All categories

3 years ago

What is the next number in the sequence 1,2,3,5,8,13,21,?

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

5 0

The next number in the sequence is 34. as you add the previous two numbers to get the next.

You might be interested in

The line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5)

velikii [3]

I think what you are looking for is to indicate an ecuation for this. So lets do the procedure:
First you need to find the slope of this line.
(5 - 6)/(5 + 1) = -1/6 
So, The slope of the perpendicular line is the opposite reciprocal, which is 
+6/1.Now we know the slope of the line but still have to find the mid point of the line. 
That is why we are going to use the mid point equation 
x = (-1 + 5)/2 = 2 
y = (6 + 5)/2 = 11/2 
(y - 11/2) = 6(x - 2) 
The last thing you do is rearrange the equation to get y = 6x - 6.5
Hope this is what you were looking for

8 0

3 years ago

Read 2 more answers

A box with a square base and open top must have a volume of 48668 cm3. We wish to find the dimensions of the box that minimize t

marin [14]

Answer:

x=46 gives us the minimum value

Step-by-step explanation:

Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by

$x^2\cdot y = 48668$ . From here, we know that $y=\frac{48668}{x^2}$

Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is $x^2$ . Recall that each side is a rectangle of base x and height y. So, the are of one side is $x\cdot y$ . Then, the area of the box is given by the function

$A(x,y) = x^2+4xy$ . Since we can relate y to x through the volume, this can be a function of one variable. Namely

$A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}$

If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form $x^n$ is $nx^{n-1}$ . Then, applying the properties of derivatives, we have

$A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}$

So, we want to solve the following equation

$2x^3-4\cdot 48668 =0$

which implies $x^3 = 97336$ . Using a calculator we get the value $x= 46$

REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0

Note that $A''(x) = 2+8\cdot\cdot 48668}{x^3}$ , note that A''(46) = 6>0, so x=46 is the minimum value of the area.

3 0

3 years ago

What does the notation f(2) mean?

Liula [17]

The expression "f(x)" means "plug a value for x into a formula f "; the expression does not mean "multiply f and x"! Don't embarrass yourself by pronouncing or thinking of "f(x)" as being "f times x". In notation, the "x" in "f(x)" is called "the argument of the function", or just "the argument".

3 0

3 years ago

Read 2 more answers

Please help i need this done by today

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

4 0

2 years ago

Heeeeeeeeeeeeeeeelp solve the following Q

Sati [7]

Answer:

$\huge\boxed{\sf \frac{y-5}{y-3} }$

Step-by-step explanation:

Solving it by mid-term break method:

$\displaystyle =\frac{y^2-3y-40}{y^2-11y+24} \\\\= \frac{y^2 -8y+5y-40}{y^2-3y-8y+24} \\\\= \frac{y(y-8)+5(y-8)}{y(y-3)-8(y-3)} \\\\Take \ (y-8) \ and \ (y-3)\ common\\\\= \frac{(y-8)(y-5)}{(y-8)(y-3)} \\\\= \frac{y-5}{y-3} \\\\\rule[225]{225}{2}$

Hope this helped!

5 0

3 years ago

Read 2 more answers