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Alexxx [7]
3 years ago
8

I need help with all of this

Mathematics
1 answer:
lord [1]3 years ago
6 0
1. 286 ft
3. 289 ft

I don’t know the rest sry
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2 gallons divided by 7 people
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2gallons/7people. This is the answer
5 0
3 years ago
Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p
Juli2301 [7.4K]
I'm reading this as

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy

with \nabla f=(2xe^{-y},2y-x^2e^{-y}).

The value of the integral will be independent of the path if we can find a function f(x,y) that satisfies the gradient equation above.

You have

\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}

Integrate \dfrac{\partial f}{\partial x} with respect to x. You get

\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx
f=x^2e^{-y}+g(y)

Differentiate with respect to y. You get

\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]
2y-x^2e^{-y}=-x^2e^{-y}+g'(y)
2y=g'(y)

Integrate both sides with respect to y to arrive at

\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy
y^2=g(y)+C
g(y)=y^2+C

So you have

f(x,y)=x^2e^{-y}+y^2+C

The gradient is continuous for all x,y, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e
8 0
3 years ago
Does it open up or down and is it shifted to the left 2 units or to the right 2 units of function g(x)
mixas84 [53]
It opens down if the lead coefficient is negative

And it shifts to the left by two. Always use the opposite of what is in parenthesis, which in this case is 2. 
7 0
3 years ago
Perform (3x3 – 2x2 + 3x – 4) ÷ (x – 3) to find the value of the remainder.
irakobra [83]
C) 88

Explanation: trust me
7 0
2 years ago
A l-meter steel rod is bent into a rectangle so that its length exceeds quadruple its width
Dmitry_Shevchenko [17]

Answer:

The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

Step-by-step explanation:

Given,

A 1 meter steel rod is bent into a rectangle.

That means the perimeter of the rectangle is 1 meter.

So, Perimeter = 1\ m=100\ cm

Let the width of the rectangle be 'x'.

Now According to question, length exceeds quadruple its width by 5 cm.

Hence framing the above sentence in equation form, we get;

Length=4x+5

Now we use the formula of  perimeter of rectangle,

Perimeter=2(Length+width)

On substituting the values, we get;

2(4x+5+x)=100\\\\(5x+5)=\frac{100}{2}\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=\frac{45}{5}=9

Now, we substitute the value of x to get the value of length;

Length=4x+5=4\times9+5=36+5=41\ cm

Thus, Width=9 cm    Length=41 cm

Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

6 0
3 years ago
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