All Answers 358179 Answers

You already have the zeroes. The vertex lies on the axis of symmetry between the zeroes.There is not enough information here to find it,or to find if the function has a maximum or a minimum value. Are you sure you were not given any other information for this problem?

Yeah.......this was a tricky one.......a graph definitely helps, IMHO....!!!!

-(-x-w)-(w-x)

Factor -1 from -(w-x)-(-x-w):
-(w-x-x-w)

Grouping like terms, w-x-x-w = (w-w)+(-x-x):
-((w-w)+(-x-x))

-x-x = -2 x:
-(-2 x+(w-w))

w-w = 0:
-(-2) x

-(-2)  =  2:
Answer: | 2x

120/1000 =.12 grams of vitamin c per 100 gram carrot

250/100 x .12 =.3 grams of vitamin c in 250 gram carrot, therefore,

2/0.3 =6 2/3 carrots needed to get 2 grams of vitamin c

tan^2x csc x=tan^2x    rearrange as

tan^2x cscx  - tan^2x   = 0      factor

tan^2x (cscx - 1)  =  0         set each factor to 0

tan^2x  = 0     take the square root of both sdes 

tan x   = 0      and this occurs    at      n * pi     where n is an integer

Also.....

cscx  - 1  =  0        add 1 to both sides

cscx  = 1        and this occurs   at    pi/2  + (n) * 2pi       where n is an integer

Just divide by 5 :)

|5|>|-9|   ???

l 5 l  = 5

l -9 l   = 9       ......so....

Is  5 > 9   ????   ......no.......it is false

Thanks for the points Chris.   

It was an interesting question.  :)

30 * 30 *30 = 27000cm^3

= 27,000ml

= 27Litres

 Use the method of completing the square to solve,

x2 + bx+ c = 0

where b and c are real numbers.

\(x^2+bx+c=0\\ x^2+bx=-c\\ x^2+bx+(\frac{b}{2})^2=-c+(\frac{b}{2})^2\\ (x+\frac{b}{2})^2=-c+\frac{b^2}{4}\\ (x+\frac{b}{2})^2=\frac{b^2-4c}{4}\\ x+\frac{b}{2}=\pm \sqrt{\frac{b^2-4c}{4}}\\ x+\frac{b}{2}=\frac{\pm\sqrt{b^2-4c}}{2}\\ x=\frac{-b}{2}\pm\frac{\sqrt{b^2-4c}}{2}\\ x=\frac{-b\pm \sqrt{b^2-4c}}{2}\\ \)

And there we have the quadratic formula for when a=1

Hi Asinus,

You are very lucky to be able to edit your answers - I wish I could edit mine  

Hi asinus,

It appears we have different answers    

A carrot has 120mg of vitamin c per 100g. if the average carrot weighs 250 gram. how many carrots do i need to eat to get 2grams of vitamin c?

\( \frac{120 mg (of\; vitamin )}{100g (carrot) },\qquad \frac{ 250g (of\; carrot) }{1carrot} \qquad, 2grams\; of\; vitC, \quad ?Carrots\\ \frac{120 mg (of\; vitamin )}{100g (carrot) },\qquad\frac{1carrot}{ 250g (of\; carrot) }\qquad, 2grams\; of\; vitC, \quad ?Carrots\\ \mbox{Carrot must be first and on the top}\\ \frac{1carrot}{ 250g (of\; carrot) }\times\frac{100g (carrot) }{120 mg (of\; vitamin )}\times 2grams\; of\; vitC\\ =\frac{1carrot}{ 250g (of\; carrot) }\times\frac{100g (carrot) }{120 mg (of\; vitamin )}\times 2000mg\; of\; vitC\\ \mbox{Now I can cancel all the units out except for the carrots}\\ =\frac{1carrot}{ 250}\times\frac{100 }{120}\times 2000\\ =\frac{1carrot}{ 5}\times\frac{1 }{3}\times 100\\ =\frac{20carrot}{ 3}\\ =6\frac{2}{3}\;carrots \)

Hello guest!

a carrot has 120mg of vitamin c per 100g. if the average carrot weighs 250 gram. how many carrots do i need to eat to get 2grams of vitamin c?

100g / 0.12g = x * 250g / 2g

0.12g * x * 250g = 100g * 2g

x = 100g * 2g / (0.12g * 250g) 

x = 6. 2/3

You need to 6 2/3 carrots.

Greeting asinus :- )

  !

Thank you, Melody! I have corrected the error.

Hi again Gibsonj338,

\(|5|>|\sqrt{-x+x^2}|\)

\(5>\sqrt{-x+x^2}\\ \qquad \mbox{For real solutions }\\ \qquad -x+x^2\ge0\\ \qquad x(x-1)\ge0\\ \qquad x\le0\quad or \quad x\ge1\\~\\ 25>x^2-x\\ 0>x^2-x-25\\ x^2-x-25<0\\ \mbox{This is a concave up parabola so this will be true between the roots}\\~\\ roots:\\ x=\frac{1\pm\sqrt{1+100}}{2}\\ required \;\;region:\\ \frac{1-\sqrt{101}}{2}<x<\frac{1+\sqrt{101}}{2}\\ BUT\\ \mbox{The region is also restrained by }\quad x\le0\quad and \quad x\ge 1\\ so\\~\\ \mbox{The region where this is true is }\\ \frac{1-\sqrt{101}}{2}<x\le0 \quad \cup \quad 1\le x < \frac{1+\sqrt{101}}{2}\\~\\ \mbox{This can also be expressed as} \\ (\frac{1-\sqrt{101}}{2},\; 0 ] \quad \cup \quad [1,\; \frac{1+\sqrt{101}}{2}) \)

Another look

There is a small inaccuracy in my positioning of the points in the graph above. The lower x-coordinate should be at -4.52 and the upper one at 5.52.

Graph might help

Hello Michael!

As Chloe and Ivan canoe across a lake, they notice a campsite ahead at an angle of 22 degrees to the left of their direction of paddling. After continuing to paddle in the same direction for 800 m, the campsite is behind them at an angle of 110 degrees to their direction of paddling. How far away is the campsite at the second sighting?

According to the law of sines behave 

800m / sin (180 - 22 - (180 - 110))° = x / sin 22°

800m / sin (180 - 22 - 70)° = x / sin 22°

x = 800m * sin 22° / sin 88° = 299.868m

The campsite is 300m from Chloe and Ivan.

Greeting asinus :- )

  !

Hello Guest!

What is the total surface area of a hemisphere and a cone ?

If they are put together, is the surface:

A = O + M

A = 2 * pi * r² + r * s * pi

s = √(r² + h²)

Greeting asinus :- )

  !

\(A=\pi{r}^{2}\)

\(A=Area\)

\(\pi=pi\)

\(r=radius\)

307

Solve for n:
n^2-50 n-600 = 0

The left hand side factors into a product with two terms:
(n-60) (n+10) = 0

Split into two equations:
n-60 = 0 or n+10 = 0

Add 60 to both sides:
n = 60 or n+10 = 0

Subtract 10 from both sides:
Answer: |  n = 60      or      n = -10

Which is the better investment?. In reality, it means which investment has a greater yield.

1) Bond yields cannot be solved directly, but only through iterations. My computer has this formula programmed in it and can solve for any variable:

1.5*[(1-(1+R)^-10)/(R)]+100*(1+(R))^-10-90=0, solve for R,

R=2.65155365262 per 1/2 year. Multiply it by 2 to get annual rate:

R=5.30310730524% compounded semi-annually.

2) The second bond's yield is found through "Cash Flow Analysis" Even though, the same as the first bond, there is no direct solution, again iterations can be used to find the yield, which is called "IRR", or Internal Rate of Return. This common formula is used: PV=FV[1 + R]^-N. The PV of all the payments plus the PV of the par value is calculated until it equates to the purchase price of $100. Again, this formula is programmed into my computer and can do many iteration per second. As a result, it found

R=2.62798318041 per 1/2 year. Multiply it by 2 to get annual rate.

R=5.25596636082% compounded semi-annually.

As can easily be seen, there isn't that much difference between the two bonds. The first bond has a slightly higher yield.

Pi x radius squared