Given the function y=-\frac{3\sqrt{x^5}}{4},y=− 4 3 x 5 ​ ​ , find \frac{dy}{dx}. dx dy ​ . Express your answer in radical form without using negative exponents, simplifying all fractions.

Answers

Answer 1

Given:

The function is:

[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]

To find:

The value of [tex]\dfrac{dy}{dx}[/tex].

Solution:

We have,

[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]

It can be written as

[tex]y=-\dfrac{3}{4}x^{\frac{5}{2}}[/tex]        [tex][\because \sqrt[n]x=x^\frac{1}{n}][/tex]

Differentiate with respect to x.

[tex]\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}[/tex]       [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}[/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}[/tex]

[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}[/tex]

Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is [tex]-\dfrac{15}{8}\sqrt{x^3}[/tex].


Related Questions

pleaseee help im really confused

you are shopping for a Nintendo Switch and you have a choice to make. You can pay $420 and add 10% for shipping or pay $400 and add 20% for shipping. Which costs less?

Answers

Answer:

420 x .1 = 42

420 + 42 = 462

400 x .2 = 80

400 + 80 = 480

The first one is cheaper


2y +3<11
What is the largest value of y could be?

Answers

the greatest value of y is 2y+3=11 => y=4

Answer:

Step-by-step explanation:

2y + 3<11                       Subtract 3 from both sides

2y < 11 - 3

2y < 8                           Divide by 2

2y/2 <8/2                  

y < 4

The question is very hard to answer. That's because the answer is very close to 4, but it is not 4.

For example 3.8 is a possible answer. Try it

2*3.8 + 3 < 11

7.6 + 3 < 11

10.6 < 11

But is that the largest value possible? No.

For example

y could be 3.99999999 Well maybe that could be the answer. No it isn't. Because, though very close to 11, it still cannot be 11. It might round to 11, but it does not equal 11.

I don't exactly know what you are expected to answer. I can only say that y cannot be 4, but it can be as close to 4 as you care to make it. If the question means what is the largest integer that y could be, then the answer is 3.

Answer the question for 10 points

Answers

Answer:

(3x + 8) (3x - 8)

Step-by-step explanation:

Not sure if you need the steps

Find the measure of angle h

Answers

Answer:

62 degrees

Step-by-step explanation:

Since we know 3 sides of the triangle, we can use law of cosines.

[tex] {gk}^{2} = {gh}^{2} + {kh}^{2} - 2(gh)(kh) \times \cos(h) [/tex]

[tex] {8}^{2} = {17}^{2} + {15}^{2} - 2(17(15) \times \cos(h) [/tex]

[tex]64 = 289 + 225 - 510 \times \cos(h) [/tex]

[tex]64 = 314 - 510 \times \cos(h) [/tex]

[tex] - 250 = - 510 \times \cos(h) [/tex]

[tex] \frac{250}{510} = \cos(h) [/tex]

[tex] \frac{25}{53} = \cos(h) [/tex]

Take the arcos or cosine inverse

[tex] \cos {}^{ - 1} = \frac{25}{53} [/tex]

Which is about 62 degrees.

Amy’s dog weighs 14 pounds.

What is the dog’s weight in ounces?


30


64


210


224

Answers

Answer:

64

Step-by-step explanation:

thats all my answer...

Answer:

16 ounces in a pound

14 x 16= 224 ounces

What do you want to be when you grow up? According to a nationwide survey of a random sample of 1000 kids under the age of 12 some kids want to be a ninja, a dragon keeper, a dancing unicom, and even an octopus. Fifty-five of the 1000 kids want to be a doctor. We would like to use this study to find a 98% confidence interval for the true proportion of kids who want to be a doctor.

a. Identify the parameter of interest.

b. Check if the conditions for constructing a confidence interval for p are met.

C. Find the critical value for a 98% confidence interval. Then calculate the interval

d. Interpret the interval in context

Answers

i think it is b i’m so sorry if i’m wrong

Using the z-distribution, we have that:

a) The parameter of interest is the proportion of kids who want to be a doctor.b) Since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.c) The critical value is [tex]z = 2.327[/tex]. The interval is (0.0339, 0.066).d) We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.

Confidence interval of a proportionIn a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

Item a:

We are interested in the confidence interval for the true proportion of kids who want to be a doctor, hence the parameter of interest is the proportion of kids who want to be a doctor.

Item b:

Fifty-five of the 1000 kids want to be a doctor, hence, since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.

Item c:

Fifty-five of the 1000 kids want to be a doctor, hence [tex]n = 1000, \pi = \frac{55}{1000} = 0.055[/tex].98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is [tex]z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.0339[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.066[/tex]

The interval is (0.0339, 0.066).

Item d:

We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.

You can learn more about the use of the z-distribution to build a confidence interval at https://brainly.com/question/25649070

What Is The Measure Of X?

Answers

Answer:

114°

Step-by-step explanation:

here's your solution

=> x° + 66° = 180°

=> x = 180° - 66°

=> x = 114°

hope it helps

Answer:

66°+x=180°[by linear pair]

x=180°- 66°

x=114°.

4)What kind of shape do the parametric equations make?X= 7sin(theta), y= 2cos(theta)

A) Circle

B) Ellipse

C) Square

D) Parabola

Answers

Answer:

Ellipse

Step-by-step explanation:

Given

[tex]x = 7sin\theta[/tex]

[tex]y= 2cos\theta[/tex]

Required

The kind of shapes with such equations

This answer to this question is(B) Ellipse

The parametric equation of an ellipse is represented as:

[tex]x = asin(\theta)[/tex] and [tex]y = bcos(\theta)[/tex]

In this case:

[tex]a=7\ b = 2[/tex]

So:

[tex]x = 7sin\theta[/tex] and [tex]y= 2cos\theta[/tex]

PLZ NEED HELP ASAP!!!!!!!!....
Choose the inequality that best matches each given situation.

The Garden Club is planting fruit trees in their school’s garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need pound fertilizer each.
A:25 x + 5 ≤ 12
B:1/2 x + 5 ≤ 25
C:1/2 x 25 ≤ 5
D:5 x + 1/2 ≤ 25
NEED HELP

Answers

Im not 100% sure but i believe it would be C

Answer:

im positive you don't need the answer anymore but i'm 96% sure it's B for anyone who's searching up the question

Step-by-step explanation:

(when I answered the question it had a check your answer thing and said B was right)

1 Factorise completely.
(a) 2a+4+ap+2p
(b) 162 – 8t^2

Answers

Answer:

Step-by-step explanation:

a) 2a + 4 + ap + 2p = 2*a + 2*2 + a *p + 2*p

                               = 2(a + 2) + p(a + 2)

                              =  (a +2) (2 + p)

b) 162 - 8t² = 2*81 - 2*4t²

                 = 2 (81  - 4t²)

                = 2( 9² - (2t)² )          {a² - b² = (a + b)(a -b)

                = 2 ( 9 + 2t) (9 - 2t)

Step-by-step explanation:

a. 2a + 4 + ap + 2p

2a + ap + 4 + 2p

a (2 + p) + 2 (2 + p)

= ( a + 2) ( 2 + p)

b. 162 - 8t^2

2( -4t^2 + 81)

Calculate the missing measure in the triangle 35º and 85º

Answers

Answer:

60º

Step-by-step explanation:

180º-35º-85º=60º

please help with my geometry

Answers

Answer: 9.90

Step-by-step explanation:

tan 48= 11/x

1.11=11/x

1.11x=11

x=9.90

I could use some help

Answers

Answer:

[tex]\boxed{50cm^2}[/tex]

Step-by-step explanation:

Hello There!

The shown figure is a trapezoid

The formula for area of a trapezoid is

[tex]A=\frac{a+b}{2} h[/tex]

where a = base 1

b = base 2

h = height

the dimensions given are

13 & 7 - bases

5 - height

so all we have to do is plug in the values into the formula

[tex]A=\frac{7+13}{2} 5\\7+13=20\\\frac{20}{2} = 10\\10*5=50\\A=50[/tex]

So we can conclude that the area of the trapezoid is 50 cm²

How can you determine the transformation of an exponential function?

Answers

Answer:

shifts to the right 3 units and up 2 units

Step-by-step explanation:

PLS HELP ILL GIVE BRAINLIEST


Explain how symmetry can help you find a figure's perimeter on the coordinate plane.

Answers

Answer: Think of it this way, symmetry is basically a mirror and you can better find the perimeter because you'll know that the sides are the same length

Step-by-step explanation:

Well if you have two sides that are symmetrical or an entire shape is symmetrical you can find the perimeter easier. So let's say two lines are symmetrical and one has the length of 2 the other one can also be two. If we have a symmetrical shape, then is would be a complete reflection.

A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.

what is symmetry ?

The definition of symmetry is a proportionate and balanced similarity between two sides of an object, where one half is the mirror image of the other. For instance, certain geometric forms like, rectangle, and circle are symmetric along their respective axes of symmetry.

since the shape's two halves would perfectly match if you folded it along the line. The shape will also remain unchanged if a mirror were positioned along the line , a square has four lines of symmetry.

A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.

To know more about symmetry visit :-

brainly.com/question/15970176

#SPJ2

If an object is projected upward with an initial velocity of 64ft per second from ground level, then its height in feet t seconds after it is projected is a function defined by: h(t)= -16t^2 + 64t. how long after it is projected will it be 48 feet above the ground?

Answers

Answer:

not sure

Step-by-step explanation:

x^2 - 6x+ 5= -11 number and type of solutions

Answers

Answer:

no real solutions

3±32i

Step-by-step explanation:

used quadratic formula

Which function below has a Domain of all Real Numbers (i.e. (-∞,∞))
A. Linear
B. Exponential
C. Quadratic
D. All of these functions have a domain of all real numbers (-∞,∞)

Answers

Answer:

all have domain of real numbers

Step-by-step explanation:

Evaluate the expression 3.2t when t is 1

Answers

Answer:

3.2

Step-by-step explanation:

3.2t when t=1

replace t with 1 so 3.2(1)

hence =3.2

I need help with all my 7 questions can someone help me with the first one ?

Answers

Answer:

x = 53

Step-by-step explanation:

x = 53 (Vertically Opposite Angles)

If you need to construct a dog run for your dog and the total perimeter needs to be 40 feet, and you only have enough room to make it 5 feet wide, how long can you make the dog run?

Answers

Answer:15 ft

Step-by-step explanation:

Given

The total perimeter needed is [tex]40\ ft[/tex]

The available width of the room is [tex]w=5\ ft[/tex]

Suppose l is the length of the room

So, the perimeter of a rectangle-shaped room is [tex]2(l+w)[/tex]

Putting values

[tex]\Rightarrow 40=2(l+5)\\\Rightarrow l+5=20\\\Rightarrow l=15\ ft[/tex]

p(x)+p(x+3)=10x-7 find p(3)​

Answers

Answer:

Simplify each term.

Px+px+3p=10x−7

Move all terms not containing P to the right side of the equation.

Px=10x−7−px−3p

Divide each term by x and simplify.

P=10−7/x−p−3p/x

Step-by-step explanation:


Need help ASAP plz. Right answer plz.

Answers

25.5 dollars.

Graph the equation and see where the highest point on the graph is. The x coordinate is the price and the y coordinate is the profit.

Remind???? anybody, or nobody???

Answers

Answer:

wdym? like the app remind?

Answer:

you have to download the remind app

Edwin goes to a restaurant with some friends.

Here are the meals they have

2 fish and chips at £9.25 each
1 chicken and chips at £9.50
1 roast lamb at £10.55
4 puddings at £4.55 each.

Edwin pays for the meals with three £20 notes.

How much change should Edwin get?

Answers

Answer:

£3.25

Step-by-step explanation:

£9.25×2+ £9.50+£10.55+£4×4.55

18.5+9.50+10.55+18.2

=£3.25

Answer:

£2.75

Step-by-step explanation:

2(9.25) + 1(9.50) + 1(10.55) + 4(4.55) = x

19.00 + 9.50 + 10.55 + 18.20 = x

28.50 + 28.75 = x

57.25

60 - 57.25 = 2.75

trigonometry please help! work need to be shown

Answers

Given:

The figure of a right angle triangle.

To find:

The value of x to the nearest hundredth.

Solution:

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

Using the above trigonometric ratio for the given triangle, we get

[tex]\cos 46^\circ=\dfrac{x}{8}[/tex]

[tex]0.6947=\dfrac{x}{8}[/tex]

[tex]0.6947\times 8=x[/tex]

[tex]5.5576=x[/tex]

Approximate the value to the nearest hundredth.

[tex]x\approx 5.56[/tex]

Therefore, the value of x is 5.56 units.

Which situations illustrate that the sum of opposite numbers is zero? Which situations illustrate that the sum of opposite numbers is zero?A) Shelley finds $50 in an old purse and deposits it in her bank account.B) Sara deposits $500 in her checking account and withdraws $500 from the ATM.C) After 3 forward flips and 3 backward flips, Anna is back where she started.D) Evan wins 1,000 points on a video game and wins another 1,000 points on the next game.E) At daybreak, the temperature is 18 degrees below zero. The temperature at noon is zero

Answers

Answer:

Step-by-step explanation:

b

Answer:

B)  C)  and E)    (i just took this in USA TestPrep

Step-by-step explanation:

Brenda bought 2 and one-half dozen donuts for 8.10. What was the cost per donut

Answers

Answer:

I came up with $3.20 each donut cost.

A television costs $400,00 cash. When bought on hire purchase, a deposit 1 point
of $60.00 is required with 12 equal monthly installments of $42.50. How
much is saved by paying cash?
O A. $60.00
O B. $80.00
O C. $110.00
O
D. $170.00

Answers

Answer D. 170
$42.50 x 12 months = $510 + the $60.00 deposit is $570. You subtract $570-400 and you get $170.

Circle the greater number:
0.0853 or 0.09

Answers

Circle 0.09 is larger
Other Questions
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Relationship between altitude and barometric pressure. A leading beverage company sells its signature soft drink brand in vending machines for $0.87 per 12 oz. can. A vending machine has monthly fixed costs of space rental, energy consumption, and capital depreciation of $146. Variable cost for a can of soda is $0.48. The more pessimistic operations manager was concerned about rising costs and asked the sales manager, if fixed costs increase to $190 per month, and the variable costs increase by $.10 due to rising sugar costs, what is the new breakeven volume in units at the original price Which of the following phase changes is exothermic?gas to solidsolid to liquidsolid to gasliquid to gas Looking for constructive criticism on my art. Im kinda stuck in a place where my art isnt getting much better and just wondering if any artists out there have any tips! Will give brainliest if you can give the best answer!! 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