Given:
The given function is:
[tex]\dfrac{(x^3+1)(x-2)}{x^2}[/tex]
To find:
The differentiation of the given function.
Solution:
Consider the given function,
[tex]y=\dfrac{(x^3+1)(x-2)}{x^2}[/tex]
It can be written as:
[tex]y=\dfrac{(x^3)(x)+(x^3)(-2)+(1)(x)+(1)(-2)}{x^2}[/tex]
[tex]y=\dfrac{x^4-2x^3+x-2}{x^2}[/tex]
[tex]y=\dfrac{x^4}{x^2}-\dfrac{2x^3}{x^2}+\dfrac{x}{x^2}-\dfrac{2}{x^2}[/tex]
[tex]y=x^2-2x+\dfrac{1}{x}-\dfrac{2}{x^2}[/tex]
Differentiate with respect to x.
[tex]y'=\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(x^{-1})-\dfrac{d}{dx}\2(x^{-2})[/tex]
[tex]y'=2x-2(1)+(-x^{-2})-2(-2x^{-3})[/tex]
[tex]y'=2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex]
Therefore, the differentiation of the given function is [tex]2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex].
Bob has 3 pounds of hamburger meat. Each hamburger is 1/2 pound
Which equation is correct to figure out how many hamburgers Bob car
make?
Answer:
6
Step-by-step explanation:
3 divided by 1/2 = 6
2 hambugers = 1 pound
the cost of fun for kids magazine for x number of months is shown below
The cost (C) of another magazine, Family Fun, for x number of months is
given by C-1.99x.
The cost of another magazine, Kidz Comics, is $1.85 for each month. The
annual subscription includes a delivery charge of $10, while the annual
subscription for Fun for kids and Family Fun has no such extra charge
Which annual subscription costs the most?
Answer:
Kidz comic costs the most
Step-by-step explanation:
Given
Family Fun
[tex]C(x) = 1.99x[/tex]
Kidz Comics
[tex]m = 1.85[/tex] --- monthly rate
[tex]b = 10[/tex] --- delivery charge
Required
Which is more expensive
A linear function is represented as:
[tex]f(x) = mx + b[/tex]
Where
[tex]m = rate[/tex]
[tex]b = y\ intercept[/tex] --- i.e. the base charge
So, for Kidz comic; We have:
[tex]f(x) = mx + b[/tex]
[tex]C(x) = 1.85x + 10[/tex]
To calculate the annual cost, we set x = 12; i.e. 12 months.
So, we have:
[tex]C(x) = 1.99x[/tex] ---- Family Fun
[tex]C(12) = 1.99 * 12[/tex]
[tex]C(12) = 23.88[/tex]
[tex]C(x) = 1.85x + 10[/tex] --- Kidz comic
[tex]C(12) = 1.85*12 + 10[/tex]
[tex]C(12) = 22.2 + 10[/tex]
[tex]C(12) = 32.2[/tex]
By comparison
[tex]32.2 > 23.88[/tex]
Hence, Kidz comic is more expensive
I WILL GIVE 30 POINTS!!!!!!
Answer:
Option D would be the correct answer:
Step-by-step explanation:
=> If we 15 is the why intercept, then it means when x = 0, y = 15. Now if the slope is 12.5x, it means that the graph is increasing by 12.5 units each time. This means if we say 15 + 12.5 + 12.5 (since we are given an x value for y = 2) we would get 40.00. And that we get, hence option D is the correct answer.
Hope this helps!
PLEASE SOMEONE HELP IM SO CLOSE TO BEING DONE FOR THE YEAR
NO LINKS OR FILES
Answer:
Step-by-step explanation:
The negative out front only tells us which way the parabola will open. That means that the first one will open upside down, since it's got a negative out front. The value of the number that serves as the leading coefficient (the number stuck to the x-squared) determines how steep or wide-open the parabola's shape is. The leading coefficient in the first one is a 1, so it opens up exactly as wide as its parent graph does. The leading coefficient in the second one, a 2, means that the parabola will be skinnier or narrower than its parent. If the leading coefficient is greater than 1, the parabola will be narrower than its parent; if the leading coefficient is greater than 0 but less than 1, the parabola will open wider than its parent.
A bag contains n counters. one counter is blue and the rest are red. Two counters are taken at random from the bag. a) express, in terms of n, the probability that a counter of each colour is taken. Give your answer as a fraction. b) the probability that a counter of each colour is taken is 0.125. How many red counters are in the bag?
Answer:
A] Probability = 1/n ; B] Number = 8
Step-by-step explanation:
Total counters = n , Blue counter = 1 , Red counters (remaining) = n -1
A] Prob (One blue, & One red counter) = (Blue counter / Total counters) x (Red counters / Total remaining counters) = [1 / n] x [ (n -1) / (n-1)] = 1 / n
Alternative, Prob (One red, & one blue) = (Red counter / Total counters) x (Blue counters / remaining counters) = [ (n-1) / n ] x [1 / (n-1) ] = 1 / n
B] Prob (each color , a blue & red counter taken) = 0.125 {Given}
By A], this Prob = 1/n.
So, 0.125 = 1/n → n = 1 / 0.125 = 8
Which function has the greater maximum value: f(x) = -3x2 + 6x + 4, or g(x),
the function in the graph?
Answer: f(x)
Step-by-step explanation:
The function g(x) has the greater maximum value. So, option (A) is the correct answer.
What is the graph of a function?"The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation".
For the given situation,
The function f(x) is expressed as -3x^2 + 6x +4
The function g(x) is shown in the graph.
Plot the function f(x) in the graph to compare with g(x).
The graph for f(x) is shown below.
The function f(x) is the decreasing function, so it has only a minimal value.
The function g(x) is the increasing function, so it has a maximum value.
Hence we can conclude that the function g(x) has the greater maximum value. So, option (A) is the correct answer.
Learn more about the graphs of functions here
https://brainly.com/question/18422775
#SPJ2
What is the mode interval for the set of data?
80 - 89
70 - 79
90 - 99
60 - 69
Answer:
80-89
Hope this helps
Answer:
A
Step-by-step explanation:
A rappelling rope used for outdoor programs, rescue and industrial work, can safely support a weight "W" (in pounds) provided, where "d" is the rope's diameter (in inches). Determine the diameter of rope that would be needed to support a weight of at least 5,500 pounds.
Answer:
D = ( d * 5500 ) / W
Step-by-step explanation:
Diameter of rope " d " supports "w" weight
i.e. d = W
d ( inches ) = W ( pounds )
? ( inches ) = 5500 pounds
The Unknown diameter D ( ? ) = d * 5500 / W
What are the solutions of 2x^2 + 7x = 4
½
4
-½
-4
7
-7
PLEASE HELP FAST!!!!!!!!!!
hey! i’ll give brainliest please help!
Answer:
i think Muhammad
Step-by-step explanation:
Answer:
Look Down
Step-by-step explanation:
I believe its B Zoroastar
How would you "say" the image on the right?
A.) Prime A, B, C, and D
B.) A prime, B prime, C prime, D prime
Answer:
a
Step-by-step explanation:
prime abc and d
hope this helps
How would you find the value of x
Answer:
where is the question
Step-by-step explanation:
send me the question on comment and i will solve it for you
Will give brainiest if someone answers correctly
x=
Length=
Width=
(~‾▿‾)~
what's the answer ?
[tex] \sqrt{ {4}^{4} \times 0} [/tex]
Answer:
/~ 4× 4= 4^2= +4
Step-by-step explanation:
I dont have the right lines so ill show you from another example
Answer:
Solution given;
[tex] \sqrt{ {4}^{4} \times 0} [/tex]
[tex] \sqrt { 0} [/tex]=0
Solve X2--169. (4 points)
Answer:
Replace all occurrences of
−
−
with a single
+
. Two consecutive minus signs have the same mathematical meaning as a single plus sign because
−
1
⋅
−
1
=
1
x
2
+
169
Step-by-step explanation:
order the followng numbers from least to greatest -14/3 -4 -5/1
Find the amount of time. I=$70, P=$350, r=4%
Answer:
5years
Step-by-step explanation:
I=70
P=350
R=4
I=PRT/100➜PRT=100 I
➜T=100 I/PR
➜100×70/350×4
➜7000/1400
➜5years
Which statement is true
A. If a relationship is non - linear, it is not a function
B. A graph of a curve is linear
C. A graph that shows a constant rate of change is linear
D. A non - linear relationship has a constant slope.
Answer:
C is correct
Step-by-step explanation:
I just know this from having previously learned it, I'm not sure how to explain it but hope the answer helps!
#2 find the r and h
find the surface area as we
Answer:
2) 96
3) 121
Step-by-step explanation:
2) 8 x 12 = 96
3) 11 x 11 = 121
Answer:
surface area of the cyclinder=2πr²+2πrh
=(2×3.14×12²)+(2×3.14×12×8)
=904.32+602.88
=1507.2mi²
Find the volume of the rectangular prism.
90.625 cubic feet
107.5 cubic feet
281.25 cubic feet
20.75 cubic feet
Answer:
The answer is C, 281.25 cubic feet.
Step-by-step explanation:
First, you need to multiply all three sides of the rectangular prism.
10x4.5=45
45x6.25=281.25
So the answer is 281.25
Hope this helps!
Answer pls I dont know maths
Answer:
well learn math
Step-by-step explanation:
did you know that everyday is someone's birthday? if you don't
then Three piggies in the city.
Nurse Jackson examines immunization records for this past winter at the school where she works. Got flu Didn't get flu Total Vaccinated 120 380 500 Not vaccinated 160 140 300 Total 280 520 800 How many students were not vaccinated and did not get the flu? O A. 300 B. 380 O C. 160 D. 140
Answer:
140
Step-by-step explanation:
ap3x
solve this inequality:
-1/3n - 8 < -25
Con k expresion decimal se corresponden los siguientes porcentajes a.Pequeños agricultores :45 b.Pasto para ganado :25 c.Agricultora a gran escala :20 d.Explotacion forestal:10
Respuesta:
0,45
0,25
0,20
0,10
Explicación paso a paso:
Para convertir un porcentaje dado a decimal; el valor dado se divide por 100;
Es decir ; el equivalente decimal de x% será: x / 100
Por lo tanto, convertir los porcentajes dados a decimal:
una. Pequeños agricultores: 45/100 = 0,45
B. Pasto para ganado: 25/100 = 0,25
C. Granjero: 20/100 = 0,20
D. Explotación forestal: 10/100 = 0,10
In a survey, 80 percent of those
surveyed had at least one brother or
sister. What fraction of those surveyed
had at least one brother or sister? Write
your answer in the simplest form.
Answer:
4/5
Step-by-step explanation:
If we are given this value as a percent we can simply turn that percentage into a fraction. 80% would be 8/10 but since the question wants the fraction in simplest form we can achieve this by dividing both the numerator and denominator by 2. This would give us 4/5, which if we divide the numerator by the denominator we get 0.80 which is 80%. Therefore, the fraction of those surveyed that had at least one brother or sister is 4/5
3) Find the percent of each number
38% of 50=
27% 300=
60% 75=
Answer:19, 81, 45
Step-by-step explanation:
plz help quickly links will get banned. and branily
Answer:
273, depending on what the tent design is
Step-by-step explanation:
Using the surface area of a trianglar prism formula, or simply just intuitively solving this, you can get an answer of 273 ft^2. But that's considering if your tent is completely covered by fabric, and the bottom side isn't missing.
Ann had 96 filers to post around town. Last week, she posted 1/4 of them. This week, she posted 1/3 of the remaining filers. How many filers has she still not posted
Answer:
48 [fliers]
Step-by-step explanation:
Ann starts with 96 fliers. After she posts 1/4 of them, she will have 3/4*96=72 fliers left. She now has 72 remaining flyers. After posting 1/3 of these, she will have 2/3*72=48 fliers left.
COINS: Find the number of possible outcomes if 2 quarters, 4 dimes, and 1 nickel are tossed.