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k0ka [10]
3 years ago
9

Anwer with explanation

Mathematics
1 answer:
alex41 [277]3 years ago
7 0

Answer:

Step-by-step explanation:

\frac{y^2}{2x^2} +\frac{4y}{x} +18 ln(\frac{y-5x}{x} )=ln x+42\\diff.~w.r.t.~x\\\frac{1}{2} \frac{x^2 *2y \frac{dy}{dx} -y^2*2x}{x^4} +4\frac{x\frac{dy}{dx} -y*1}{x^2} +18*\frac{x}{y-5x} *\frac{x(\frac{dy}{dx} -5)-(y-5x)*1}{x^2} =\frac{1}{x} +0\\or \frac{xy\frac{dy}{dx} -y^2}{x^3} +\frac{4x\frac{dy}{dx} -4y}{x^2} +\frac{18\frac{dy}{dx} -90}{y-5x} -\frac{18}{x} -\frac{1}{x} =0\\\\multiply~by~x^3(y-5x)\\(y-5x)(xy\frac{dy}{dx} -y^2)+x(y-5x)(4x\frac{dy}{dx} -4y)+x^3(18\frac{dy}{dx} -90)-19x^2(y-5x)=0\\

(xy^2-5x^2y)\frac{dy}{dx} -y^3+5xy^2+(4x^2y-20x^3)\frac{dy}{dx} -4xy^2+20x^2y+18x^3\frac{dy}{dx} -90x^3-19x^2y+95x^3=0\\(xy^2-5x^2y+4x^2y-20x^3+18x^3)\frac{dy}{dx} =y^3-5xy^2+4xy^2-20x^2y+90x^3+19x^2y-95x^3\\(xy^2-x^2y-2x^3)\frac{dy}{dx} =y^3-xy^2-x^2y-5x^3\\\frac{dy}{dx} =\frac{y^3-xy^2-x^2y-5x^3}{xy^2-x^2y-2x^3}

Hence the result.

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The sum of two numbers is 68. The second number is 2 more than twice<br> the first.
e-lub [12.9K]

Answer:

22 and 46

Step-by-step explanation:

let

one number is x

another is 2x+2

now 2x+2+x=68

or, 3x+2=68

3x=66

or x=66/3=22

so one number is 22 and another is (22X2+2)=46

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3 years ago
Use the properties of exponents to simplify the expression: y^(y3)2
iren [92.7K]

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By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

8 0
3 years ago
Consider the integral 8 (x2+1) dx 0 (a) Estimate the area under the curve using a left-hand sum with n = 4. 250 Is this sum an o
Leya [2.2K]

Answer:

  (a) 120 square units (underestimate)

  (b) 248 square units

Step-by-step explanation:

<u>(a) left sum</u>

See the attachment for a diagram of the areas being summed (in orange). This is the sum of the first 4 table values for f(x), each multiplied by 2 (the width of the rectangle). Quite clearly, the curve is above the rectangle for the entire interval, so the rectangle area underestimates the area under the curve.

  left sum = 2(1 + 5 + 17 + 37) = 2(60) = 120 . . . . square units

<u>(b) right sum</u>

The right sum is the sum of the last 4 table values for f(x), each multiplied by 2 (the width of the rectangle). This sum is ...

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3 0
4 years ago
What is the product of – 7.2 x -3?
IrinaK [193]
The answer would be -21.6
6 0
3 years ago
A park is 4 times as it is wide. If the distance around the park is 12.5 kilometers what is the area of the park
MaRussiya [10]

Answer:

6.25 km

Step-by-step explanation:

Here is the correct question: A park is 4 times as long as it is wide. If the distance around the park is 12.5 kilometers, what is the area of the park?

Given: Perimeter (Distance) of the park= 12.5 km

Considering park is in rectangular shape.  

Let the width of park be x

∴ as given length will be 4x.

Formula for perimeter of rectangle =2\times (length + width)

Perimeter is given 12.5 km

⇒ 12.5= 2\times (4x+x)

⇒ 12.5= 10x

∴ x= 1.25 km, which means width is 1.25 km and length is 5 km.

Now, finding the area of park

Formula; Area of rectangle= length\times width

∴ Area of rectangle= 5\times 1.25 = 6.25 km

∴Area of park will be 6.25 km.

6 0
4 years ago
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