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Afina-wow [57]
3 years ago
12

If L=√(x^2+y^2), dx/dt =-4, dy/dt=3, find dL/dt when x=4 and y=3

Mathematics
1 answer:
yulyashka [42]3 years ago
5 0

Hello,

L=\sqrt{x^2+y^2} \\\\\dfrac{dx}{dt}=-4\\\\\dfrac{dy}{dt}=3\\\\x=4, y=3\\\\\dfrac{\partial L} {\partial x} =\dfrac{x}{\sqrt{x^2+y^2}} \\\\\dfrac{\partial L} {\partial y} =\dfrac{y}{\sqrt{x^2+y^2}} \\\\\dfrac{dL}{dt} =\dfrac{\partial L} {\partial x}*\dfrac{dx}{dt}+\dfrac{\partial L} {\partial y}*\dfrac{dy}{dt}\\\\=-4*\frac{-4}{\sqrt{4^2+3^2}} +3*\frac{3}{\sqrt{4^2+3^2}}\\\\=\dfrac{16}{5} +\dfrac{9}{5} \\\\=5\\

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Solve for the missing variables, I know they add up to 360 but where do i start?
iren2701 [21]

Answer:

Step-by-step explanation:

a°=180°-36°=144° b°=180°-113°=67°

a°=144° and b°=67°

144+67=211

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3 0
1 year ago
How many times does the equation f(x)=2x^2+9x-5 intersect the x-axis
Komok [63]

Answer:

2

Step-by-step explanation:

f(x)=2x^2+9x-5

When we are find how many times it intersects the x axis, we are finding the zero's. Set the equation equal to zero

0=2x^2+9x-5

Factor the equation

0 = (2x+1) (x-5)

2*1

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2*-5 +1*1 = -9

This checks for the first last and middle terms so we factored correctly

Then using the zero product property

2x+1 = 0 and x-5 =0

2x = -1    x=5

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3 years ago
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground need
dalvyx [7]

Answer:

Length = 20.49 yards and Width = 12.49 yards.

Step-by-step explanation:

The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:

Area of the rectangle = length * width.

256 = x*(x+8)

x^2 + 8x = 256. Applying the completing the square method gives:

(x)^2 + 2(x)(4) + (4)^2 = 256 + 16

(x+4)^2 = 272. Taking square root on both sides gives:

x+4 = 16.49 or x+4 = -16.49 (to the nearest 2 decimal places).

x = 12.49 or x = -20.49.

Since length cannot be negative, therefore x = 12.49 yards.

Since smaller side = x yards, thus smaller side = 12.49 yards.

Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.

Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!

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3 years ago
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