Joseph is playing with blocks to create a design. With each step he continues to add blocks. How many blocks will be required in the 5th and 6th step? Explain how you
know.

times by 2 because it keeps going up by times 2 the number of blocks

9514 1404 393

  5th: 32

  6th: 64

The number doubles at each step.

Step-by-step explanation:

Sequence problems are always tricky. Any finite list of numbers can always be represented by a polynomial, and can include any arbitrary next number. Generally, you are asked to find a simple rule that can explain the sequence shown and can be used to predict the continuation of the sequence.

It is often useful to look at the differences between values and/or their ratios. The sequence of block counts is ...

  2, 4, 8, 16

1st differences are 4 -2 = 2, 4, 8 . . . . . the differences match the sequence

ratios are 4/2 = 2, 8/4 = 2, 16/8 = 2 . . . . . . the ratio is common: 2

We observe that each number of blocks is double the one before, and that the number of blocks is a power of 2 equal to the step number.

The blocks in the 5th step will be 2^5 = 32.

The blocks in the 6th step will be 2^6 = 64.

Additional comment

It also looks like the shape alternates between a rectangle and a square. The 5th step will probably be a rectangle, and the 6th step will be a square.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

62.5 paisa

step-by-step explanation:

4000*70 = 280000

280000-(2000*90) = 100000

4000-2400 = 1600

100000/1600 = 62.5

( give brainliest)