4

Write a formula to describe the sequence

Dominik [7]

Answer:

d

Step-by-step explanation:

A(n) = 1 - 0.1(n-1)

A(1) = 1- 0.1*(1-1) = 1 - 0.1*0 = 1

A(2) = 1- 0.1*(2-1) = 1 - 0.1*1 = 1- 0.1 = 0.9

A(3) = 1 - 0.1(3-1) = 1 - 0.1*2 = 1-0.2=0.8

Method:

A(1)=1

D = A(2)-A(1) = 0.9 - 1 = -0.1

A(n) = A(1)+(n-1)*d = 1 + (n-1)*(-0.1)

= 1 - 0.1(n -1)

8 0

3 years ago

Find the number of real number solutions for the equation.

daser333 [38]

Determinant = b² - 4ac = (-10)² + 4*1*25 = 100 - 100 = 0

So it has 1 solution.
Answer is D

5 0

3 years ago

Read 2 more answers

2. U svakome od pet redova pjevačkoga zbora nalazi se po 24 pjevača. Može li se cijeli zbor

Dmitriy789 [7]

Answer:Nem tudom

Step-by-step explanation:

8 0

3 years ago

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

List three examples of physical traits affected by tye environment?

german

Some answer's would be
hair
height and
eyed

5 0

3 years ago