Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-4}{3x^5}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{\frac{1}{x^4}}{3}[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx} \bigg[ \frac{1}{x^4} \bigg][/tex]Rewrite: [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx}[x^{-4}][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{3}(-4x^{-5})[/tex]Simplify: [tex]\displaystyle y' = \frac{-4}{3x^5}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Problem 3.1
Jaleel wrote a book. He wants to print some copies for his
friends and family. The printing company charges a one-
time fee of $200, plus $2 for each printed book.
Is Jaleel's total cost a function of the number of books he
prints?
Answer:
C(n) = 200 + 2n
Step-by-step explanation:
Given:
Fixed cost state by printing company = $200
Variable charges per book print = $2
Find:
Cost function of number of books print
Computation:
Assume:
Number of books printed = n
Total cost of n books printed = Fixed cost state by printing company + Variable charges per book print[Number of books printed]
C(n) = 200 + 2n
Where n = number of book
C = Total cost
Jaleel's total cost as a function of the number of books he print is [tex]c = 2n + 200[/tex] (in dollars)
How to form mathematical equations from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.
If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions or equations.
For the considered case, we don't know exactly how many books will Jaleel gets printed. So we can use variable here.
Let we have:
n = number of books Jaleel gets printed.c = total cost Jaleel has to pay for printing those booksThen, as stated in the problem, for each book there is $2 price, and there is a fixed one-time charge of $200
Thus, we get total cost as:
c = Cost for n books + Fixed one-time cost.
Cost for n books = 2 + 2 + ... + 2 (n times ) (in dollars) = [tex]2n[/tex](we don't write symbols like of currency generally, and understand it from context. Also, sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
Fixed one-time cost = $200Thus, total cost is written as:
c = Cost for n books + Fixed one-time cost.
c = 2n + 200 (in dollars)
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HELP!?? Please hurry due today!!!!
Answer:
348m^2
Step-by-step explanation:
If someone is good at math, can someone help me solve this question? (tip if the photo is upside down, flip it.)
Answer: $880.45
Step-by-step explanation:
find the cost of tickets
18*11.50= $207
now add the other costs
207+625+25+23.45= $880.45
Please answer correctly math problemo
Answer:
2*3*4=24 (units)
l*w*h=V
brainliest plz
Step-by-step explanation:
Answer:
the answer is 24
Step-by-step explanation:
you do 3 times 4 and you get twelve and then you times it by 2
HELP!! What do I do ?
A local city collects 8% sales tax. If the
total purchase was $216.00, then how
much was collected for sales tax?
Answer:
156.00
Step-by-step explanation:take away 8% sales tax away from it
In the figure, the angles are formed by a transversal and two parallel lines. Which angles are congruent?
Answer:
A is your correct answer.
1, 3, 5, and 7 are equal to each other and 2, 4, 6, and 8 are equal to each other.
Step-by-step explanation:
Congruent angles are angles that have the same measure. In this example, where two parallel lines are cut by a transversal line, the angles in the same position on the top line and bottom line are congruent. For example, angle 1 and 5 are in the same position, so they have the same measure.
Also, vertical angles (opposite angles, like 5 & 7 in your example) have the same measure.
Please let me know if you have questions about this.
helpp i beg u its due in one hour!!! plz
Answer:
113.1 cm²
Step-by-step explanation:
we are given the diameter of the circle (length is 12 cm), and the formula for the area of the circle, which is πr², where r is the radius
so first, we need to find the radius
the length of the radius is half the length of the diameter
so that means that r=d/2
r=d/2
r=12/2
r=6
therefore the length of the radius is 6
now square 6, which is the same as multiplying it by itself
6²=36
now, multiply the radius squared by π, which is often substituted for as 3.14 or 22/7
so if we were to do 22/7 for instance,
36*22/7≈113.14
round that to 113.1
there's your answer :)
Hope this helps!
Help be genuine will mark brainliest
Answer: 15.45133224
Step-by-step explanation:
Find the area of the half circle.
r=6
pi (6)^2/2
Divide by two because it is a half circle not a circle.
pi (6)^2/2=18 Pi
We know there are two square with even side lengths so we know the sides of the two squares are 6 it is the same as the radius of the circle.
We multiply B*H= Area of the square
6*6=36 is the length of half of the rectangle aka the square
So we multiply that by 2 because there are 2 squares so we get 72
72-18 Pi= 15.45133224
Answer:
15.48 is the answer
Step-by-step explanation:
6×6×3.14=113.04
113.04÷2= 56.52
6×12= 72
72-56.52= 15.48
find the erea of the trapezoid.
Answer:
36
Step-by-step explanation:
A (base) 6
B (Base) 12
H (height) 4
If X = 9 units, Y = 7 units, Z = 18 units, and h = 8 units, what is the surface area of the triangular prism shown above?
Answer: 506 square units (answer choice B)
Step-by-step explanation:
The formula for the surface area of a triangular prism is:
SA = bh + 2ls + lb,
where b is the base, h is the height, l is the length, and s is the side of the triangle.
In this case, the base is 7 (Y), the height is 8 (h), the length is 18 (Z), and the side of the triangle is 9 (X).
So, by subsituition, we have:
SA = (7)(8) + 2(18)(9) + (18)(7)
SA = 56 + 324 + 126
SA = 506
The surface area is 506 square units.
Hope this helps! :)
32 is 4 more than twice a number. What is the number?
different solution of salt are made up what valumo of
Answer:
Salt is sodium.
Answer:
Salt is Sodium.
Step-by-step explanation:
When you break down the compounds of salt you find molecules of sodium thus saying that salt is made up of sodium molecules.
The Value of X________
Answer:
x = 59.5
Step-by-step explanation:
the angles of a quadralateral equal 360 degrees, one angles is 90 degrees, the other i 151, 90 + 151 = 241, 360 - 241 = 119, 119/2 = 59.5, x = 59.5
Which only lists multiples of 16? *
Mark only one oval.
1, 2, 4, 8, 16
16, 24, 32, 40
16, 32, 48, 64
Use the diagram to complete the statement!
Due in 10 min! Please help!
Will give brainliest!
Answer:
m>NQR=30°
m<LNS=61°
RQ=7
Step-by-step explanation:
m>NQR=180-89-61=30°
m<LNS=61°
RQ= 8/4=x/3.5 = 7
Pythagorean theorem 3d
The Flat Family’s roof is 60 feet long and 32 feet wide. The TV antenna is 30 feet tall. The wires are attached 5 feet below the top of the antenna.
Mr. Flat needs to buy wire at his local hardware store. He decides to buy an additional 10% more than the amount we calculate…so he has enough to attach each wire on each end. How much total wire should he buy? Show all of your work so that Mr. Flat can understand it, and round your answer reasonably.
Answer:
ihhrhi2rhhb4rhbur4hbur4hb43hubr4u3br
Step-by-step explanation:
I need help please ?!!!!
Carissa recently retired, and has $540,000 in savings. She wants to invest as much as possible in a safe CD account paying 1.2% interest, and as little as possible in a riskier bond paying 4.7% interest. She needs to earn $14,880 a year in interest to cover expenses above SSI. How much should she invest in each account?
Answer:
Don't awnser the bots
Step-by-step explanation:
They will try ro scam you
How many small cubes are needed to make the large figure shown below?
Key
represents
1 small
cube
9
15
18
21
Answer:
Step-by-step explanation:
represent 11 by 9 on a number line
Answer:
Fraction mulitiplication adding its c
Step-by-step explanation:
1. The total area of all the faces of a three-dimensional figure is called the?
Pls Answer Fast PLS PLS PLS
True or false a polygon that has four sides and four angles is a pentagon
Answer:
I think that is false
Step-by-step explanation:
A pentagon has 5 sides
The statement "a polygon that has four sides and four angles is a pentagon" is false.
What is a quadrilateral?A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.
A polygon with four sides is known as a quadrilateral, therefore, the statement "a polygon that has four sides and four angles is a pentagon" is false.
Learn more about Quadrilateral:
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giving brainliest *easy*
Answer:
1130.4
Step-by-step explanation:
2x100pi + 160pi
Help me please!!!!!!!
Answer:
48%
Step-by-step explanation:
25 total students, 12 got either 0-4 or 5-9, 12/25 as a percent is 48 percent. Hope this helped! Good luck!
Solve for x
X/16=45/40=
Answer:
18 will be your answer
Step-by-step explanation:
Answer:
The answer is 18.
Step-by-step explanation:
[tex] \frac{x}{16} = \frac{9}{8} [/tex]
[tex]x = \frac{9}{8} \times 16[/tex]
[tex]x = \frac{9 \times 16}{8} [/tex]
[tex]x = \frac{144}{8} [/tex]
[tex]x = 8[/tex]
Therefor, the answer is x = 8.
A cook makes vegetable barley soup by mixing 2 pounds of barley into 7 quarts of vegetable broth. Assume that the cook continues to use the same rate to make more batches of soup. How many pounds of barley should the cook mix with 35 quarts of broth?
Answer: The answer to this question is 10 :D
Step-by-step explanation:
The answer is 10 pounds.
2 pounds 7 quarts
4 14
6 21
8 28
10 35
Help!!!
Ellie and three of her friends each bought two hamburgers and a drink at the soccer game. If the drink cost $1.25 and the total cost for all four girls was $18.20, what was the cost of a hamburger?
Which function is decreasing on the same interval as the function graphed here?
The function that is decreasing on the sale interval as the function graphed in the attached image is " F(x) = -x² + 4x -4.
What does it mean for a function to be decreasing?
When the y-value of a function is decreasing as the x-value goes up, that function is said to be a decreasing function.
That is when x1 < x2 then f(x1) ≥ f(x2)
What is the Proof of the above?Let F(x) = 4
Thus
f(4) = -(4)² + 4(4) -4
= 16 + 16 - 4
= 28
Now, let F(x) = 2
Thus
f(2) = -(2)² + 4(2) -4
= 4 + 8 - 4
= 8
Note that X1 = 4 and X2 = 2
Thus x1 < x2 then f(x1) ≥ f(x2).
Hence Option C is the decreasing function.
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Plzzz help asappppppoppp
Answer:
C
Step-by-step explanation:
