Help mw with this one

A rule for nth term of -2 , -5/4 ,-1/2,1/4

miv72 [106K]

Answer:

Step-by-step explanation:

This is an arithmetic sequence

a1 = -2

Difference = 2nd term - first term

$=\frac{-5}{4}-[-2]\\\\=\frac{-5}{4}+2\\\\=\frac{-5}{4}+\frac{2*4}{1*4}\\\\=\frac{-5+8}{4}=\frac{3}{4}$

$a_{n}=a+(n-1)d\\\\=-2+(n-1)*(\frac{3}{4})\\\\=-2+\frac{3}{4}n-\frac{3}{4}\\\\=\frac{-2*4}{1*4}-\frac{3}{4}+\frac{3}{4}n\\\\=\frac{-8-3}{4}+\frac{3}{4}n\\\\=\frac{-11}{4}+\frac{3}{4}n$

6 0

4 years ago

Gideon is painting all sides of a square pyramid-shaped decoration at the top of his fence post. A net of the decoration is show

frez [133]

Gideon is painting all sides thus we find the overall area of the square pyramid given in the picture. A square pyramid is a polyhedron that consists of a square and 4 triangles. To solve the area that Gideon will have to paint, we can calculate the area of the square and the area of the triangles then add these two values of area. We proceed as follows:
Area of the square = s^2 where s is the measure of the side
Area of the square = 4^2 = 16 in^2

Area of the triangle= 1/2 bh where b is the base of the triangle and h is height of the triangle
Area of the triangle = 1/2 (4) (5) = 10 in^2
We multiply the area of the triangle to four in order to obtain the total area of the triangles.
Total area of the triangles = 4 x 10 = 40 in^2

We then add the two areas,
Total Area = 16 + 40 = 56 in^2

Thus the total area that Gideon will have to paint for one square pyramid is 56 in^2.

6 0

3 years ago

Identify the next two in the pattern: 28,26,24,22,...

UNO [17]

20, 18 because they are decreasing by a factor of 2

4 0

3 years ago

A thin rectangular sheet of metal is 6 inches wide and 10 inches long. The sheet of metal is to be rolled to form a cylinder so

Firdavs [7]

Answer:

Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77 $in^3$

Step-by-step explanation:

The given dimensions are

Width of the rectangle is 6inches.

Length of the rectangle 10inches.

Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.

so lets consider two cases

CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder

2*pi*r = 6

r = $\frac{6}{2pi}$

r = $\frac{3}{pi}$ Inch

and the height = 10inch.

Volume of the resultant cylinder will be

= $pi*r^2*h$

= $pi*(\frac{3}{pi} )^2*10$

= $\frac{9}{pi}*10$

= $\frac{90}{pi}$ = 28.662 $in^3$

CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.

2*pi*r= 10

r = $\frac{5}{pi}$

and the height of the cylinder is 6 inch

Now the volume of the cylinder will be

Volume= $pi*r^2*h$

= $pi*(\frac{5}{pi} )^2*6$

= $\frac{25}{pi}*6$

= $\frac{150}{pi}$ = 47.77 $in^3$

Clearly we have the second case in which the resulting Cylinder will have the maximum volume.

Therefore the CASE-2 will provide the maximum Volume of 47.77 $in^3$ to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.

5 0

3 years ago

How do you do this?<br> Please help x

kirill115 [55]

Answer:

Step-by-step explanation:

a). Given equation is y = 3x - 4

Table for the input-output values is,

x -1 0 1 2 3

y -7 -4 -1 2 5

Now we can plot these points on the graph (graph attached).

b). Equation is y = -2x + 3

Table for the input-output values will be,

x -1 0 1 2 3

y 5 3 1 -1 -3

3 0

3 years ago