Ooh, quadratic equations!
alright, you see that zero at the end right?
that means you are trying to find the two factors
I'll write out the equation on paper to show you
take note of the signs in b and c
(ax²+bx+c)
because 5x is a negative (-5x), when you factor it out, the two, when multiplied together, should be negative. and because 30 is negative, the numbers will have two different signs. in other words, one will be positive and one will be negative.
now that that's cleared, we need to find all of the multiples of 30
there is:
30×1
15×2
10×3
and 6×5
of all of them, 10 and 3 would give you the -5 needed in -5× since one of them are going to be multiplied times 5
now let's factor it:
(5x+10)(x-3)
finally, divide everything
I wrote everything down for you to see
Sum of the radius of the base and height of a cylinder is 21 cm and the curved surface area of the cylinder is 616 sq.cm,find the total surface area of the cylinder. Help me with this question
Answer:
the E is the same as the circles
Step-by-step explanation:
Answer:
The volume is increasing at a rate of 16286 in³/min.
Step-by-step explanation:
a) The volume of a cone is given by:

Where:
r: is the radius
h: is the height
The rate of change of the volume can be calculated by using the chain rule:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bdh%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20h%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
Since h = 4/3 r we have:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bd%28%5Cfrac%7B4r%7D%7B3%7D%29%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20%5Cfrac%7B4r%7D%7B3%7D%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
(1)
With:
= 3 in/min

And by entering the above values into equation (1) we have:
![\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5B%283%20in%2Fmin%29%2A%2836%20in%29%5E%7B2%7D%20%2B%202%2A%2836%20in%29%5E%7B2%7D%2A3%20in%2Fmin%5D%20)

Therefore, the volume is increasing at a rate of 16286 in³/min.
I hope it helps you!
Answer:

Step-by-step explanation:
We want to find the equation in point-slope form of the line that passes through the point
and has slope
.
The point-slope form is given by the formula;

where
is the slope and
is a point on the line,
We substitute the values into the formula to obtain;
The required equation is 