differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².​

Answers

Answer 1

Step-by-step explanation:

Let [tex]y(x)=f(x)g(x)h(x)[/tex] where

[tex]f(x) = x^4[/tex]

[tex]g(x)= (1 -2x^5)^6[/tex]

[tex]h(x)= (5 - 8x^3)^2[/tex]

so that

[tex]y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2[/tex]

Recall that the derivative of the product of functions is

[tex]y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)[/tex]

so taking the derivatives of the individual functions, we get

[tex]f'(x) = 4x^3[/tex]

[tex]g'(x) = 6(1 - 2x^5)^5(-10x^4)[/tex]

[tex]h'(x) = 2(5 - 8x^3)(-24x^2)[/tex]

So the derivative of y(x) is given by

[tex]y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)[/tex]

or

[tex]y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2[/tex]

[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)[/tex]


Related Questions

PLS HELP !!!! WILL MARK BRAINLIEST !!

Answers

Answer: Choice C) no solution

=============================================================

Explanation:

The first equation says that y and 3x-4 are the same thing.

So we can replace every copy of "y" in the second equation with "3x-4" like so

9x - 3y = 14

9x - 3(3x-4) = 14

9x - 9x + 12 = 14

0x + 12 = 14

0 + 12 = 14

12 = 14

The last equation is false because we get different values on either side. Because the last equation is false, it means the equation 9x-3y = 14 is false when y = 3x-4.

In short, the overall systems of equations is inconsistent and that leads to no solution (choice C).

If you were to graph each equation, you should find that both lines are parallel. Parallel lines never intersect. The solution is the intersection point of any graphed system.

Answer:

there is no solution to this problem

Step-by-step explanation:

I hope this helps

how are they the same

Answers

Answer:

Step-by-step explanation:

The ways that they are the same are.

The slope is the same.Since the slope is the same for both of them, there is no possible solution meant for both of them. The slope is 1/4They are both written in slope y intercept form.The only difference is the y intercept is different. y intercept for y = 1/4 x is 0,0y intercept for y = 1/4 x is 0,5

In how many ways can 10 people be seated in 10badjacenr seats in a theater​

Answers

3,628,800 is the correct answer

my last question 30 pts plzzzzzzzzz help
An expression is shown below:

4(m + 3 + 5m)

Part A: Write two expressions that are equivalent to the given expression. (3 points)

Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)

Answers

Answer:

A) 48m + 12 and 3(2m + 4 + 14m)

B) 48m + 12 is equivalent to 6(m + 2 + 7m) because if you distribute the 6 to everything inside the parentheses, you get 6m + 12 + 42m. This can be simplified further by adding 6m and 42m together, leaving you with 48m + 12.  

C) m = 2

6(m + 2 + 7m)

6[2 + 2 + 7(2)]

6(4 + 14)

6(18) 1

108

3(2m + 4 + 14m)

3[2(2) + 4 + 14(2)]

3(4 + 4 + 28)

3(8 + 28) 3

(36) 108

108 = 108  

What is the correct answer to this problem?

Answers

En queeeeeeeeeeeeeeeeeee?

Answer:

Y=51.34019175

Step-by-step explanation:

We first use Pythagoras theorem to find the hypo...

[tex] \sqrt{ {8 }^{2} + {10}^{2} } = 12.8062487[/tex]

After we use sine rule

12.8062487/sin90 = 10/siny

Sin y=10sin90/12.8062487

Y=51.34019175

Helpppppppppppppp:))))

Answers

Given:

Principal value = $1500

Rate of interest = 7% per annum compounded daily

Time = 2 years.

To find:

The amount after 2 years.

Solution:

Formula for amount:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimals, n is the number of time interest compounded in an year and t is the number of years.

We know that 1 year is equal to 365 days and the interest compounded daily. So, n=365.

Substituting [tex]P=1500,\ r=0.07,\ n=365,\ t=2[/tex] in the above formula, we get

[tex]A=1500\left(1+\dfrac{0.07}{365}\right)^{365(2)}[/tex]

[tex]A=1500\left(\dfrac{365+0.07}{365}\right)^{730}[/tex]

[tex]A=1500\left(\dfrac{365.07}{365}\right)^{730}[/tex]

Using calculator, we get

[tex]A\approx 1725.39[/tex]

The amount after two years is $1,725.39. Therefore, the correct option is (c).

distribute and simplify these radicals 2^3 x (^2+^3)

Answers

the add of the 56+45/98+5000+12538+567

A bicycle wheel has a diameter of 26 inches. What is the circumference?

Answers

Answer:

81.64 Inches

Step-by-step explanation:

Given :

Diameter of wheel =26 inches

Radius of wheel (r)=26/2=13 inches

Circumference (C) of wheel can be calculated as :

C=  2πr

C=6.28(13)

C=81.64 Inches

Hakim is making birdhouses. Each birdhouse uses 78 yard of wood.
What is the total length of wood Hakim will need to build 5 birdhouses?
A. 438 yards
B. 578 yards
C. 148 yards
D. 928 yards

Answers

Answer:

390 yds

Step-by-step explanation:

Take the amount of wood per birdhouse and multiply by the number of birdhouses being made

78 * 5 =390 yds

Answer:

390 yds

Step-by-step explanation:

Take the amount of wood per birdhouse and multiply by the number of birdhouses being made

78 * 5 =390 yds

Hope this helps!!!

natally needs to cut a pice of paper so that she has exactly 1/3 of it.if the length of the paper is 11 inches, how long will be the paper if she cuts . help me please

Answers

Answer:

3 [tex]\frac{2}{3}[/tex] inches long

Step-by-step explanation:

Find how long the paper will be by dividing 11 by 3. This will find how much 1/3 of the 11 inch paper is.

11/3

= 3 [tex]\frac{2}{3}[/tex]

So, if she cuts the paper, the paper will be 3 [tex]\frac{2}{3}[/tex] inches long

Find the missing probability
P(A) = 0.8
P(B) = 0.05
P(A or B) = 0.6
P(A and B) =

Answers

Answer:

2

Step-by-step explanation:

What is the horizontal distance between (−5/3, -2) and (4, -2)?


ANSWER QUICK GIVING BRAIN LEST

Answers

Answer:

-2?

Step-by-step explanation:

use y2-y1 over x2-x1 to find the answer. So you would do -2--5/3 over 4--2. The two negitives turn into a positive. SO it is now -2+5/3 over 4+2. -2+5/3= -1/3 over 4+2=6 it is now -1/3/6 which equals -2. So I think the answer is -2. I do not know if you should trust me on this but I tried.

all the cubes root of
[tex] \sqrt{3 + i} [/tex]

Answers

If you're looking for the cube roots of √(3 + i ), you first have to decide what you mean by the square root √(…), since 3 + i is complex and therefore √(3 + i ) is multi-valued. There are 2 choices, but I'll stick with 1 of them.

First write 3 + i in polar form:

3 + i = √(3² + 1²) exp(i arctan(1/3)) = √10 exp(i arctan(1/3))

Then the 2 possible square roots are

• √(3 + i ) = ∜10 exp(i arctan(1/3)/2)

• √(3 + i ) = ∜10 exp(i (arctan(1/3)/2 + π))

and I'll take the one with the smaller argument,

√(3 + i ) = ∜10 exp(i arctan(1/3)/2)

Then the 3 cube roots of √(3 + i ) are

• ∛(√(3 + i )) = ¹²√10 exp(i arctan(1/3)/6)

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + π/3))

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + 2π/3))

On the off-chance you meant to ask about the cube roots of 3 + i, and not √(3 + i ), then these would be

• ∛(3 + i ) = ⁶√10 exp(i arctan(1/3)/3)

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/3 + 2π/3))

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/6 + 4π/3))

Bernardo woke up one morning and saw frost on the windows. It was -15°C outside. Later in the day, the frost melted. At 3 p.m. it was 14°C outside. Which expression represents the difference between the two temperatures?

Answers

Answer:

something like: 14 - (-15)

Step-by-step explanation:

PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!

Answers

Answer:

50 %

Step-by-step explanation:

Please mark me as the brainlist

Answer:

answer is 37.5%

Step-by-step explanation:

the only prime numbers after adding are

4+9= 13

4+7=11

3+8=11

place the sum # of prime numbers over the total some of numbers

3÷8= 0.375

now multiply by 100 to give you in percentage

0.375 x 100% = 37.5%

Giving out brainliestttt answer !!! help me out?!!!

Answers

Answer:

F= 60.256

D = 29.744

Step-by-step explanation:

This is a completely different from the way usually I do it

B = arcsin(b·sin(A)a)

= 1.05166 rad = 60.256°

180-60.256-90 = 29.744°

Please help quickly I really don’t understand this question and i’m freaking out.

Answers

Answer:

[tex] \frac{4 \sqrt{3x} }{9} [/tex]

Step-by-step explanation:

[tex] \frac{4 \sqrt{ {21x}^{2} } }{3 \sqrt{63x} } [/tex][tex] \frac{4 \sqrt{ \frac{21 {x}^{2} }{63x} } }{3} [/tex][tex] \frac{4 \sqrt{ \frac{x}{3} } }{3} [/tex][tex] \frac{4 \sqrt{ \frac{x \times 3}{3} } }{3} [/tex][tex] \frac{\frac{4 \sqrt{3x} }{3} }{3} [/tex][tex] \frac{4 \sqrt{3x} }{3} \times \frac{1}{3} [/tex][tex] \frac{4 \sqrt{3x} }{9} [/tex]Hope it is helpful...


Which point on the x-axis lies on the line that passes point C and is parallel to line AB

Answers

Answer:

(2,0)

Step-by-step explanation:

Suppose we are interested in bidding on a piece of land and we know one other bidder isinterested. The seller announced that the highest bid in excess of $10,000 will be accepted.Assume that the competitor’s bid x is a random variable that is uniformly distributedbetween $10,000 and $15,000.a. Suppose you bid $12,000. What is the probability that your bid will be accepted?b. Suppose you bid $14,000. What is the probability that your bid will be accepted?c. What amount should you bid to maximize the probability that you get theproperty?d. Suppose you know someone who is willing to pay you $16,000 for the property. Wouldyou consider bidding less than the amount in part (c)? Why or why not?

Answers

Answer:

a. 0.4 = 40% probability that your bid will be accepted

b. 0.8 = 80% probability that your bid will be accepted.

c. $15,000.

d. Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000.

This means that [tex]a = 10, b = 15[/tex], considering the measures in thousands of dollars.

a. Suppose you bid $12,000. What is the probability that your bid will be accepted?

Probability that the other bidder's bid is less than 12000(X < 12). So

[tex]P(X < 12) = \frac{12 - 10}{15 - 10} = \frac{2}{5} = 0.4[/tex]

0.4 = 40% probability that your bid will be accepted.

b. Suppose you bid $14,000. What is the probability that your bid will be accepted?

Probability that the other bidder's bid is less than 14000(X < 14). So

[tex]P(X < 14) = \frac{14 - 10}{15 - 10} = \frac{4}{5} = 0.8[/tex]

0.8 = 80% probability that your bid will be accepted.

c. What amount should you bid to maximize the probability that you get the property?

The upper bound of the uniform distribution, that is, $15,000.

d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).


A weatherman predicted 8 inches of snow would fall last night.
Instead, 20 inches of snow actually fell.
What is the percent error of the prediction?
about 12%
about 40%
about 60%
about 150%

Answers

Answer:

The correct answer is - about 60%

Step-by-step explanation:

Given:

predicted value: 8 inches

measured value - 20 inches

formula:

Prediction percentage error is the error or differences between the prediction made and the observed or actual value. Calculation of the percentage error by the following equation.

prediction percentage error = (measured value - predicted value)*100/measured value

solution:

putting value in the formula

= (20-8)*100/20

= 12*5

= 60 %

a) Find the center and radius,
b) Graph -not necessary-
c)Find intercepts if there are any


4. (x-1)² + (y+4)² = 9​

Answers

Answer:

Radius: 3units

center: (1,-4)

Calculamos el volumen (V) de un prisma cuadrangular expresado en unidades cúbicas. Respondemos: ¿cómo se calcula?........................... entonces, la expresión para calcular el volumen es: V = ……………………

Answers

Answer:

a) El procedimiento queda resumido en lo que sigue:

1) Se halla el área de la base del cuadrilátero.

2) Se multiplica el resultado anterior por la longitud del prisma.

b) La expresión para calcular el volumen del prisma ([tex]V[/tex]), en unidades cúbicas, es:

[tex]V = w\cdot h \cdot l[/tex]

Donde:

[tex]w[/tex] - Ancho de la base, en unidades.

[tex]h[/tex] - Altura de la base, en unidades.

[tex]l[/tex] - Longitud del prisma, en unidades.

Step-by-step explanation:

a) Dimensionalmente hablando, la unidad de volumen es igual al cubo de la unidad de longitud. Se explica a continuación los pasos necesarios para el cálculo de prisma cuadrangular:

1) Se halla el área de la base del cuadrilátero.

2) Se multiplica el resultado anterior por la longitud del prisma.

b) En consecuencia, se deriva la expresión para el volumen del prisma:

[tex]V = A\cdot l[/tex] (1)

Donde:

[tex]A[/tex] - Área de la base del prisma, en unidades cuadradas.

[tex]l[/tex] - Longitud del prisma, en unidades.

[tex]V = w\cdot h \cdot l[/tex] (2)

Donde:

[tex]w[/tex] - Ancho de la base, en unidades.

[tex]h[/tex] - Altura de la base, en unidades.

Question 4
Solve for m.
m+7=3* mull
no solution
Infinite
solutions

Answers

Answer:

m= -4

Step-by-step explanation:

the answer to this is m= -4

a) Two thirds of the class are freshman

Is it parameter or statistic

Answers

Answer:

parameter

Step-by-step explanation:

Parameter is the answer

What is the slope of the line containing (-3, 1) and (1, -2

Answers

Answer:

-3 on 4

Step-by-step explanation:

slop is given by change in y coordinate over change in x coordinate

It will be -3, 4 !!!

Part A

Will be marked brainliest

Monique’s group will design a float for the I love my city parade. They plan to highlight the city’s train system by making a float of the MetroPass.

*SEE PICTURES FOR ACTUAL MEASURES*

The actual MetroPass is 2.1 inches wide and 3.4 inches long. Moniques group wants the MetroPass float to be 74.8 ft long. Her group needs to find the width of the MetroPass float.

How wide, in feet, will the MetroPass float be? Round you answer to the nearest tenth. Show your work.

*WILL BE MARKED BRAINLIEST*

Answers

Answer:

74.8 ft÷3.4 inches=264

2.1 in x 264=46.2 inches so the width should be 46.2 inches

COLOR THEME
Q ZOOM
7. The dimensions in the drawing below are given in units.
3V10
х
36
Р
118
S
R
90
18V5
What is the value of x?
45
CLEAR ALL

Answers

Given:

In triangle PQR, QS⊥PR, QS=x, PR=90 and RS=18.

To find:

The value of x.

Solution:

According to right triangle altitude theorem (geometric mean theorem), if an altitude of a right triangle divides the base into two segments then the square of altitude is equal to the product segments of the base.

Using right triangle altitude theorem, we get

[tex]\dfrac{QS}{PS}=\dfrac{RS}{QS}[/tex]

[tex]QS^2=RS\times PS[/tex]

[tex]x^2=18\times (90-18)[/tex]

[tex]x^2=18\times 72[/tex]

[tex]x^2=1296[/tex]

Taking square root on both sides, we get

[tex]x=\sqrt{1296}[/tex]

[tex]x=36[/tex]

Therefore, the correct option is B.

Which of the following is not a property of a rectangle

Answers

Answer:

I would like to say A because Diagonals of a rectangle Bisect each other at a right angle.

This seems likely

Please Mark as Brainliest

Hope this Helps

Answer:

I think C would be the best answer.

Step-by-step explanation:

Sorry if it was not right ):

I kinda need help!!!!!!!!!!!!!!!!

Answers

Answer:

15+15+15=45

Step-by-step explanation:

8+8+8=24

4+4+4=12

4+15*8=

124

Answer:

Answers is hear that.

4+15+8=27

guys i need so so so help :(((((( thankss ​

Answers

Answer:

38,78461

Step-by-step explanation:

The triangle is composed by two right triangles. the sum of inner angles of a triangle is 180 degrees. If we look at the right one we can say that it’s top angle is 60 degrees. In fact 30 + 60 + 90 = 180

So also the top angle of the biggest triangle is right:

60 + 30 = 90

We can also say that the leg of that triangle on left that lies on the hypotenuse is half of its hypotenuse thanks to the its angles.

Thanks to these informations we can use a theorem, called first Euclid’s theorem that allow us to build a proportion:

6 : 12 = 12 : hypotenuse

6 * hypotenuse = 144

hypotenuse = 24

x = 24 - 6 = 18

For the same theorem:

18 : y = y : 24

y^2 = 432

y = 20,78461

18 + 20,78461 = 38,78461

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