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zaharov [31]
3 years ago
8

How do you use the product rule to find the derivative of y=x2⋅sin(x)y=x^2*sin(x) ?

Mathematics
1 answer:
zvonat [6]3 years ago
6 0
(f(x)\cdot g(x))'=f'(x)\cdot g(x)+f(x)\cdot g'(x)\\\\
y=x^2\sin x\\
y'=2x\cdot \sin x+x^2\cdot \cos x\\
y'=x(2 \sin x+x\cos x)
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The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\
600 = (x+5)(x+4)\\
600 =  x^{2} + 9x + 20


Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
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Answer:5400

Step-by-step explanation:9•6= 54

Add both zeros from 900 at the end and it’s 5400

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