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Mathematics

1 answer:

viktelen [127]3 years ago

5 0

Answer:

Step-by-step explanation:

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, list the first five terms of each sequence, and identify them as arithmetic or geometric.

Scrat [10]

Each element is 2/3 times the previous one, so that's a geometric sequence.

6×(2/3)=4, 4×(2/3)=8/3, 8/3×(2/3)=16/9, 16/9×(2/3)=32/27

Answer: 6, 4, 8/3, 16/9, 32/27

4 0

3 years ago

You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

3 years ago

3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X

Llana [10]

Answer:

A total of 360 residents left Planet X in the past 3 years.

Step-by-step explanation:

120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.

8 0

2 years ago

Read 2 more answers

What is the volume of a box that will hold exactly 567of these cubes with 1.3 inch side

Bas_tet [7]

Answer:

21 inch cube

Step-by-step explanation:

(1/3)(1/3)(1/3)=1/27 is the volume of the cube

the volume of the box : 567*(1/27)=567/27=21

5 0

3 years ago