(i) Factorise 3(x + 2)^2 - 10(x + 2) + 3

Mathematics

1 answer:

Setler79 [48]4 years ago

8 0

I'm not 100% sure but i think it is 35x+13

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Sin(x+2y)=cos(2x -y)

patriot [66]

$~~~~~~~\sin (x+2y) = \cos (2x-y)\\\\\\\implies \dfrac{d}{dx} \sin(x+2y) = \dfrac{d}{dx} \cos (2x-y)\\\\\\\implies \cos(x+2y)\dfrac{d}{dx}(x+2y) = -\sin(2x-y) \dfrac{d}{dx}(2x-y)~~~~~~~~~~~;[\text{Chain rule}]\\\\\\\implies \cos(x+2y) \left(1+2 \dfrac{dy}{dx}\right) = -\sin(2x-y)\left(2-\dfrac{dy}{dx} \right)\\\\\\\implies \cos(x+2y) + 2\cos(x+2y)\dfrac{dy}{dx} = -2\sin(2x-y)+\sin(2x-y) \dfrac{dy}{dx}\\ \\\\$

$\implies \sin(2x-y) \dfrac{dy}{dx} - 2\cos(x+2y) \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \left[\sin(2x-y) -2\cos(x+2y) \right] \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos(x+2y) + 2\sin (2x-y)}{\sin(2x-y) -2\cos(x+2y) }$

7 0

2 years ago

Identify the vertex and the axis of symmetry of the parabola. <br><br> HELP PLEASE!!!

jeka94

We know that the graph goes in units of 1.

We know that the roots are -1 and 4. (Just assume it's accurate and not off by 0.0000000001.)

We can set it up as an equation: -1(x+1)(x-4) = y (I added -1 because there are two parabolas that go through those points on the x-axis, and since this parabola is facing down, I must add a negative a value.

Then multiply (F.O.I.L. - First, Outer, Inner, Last)

x^2 -4x + x - 4 = -(x^2 - 3x - 4) = -x^2 + 3x + 4

Then using -(b/2a) solve for vertex: -(3/-2) = 3/2

Plug 3/2 back into the equation.

-(3/2)^2 + 3(3/2) + 4 = -9/4 + (9/2) + 4 = 25/4

The vertex would be: (3/2, 25/4)

Axis of symmetry would be: x = 3/2

8 0

4 years ago

the ice cream store makes 140 quarts of ice cream in 7 hours.how many quarts can be made in 12 hours?

Vaselesa [24]

Ok so to find the slope meaning how much quarts can be made in 1 hour you'd need to divide 140 by 7, if you do so you'll find 20. (20 quarts are made in an hour)

Now you can multiply 20 by 12, which is 240.

So, in 12 hours : 240 quarts of ice cream is made.

3 0

3 years ago

The perimeter of the rectangle is 28 units.

avanturin [10]

The value of w is 5 units

Step-by-step explanation:

Let l be the length of the rectangle

and w be the width

Then

l = 2w - 1