758 rounded of to the nearest hundred

Answer:

dy/dx = - (y/x)^4

Step-by-step explanation:

We are given the equation:

[tex] \displaystyle \large{ \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } = {a}^{3} }[/tex]

Recall important differential formulas such as:

[tex] \displaystyle \large{ \frac{d}{dx} (f(x) + g(x)) = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)} \\ \displaystyle \large{ \frac{d}{dx} k = 0 \: \: \tt(k \: \: is \: \: a \: \: constant.)}[/tex]

Above is a basic property of differential. Looking at the equation above, differentiate both sides with respect to x. (dy/dx)

[tex] \displaystyle \large{ \frac{d}{dx}( \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } )= \frac{d}{dx} {a}^{3} }[/tex]

Apply the distribution property in.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = \frac{d}{dx} {a}^{3} }[/tex]

We treat x^3 and y^3 as function to one another, this type of differential will be called implicit once another variable of function is involved f(x,y).

But we treat a^3 as a constant so we just put 0.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Recall the quotient rules for the numerator = 1.

[tex] \displaystyle \large{ \frac{d}{dx} (\frac{1}{f(x)}) = -\frac{ \frac{d}{dx} (f(x))}{ {(f(x))}^{2} } }[/tex]

Thus:

[tex] \displaystyle \large{ - \frac{ \frac{d}{dy} ( {x}^{3} )}{ ({x}^{3})^{2} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 } \\ \displaystyle \large{- \frac{ 3 {x}^{2} }{ {x}^{6} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Make sure to recall power rules for differential and exponent laws.

From 3x^2 / x^6.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Now what do we do with 1/y^3? We just differentiate it normally but we multiply with dy/dx once we differentiate the y function.

[tex] \displaystyle \large{- \frac{ 3 }{ {x}^{4} } -\frac{ \frac{d}{dx}( {y}^{3}) }{ ({y}^{3})^{2} } = 0 } \\ \displaystyle \large{ -\frac{ 3 }{ {x}^{4} } - \frac{ 3 {y}^{2} }{ {y}^{6}} = 0 } \\ \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 }[/tex]

Solve for dy/dx, add both sides by 3/x^4.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{3}{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 + \frac{3}{ {x}^{4} } } \\ \displaystyle \large{ - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = \frac{3}{ {x}^{4} } } \\ [/tex]

Divide both sides by - 3/y^4.

[tex] \displaystyle \large{ \frac{- \frac{3}{ {y}^{4} } \frac{dy}{dx} }{ - \frac{3}{ {y}^{4} } } = \frac{ \frac{3}{ {x}^{4} } }{ - \frac{3}{ {y}^{4} } } } \\ \displaystyle \large{ \frac{dy}{dx} = \frac{3}{ {x}^{4} } \times (-\frac{ {y}^{4} }{3} )} \\ \displaystyle \large{ \frac{dy}{dx} = \frac{1}{ {x}^{4} } \times (- \frac{ {y}^{4} }{1}) } \\ \displaystyle \large{ \frac{dy}{dx} = - \frac{ {y}^{4} }{ {x}^{4} } } \\ \displaystyle \large{ \frac{dy}{dx} = - ( { \frac{y}{x} })^{4}}[/tex]

Answer:

stan

Step-by-step explanation:

Stan paid less price per liter of gas which is $0.95 per liter.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Harry filled the 75 L gas tank of his pickup truck for $73.88.

Therefore, The cost of 1L of gas is $(73.88/75) = $0.98 per liter.

And Stan paid $0.95 per liter, So Stan paid less per liter of fuel.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Answer:

vggyyrt5 gf t66t6

Step-by-step explanation:

yy dry t6t ty y yuri u fry uu huf yy875

Answer:

-2.5, 0.75

Step-by-step explanation:

When we need to find a solution to a system of equations using a graphing tool, we graph those two equations and find the point of intersection.

This is an informative article on how to do that:

https://www.dummies.com/education/graphing-calculators/how-to-find-points-of-intersection-on-the-ti-84-plus/

Answer:

9.7

Step-by-step explanation:

9514 1404 393

Answer:

  x = -19 or 72

Step-by-step explanation:

The range of the given numbers is 5 to 48. In order for x to make the range be 67, the value of x must be 67 less than 48, or must be 67 greater than 5.

  x is 48 -67 = -19

or

  x is 5 +67 = 72

Answer: LCM of 8, 12, and 15 is 120.

Step-by-step explanation:

I hope this helps!

Answer:

2 and 1

Step-by-step explanation:

1 is the best which can go into

8 15 and 12

Step-by-step explanation:

short - S

long - L

L=10+S

L+S = 48

SINCE L=10+S

10+S+S=48

10+2S=48

2S=48-10

S=38/2=19

SHORT=19CM

LONG=10+S=10+19=39CM

Answer:

approximately 7 cm

Step-by-step explanation:

I’m not absolutely sure so double check

Answer:

-24+48i

Step-by-step explanation:

yan po ata sagot

Answer:

A

Step-by-step explanation:

1. Get 15% of 870:

   First, get 10 percent of 870, which is 87, then half that, which is 43.5

   Get the 87 and add the 43.5 on it, to get the full 15%, you end up with $130.5, which is the monthly payment.

(Only problem is that im pretty sure you put an extra 0, because if you just wrote 87 dollar's then you would've got 13.05, the actual answer, but if you add an extra 0 then you end up with 130$, just to let you know.)

Answer:

It's the Choice A c² = 36

Answer:

Looking at the equation, k=23 is our constant of proportionality because 23 is the constant number we multiply x by.

Answer:

- 1/64 (x+4)² (x-3) (x-4) = 0

Step-by-step explanation:

f(x) = a (x+4)²(x-3)(x-4)   ... curve touch (-4,0) and not cross x axis

x=0   f(x) = -3

a (4)² * (-3) * (-4) = -3

a = - 1/64

- 1/64 (x+4)² (x-3) (x-4) = 0

before you enter the data into the regression calculator, decide which variable should be on x and y axis. then enter the data pairs. press the linear regression button to create the regression line

graphed in the image attached with points,

hope this helps :D

Answer:

Hello, There! I'll be glad to help!

1/15 + 3/12

[tex]\boxed{Option ~C. ~19/60}[/tex]

Step-by-step explanation:

[tex]\frac{1}{15} +\frac{3}{12} =\frac{1 ~x~4}{15~x~4} +\frac{3~x~5}{12~x~5} =[/tex]

[tex]\frac{4}{60} +\frac{15}{60} = \frac{19}{60}[/tex]

Therefore, Your Answer is (Option C.)

Explanation:

Multiply the numbers up top: 8*1 = 8

Multiply the numbers in the bottom: 9*4 = 36

The two fractions 8/9 and 1/4 multiply to 8/36. Reduce this to 2/9 after dividing both parts by the GCF 4.

In other words,

8/4 = 2

36/4 = 9

Hello there! :)

When multiplying fractions, we multiply the numerator times the numerator and the denominator times the denominator. We reduce if it's necessary.

So multiply:

[tex]\frac{8}{9} *\frac{1}{4} \\[/tex]

Reduce and get:

[tex]\frac{2}{9} *\frac{1}{1} \\\frac{2}{9}[/tex]

And that's our final answer. Hope it helps you!

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

15 is divided by a number

Answer:

$5.49 per pair of gloves

Step-by-step explanation:

16.47/3=5.49

Answer:

do 16.47 divided by 3  and thats ur answer

Step-by-step explanation:

the answer is $5.49  for 1 pair of gloves

Answer:

you two shares for every one share of a company you own

Step-by-step explanation:

Answer:

6740

Step-by-step explanation:

Answer:

There is no function provided

FYI

Domian is all x-values

range is all y-values

For ex..

(-3,6)

-3 is domain

6 is range

Step-by-step explanation:

Answer:

There are 3.28084 feet per meter. So if you want to convert meters to feet using your own calculator, just multiply your number of meters by 3.28084.

Answer:

A. 1/2

Step-by-step explanation:

GradPoint answer

I got it correct on the lesson.

Answer: 300 miles, $220

Step-by-step explanation:

Answer:

D 130º

Step-by-step explanation:

3x-70=x+10

so 2x-70=10

x=40

Answer:

500 Hours

Step-by-step explanation:

Yes you are right, 500 hours is not an hour and I doubt anyone can work that much, there are only 168 hours in a single week.

If we're talking reality, it would take well over a few weeks.

If its just math then yeah you would get 500.

Either way, 500 is the right answer.