Answer:
<h3>10(x + 4y)</h3><h3 />
Step-by-step explanation:
factor of 10x + 40y
Let the unknown number be x. Then (1/10)x = 0.002. To solve for x, multiply both sides by 1000 to remove the decimal fraction 0.002.
Then 1000(1/10)x = 1000(0.002), or 100x = 2. Dividing both sides by x returns
x=100/2, or x= 50 (answer)
Answer: 16 square units
Step-by-step explanation:
let the vertex in quadrant I be (x,y)
then the vertex in quadratnt II is (-x,y)
base of the rectangle = 2x
height of the rectangle = y
Area = xy
= x(12 - x²)
= -x³ + 12x
d(area)/dx = 3x² - 12 = 0 for a maximum of area
3x² = 12
x² = 4
x = ±2
y = 12-4 = 8
So, the largest area = 2 x 8 = 16 square units
Answer:
=
+ ![cot x](https://tex.z-dn.net/?f=cot%20x)
Step-by-step explanation:
To verify the identity:
sinx/1-cosx = cscx + cotx
we will follow the steps below;
We will take just the left-hand side and work it out to see if it is equal to the right-hand side
sinx/1-cosx
Multiply the numerator and denominator by 1 + cosx
That is;
= ![\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsinx%281%2Bcosx%29%7D%7B%281-cosx%29%281%2Bcosx%29%7D)
open the parenthesis on the right-hand side of the equation at the numerator and the denominator
sinx(1+cosx) = sinx + sinx cosx
(1-cosx)(1+cosx) = 1 - cos²x
Hence
= ![\frac{sinx + sinx cosx}{1-cos^{2}x }](https://tex.z-dn.net/?f=%5Cfrac%7Bsinx%20%2B%20sinx%20cosx%7D%7B1-cos%5E%7B2%7Dx%20%7D)
But 1- cos²x = sin²x
Hence we will replace 1- cos²x by sin²x
=
=
= ![\frac{sinx+sinxcosx}{sin^{2}x }](https://tex.z-dn.net/?f=%5Cfrac%7Bsinx%2Bsinxcosx%7D%7Bsin%5E%7B2%7Dx%20%7D)
=
+ ![\frac{sinxcosx}{sin^{2}x }](https://tex.z-dn.net/?f=%5Cfrac%7Bsinxcosx%7D%7Bsin%5E%7B2%7Dx%20%7D)
=
+ ![\frac{cosx}{sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bcosx%7D%7Bsinx%7D)
=
+ ![cot x](https://tex.z-dn.net/?f=cot%20x)
=
+ ![cot x](https://tex.z-dn.net/?f=cot%20x)
Note that;
=
= ![cot x](https://tex.z-dn.net/?f=cot%20x)