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationThe definition of a derivative is the slope of the tangent line: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = -4x^3 + 2x^2[/tex]
Step 2: Differentiate
[Function] Substitute in x: [tex]\displaystyle f(x + h) = -4(x + h)^3 + 2(x + h)^2[/tex]Substitute in functions [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-4(x + h)^3 + 2(x + h)^2 - \big( -4x^3 + 2x^2 \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-12hx^2 - 12h^2x + 4hx - 4h^3 + 2h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h \big( -12x^2 - 12hx + 4x - 4h^2 + 2h \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} -12x^2 - 12hx + 4x - 4h^2 + 2h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = -12x^2 - 12(0)x + 4x - 4(0)^2 + 2(0)[/tex]Simplify: [tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]∴ the derivative of the given function will be equal to -12x² + 4x.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Related Questions
Which ratio is equivalent to 9:12?
129
18:24
12:19
10:12
Answers
solve the inequality for 1>x+6 .
Answers
Answer:
-5 > x
Explanation:
To do this, you have to use the inverse operations. Subtract 6 from each side. That equals -5. Bring everything down and that is your answer!
Point B has coordinates (5,2). The x-coordinate of point A is 1. The distance between point A and point B is 5 units. What are the possible coordinates of point A?
Answers
Using Distance formula ,
[tex]\bold{d(AB) = \sqrt{ (x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } }\\ \\\bold{5 = \sqrt{(5 - 1) {}^{2} + (2 - y) {}^{2} }} \\ \\\bold\blue{ squaring \: both \: sides\:,} \\ \\\bold{ 25 = (5 - 1) {}^{2} + (2 - y) {}^{2} }\\ \\\bold{ 25 = (4) {}^{2} + (4 + y {}^{2} - 4y)}\\ \\ \bold{25 = 16 + y {}^{2} - 4y + 4}\\ \\ \bold{25 = y {}^{2} - 4y + 20}\\ \\\bold{ y {}^{2} - 4y - 5 = 0}\\ \\\bold{ y {}^{2} - 5y + y - 5 = 0} \\\\\bold{ y(y - 5) + 1(y - 5) = 0}\\ \\\bold{ (y + 1)(y - 5) = 0 }\\\\\bold{ y = - 1 \: or \: y = + 5}[/tex]
therefore ,
possible coordinates of A are either ( 1 , -1 ) or ( 1 , 5 )
hope helpful~
What is the measure of the base in the triangle below?
A. 11
B. 45
C. 25
D. 30
Answers
Step-by-step explanation:
AC+CB+BA=180
2x+23+3x-8+4x+1=180
9x+16=180
9x=180-16
9x=164
x=164/9
x=18.2
can someone help ^^; im not good with math
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2 l plus 2 w equals 16, where l represents the length of the rectangle and w represents the width of the rectangle.
Which value is possible for the length of the rectangle?
7 in.
8 in.
9 in.
10 in.
Answers
What is the surface area of a sphere with radius 3?
O A. 367 units2
O B. 1877 units
O C. 37 units2
O D. 91 units2
Answers
The solution is, SA =36π unit² is the surface area of the sphere which is correct answer Option(A).
What is surface area of the sphere?We know that, The formula for the surface area of a sphere of radius
R is 4πR².
here, we have,
According to question, we have the radius of sphere as 3 units.
So, surface area of a sphere
⇒4πR²
⇒4π(3)²
⇒36π
The surface area of a sphere is given by
SA = 4 pi r^2
SA = 4 * pi * 3^2
SA =36 pi
SA =113.10
Hence, the surface area of the sphere is 36π unit².
Learn more about surface area of a sphere here:
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Round to the nearest tenth, (need work of trig) pleas
Answers
A bus driver gets paid $38,871 a year, if he works 42 weeks a year.
How much does he earn every week ?
How many weeks will it take him to earn $5500 ?
What is the bus driver’s hourly wage if he works 40 hours a week?
Answers
Answer:
he mask 925.5 dollars every week
Answer:
$1295.70 a week
4 weeks
???
Step-by-step explanation:
hope this helps
The answer has to be in scientific notation.
1.7 x 10^4/2 x 10^-2
Answers
Answer:
Write these in Scientific Notation:
0.0002
2 x 10-4
20 x 10-4
2 x 104
20 x 104
2.) 0.000049
49 x 106
4.9 x 105
49 x 10-6
4.9 x 10-5
3.) 0.000000000845
84.5 x 1011
8.45 x 1010
8.45 x 10-10
84.5 x 10-11
4.) 0.000000000008
80 x 10-13
8 x 10-12
80 x 1013
8 x 1012
5.) 0.00000127
1.27 x 106
12.7 x 107
12.7 x 10-7
1.27 x 10-6
6.) 0.0000000000752
7.52 x 10-11
75.2 x 10-12
7.52 x 1011
75.2 x 1012
7.) 0.000000301
30.1 x 10-8
3.01 x 10-7
3.01 x 107
30.1 x 108
8.) 0.00000000633
63.3 x 1010
6.33 x 109
6.33 x 10-9
63.3 x 10-10
9.) 0.00000009
9 x 10-8
90 x 10-9
9 x 108
90 x 109
10.) 0.0000536
5.36 x 105
53.6 x 106
53.6 x 10-6
5.36 x 10-5
11.) Rewrite these in standard notation.
6 x 10-6
0.0006
0.00006
0.000006
0.0000006
12.) 4 x 10-5
0.00004
0.000004
0.0000004
400,000
13.) 1.8 x 10-11
0.000000000018
0.00000000018
180,000,000,000
1,800,000,000,000
14.) 1.7 x 10-4
17,000
170,000
0.00017
0.000017
15.) 7.6 x 10-10
0.00000076
0.000000076
0.0000000076
0.00000000076
16.) 7.79 x 10-12
0.0000000000779
0.00000000000779
779,000,000,000,000
7,790,000,000,000,000
17.) 1.98 x 10-8
19,800,000,000
198,000,000
Find the factors of each expression. x^2+36
Answers
Answer:
x²+36+2(x)(6).. is the correct answer..James bought x pounds of apples for $1.79 per pound and y pounds of bananas for $1.29 per pound. The expression shown below represents the total amount of dollars that James paid. Select the part or parts of the expression that represent the total cost in dollars of the bananas.
Answers
DOLLARS CENTS DOLLARS CENTS
hi guys I need help in this problem can someone please help me.
Answers
y=30 x=60 that should be the answer sorry if it isnt
I need help with these equations as well
Answers
Answer:
0=10
0= -5
Step-by-step explanation:
[tex]1. - 10 = - 14x + 14x[/tex]
cancel (-14) with (+14)
[tex] - 10 = 0[/tex]
so , The above equation has no solution .
-----------------------------------[tex](ii) \: 3(3 - x) + 5x = 2(x + 2) \\ \\ 9 - 3x + 5x = 2x + 4 \\ \\ 9 + 2x = 2x + 4 \\ \\ 2x - 2x = 4 - 9 \\ \\ 0 = - 5.[/tex]
The above equation has no solution .
The fraction 1/3,1/6,1/4 and 1/2 are to be arranged from the smallest to the largest.which is the correct order
Answers
From the smallest to the largest:
1/6, 1/4, 1/3, 1/2
Hope It Helps
Brainliest plss! :)
find the measure of arc ABD
Answers
Answer: 245 degrees
Step-by-step explanation:
Translate the sentence into an equationTwice the difference of a number and 2 equals 8
Answers
Answer:
(x-2)2=8
Step-by-step explanation:
Write as an algebraic expression : Two less than the product of y and 4 "
Answers
Answer:
4y-2
Step-by-step explanation:
Solve 18>12+x. Graph the solution.
Answers
Answer:
x < 6
Step-by-step explanation:
Step 1: Subtract 12 from both sides.
[tex]x+12-12 < 18-12[/tex] [tex]x < 6[/tex]Thus, the answer is x < 6.
A group of two friends each receive 612s of a pound of candy how much candy did they received total
Answers
Answer:
1224
Step-by-step explanation:
group of 2 friends each receive 612
so you do 612 x 2 = 1224
If 3 over 4 ton of pebbles covers 4 over 5 of a garden, how many tons of pebbles are required to cover the entire garden?
3 over 5 ton
15 over 16 ton
1 and 1 over 3 tons
1 and 11 over 20 tons
I am in middle school, I just clicked the wrong button.
Answers
Answer:
[tex]\frac{15}{16}[/tex] ton of pebbles will cover the whole garden.
Step-by-step explanation:
So [tex]\frac{3}{4}[/tex] ton covers [tex]\frac{4}{5}[/tex] of the garden.
Let x be pebbles required to cover the entire garden, we can set up a proportion:
[tex]\frac{\frac{3}{4} }{\frac{4}{5} } =\frac{x}{1}[/tex]
[tex]\frac{3}{4}[/tex] / [tex]\frac{4}{5}[/tex] = x
[tex]\frac{3}{4}[/tex] * [tex]\frac{5}{4}[/tex] = x
[tex]\frac{15}{16}[/tex] = x
[tex]\frac{15}{16}[/tex] ton of pebbles will cover the whole garden.
answer for a lot of points
Answers
Answer:
7. uses like or as to compare two things
8. personification - in this case, the tropical storm is being given the human quality of sleeping
Hope this helps!
8.Personification
Find the area. Use 3.14 for pi and round your answer
Answers
Answer:
329.9 ft^2
Step-by-step explanation:
area = π · r^2
diameter = 2r so radius = 10.25
area = 3.14 · 10.25^2
10.25^2 = 105.06
3.14 · 105.06 = 329.9 ft^2
Given :-
diameter = 20.5 ftπ = 3.14[tex] \\ \\ [/tex]
To find :-
Area[tex] \\ \\ [/tex]
Solution:
To find area first we should know value of radius.
Diameter is given , and from diameter we can find value of radius.
[tex] \\ [/tex]
We know :-
[tex] \bf \ddag\boxed{\rm Diameter =2 \: radius } \bf \ddag[/tex]
By using this formula we can find radius.
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf Diameter =2 \: radius [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf 20.5 =2 \: radius [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf \dfrac{205}{10} =2 \: radius [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf \cancel\dfrac{205}{10} =2 \: radius [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf \dfrac{41}{2} =2 \: radius [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf2 \: radius = \dfrac{41}{2} [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf \: radius = \dfrac{41}{2 \times 2} [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\sf \: radius = \dfrac{41}{4} [/tex]
[tex] \\ [/tex]
[tex] \hookrightarrow\bf \: radius = 10.25[/tex]
[tex] \\ \\ [/tex]
Now let's find Area
we know :-
[tex] \bf \ddag\boxed{\rm Area = \pi radius {}^{2} } \bf \ddag[/tex]
[tex] \\ \\ [/tex]
So:-
[tex] \\ [/tex]
[tex] \dashrightarrow \sf Area = \pi radius {}^{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf Area = \pi (10.5) {}^{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf Area = \pi \times 10.5 \times 10.5 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf Area = \pi \times 110.25 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \sf Area = 3.14 \times 110.25 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow \bf Area =346.19~ {ft}^{2} \{approx\}\\[/tex]
Which is a solution to x + 3 = 2x - 8? 10 11 12
Answers
Answer:
x=11
Step-by-step explanation:
Subtract 3 from both sides
x+3=2x-8
x+3-3 =2x-8-3
Then simplify it
x=2x-11
Again, subtract 3 from both sides
x-2x=2x-11-2x
Simplify
-x=-11
Divide both sides and simplify and then you get x=11
One box of cereal costs $3. How many boxes can you buy with $15?
Answers
Answer:
5 boxes
Step-by-step explanation:
Divide 15 by 3 and you'll get your answer
Hope that helps!
Step-by-step explanation:
1 = $3
x = $15
crossmultiply
3x = 15
x = 15/3
x = 5 boxes of cereal
if this helped pls give brainliest
4/6 X + 10/4 =-6/8x-10
Answers
Given :
[tex]\: {\qquad \sf \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]
⠀
To Find :
The value of x.⠀
Solution :
[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]
⠀
Subtracting [tex] \sf \: \dfrac{10}{4} [/tex] from both sides :
[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x \: \: \cancel{+ \dfrac{10}{4}} \: \: \cancel{- \dfrac{10}{4}} = - \dfrac{6}{8}x - 10 - \dfrac{10}{4} }[/tex]
⠀
Adding [tex] \sf \dfrac{6}{8} x[/tex] to both sides :
[tex]{\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{6}{8}x = \cancel{- \dfrac{6}{8}x } \: \: \cancel {+ \: \dfrac{6}{8}x} - 10 - \dfrac{10}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{4}{6} x + \dfrac{6}{8}x = - 10 - \dfrac{10}{4}}[/tex]
⠀
Adding the like terms :
[tex]{\qquad \sf \dashrightarrow \dfrac{32x + 36x}{24} = \dfrac{ - 40 - 10}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{68x}{24} = \dfrac{ - 50}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{34x}{12} = \dfrac{ - 25}{2} }[/tex]
⠀
By doing cross multiplication we get :
[tex]{\qquad \sf \dashrightarrow {68x} = - 300 }[/tex]
[tex]{\qquad \sf \dashrightarrow {x} = \dfrac{ - 300}{68} }[/tex]
[tex]{\qquad \bf \dashrightarrow {x} = \dfrac{ - 75}{17} }[/tex]
Three hundred high school seniors were surveyed about their intended college majors. The results are displayed in the Venn Diagram below: A Venn Diagram titled College Majors with two circles labeled Math and Science. In the math portion is 120. In the intersection is ??. In the Science portion is 50. The area outside the two circles is labeled 100. If a student is randomly selected from the group, what is the probability that they are majoring in both math and science? Round your answer to the nearest whole percent. 10% 17% 33% 40%.
Answers
The probability of selecting one student who is both from math and science is 1/10
There are the total number of student = 300
Out of which,the number of students who are only in Maths = 120
The number of students who are only in Science = 50 and the students who are not from any subject = 100
What is the formula for the total students?
Total no of students=science student+math students +none
Therefore,the number of student who are from both math and science = Total student - Math student (only) - science student (only) - None
= 300 - 120 - 50 - 100
= 30
That is, there are 30 students who are both from science and math,
Thus, the probability of selecting one student who is both from math and science = 30/300 = 1/10
To learn more about the probability visit:
https://brainly.com/question/24756209
Does anyone know how to do this?
Answers
Answer:
-4
Step-by-step explanation:
what is an equation of a line that passes through the point (5,4) and is parallel to the line 6x-5y=15
Answers
Answer: y-4=1.2(x-5)
Step-by-step explanation:
What is the equation
Answers
Answer:
2y = 8
Step-by-step explanation:
an equation contains an = symbol.
the others are inequalities.
also, from looking at the question, you can assume that it is 2y = 8 because the other to are the same type of inequality
Francisca has 40 paperbacks in her bookcase. This is 32% of the books in the bookcase. How many books are in Francisca's bookcase? Use an equation with a variable. Show your work
Answers
The total number of books that are in Francisca's bookcase is 125 books.
Let the total number of books be B.
Given the following data:
Number of paperbacks = 40.
Percentage = 32%.
How to calculate the total number of books.In this exercise, you're required to determine the total number of books that are in Francisca's bookcase if there she has 40 paperbacks in her bookcase. Thus, we would write a mathematical expression for the word problem.
Translating the word problem into an algebraic expression, we have;
[tex]\frac{32}{100} \times T=40\\\\0.32T=40\\\\T=\frac{40}{0.32}[/tex]
T = 125 books.
Read more on word problems here: brainly.com/question/13170908