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4 years ago

Why is baseball in all its forms – from T-ball to the major leagues – important to Americans of all ages?

1 answer:

8 0

Baseball is a fun sport with a lot of history in the USA. Many families show their kids about baseball and that is how they start to like it. It gets passed on. But sports in general help you understand yourself. You get to be free and like what team you want, on play the way you want. There are many ways to understand yourself from sports <span />

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A1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16.

ICE Princess25 [194]

$a_1=12-12=(1\times12-0)-(12+0)$
$a_2=23-13=(2\times12-1)-(12+1)$
$a_3=34-14=(3\times12-2)-(12+2)$
$a_4=45-15=(4\times12-3)-(12+3)$
$a_5=56-16=(5\times12-4)-(12+4)$

Clearly, the general for the $n$ -th term is

$a_n=(12n-(n-1))-(12+n-1)=10n-10$

(Aside: given the simple pattern, it's curious why the terms would be given the way they are. It's easier to divine $10n-10$ from $a_1=0,a_2=10,a_3=20,\ldots$ , but that's just my opinion.)

The sequence does not converge. As $n\to\infty$ , so does $a_n\to\infty$ .

8 0

3 years ago

9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

coordinates of the center: $(x_m,y_m) = (7,8)$
radius of the circle: $r = 10$

we can put this in the formula of the circle:

$(x-a)^2+(y-b)^2=r^2$

in our case the equation changes to:

$(x-x_m)^2+(y-y_m)^2=r^2$

$(x-7)^2+(y-8)^2=(10)^2$

$(x-7)^2+(y-8)^2=100$

this is the equation of the circle!

6 0

3 years ago

Describe the scale of the graph.

Volgvan

Some of those numbers are negative and some of the other numbers aren’t negative

4 0

3 years ago

Please help me with this!!

zloy xaker [14]

Answer:

i dont see anything to answer its blank

Step-by-step explanation:

5 0

3 years ago

Im almost done with my last few khan academy assignments but i think i frogot how to do this one

Strike441 [17]

Answer:

x--------------y

4--------------2

8--------------3

12-------------4

Step-by-step explanation:

y = 1/4x + 1

We substitute the values under x into the equation

Equation 1: y = 1/4(4) + 1

Equation 2: y = 1/4(8) + 1

Equation 3: y = 1/4 (12) + 1

Let's solve for equation 1:

Equation 1: y = 1/4(4) + 1

y = 1/4(4) + 1

Multiply number in parenthesis

y = 1/4 * 4/1 + 1

1/4 and 4/1 turn into 1

y = 1 + 1

Add 1 to 1

y = 2

Let's solve for equation 2:

y = 1/4(8) + 1

Multiply number in parenthesis

y = 1/4 * 8/1 + 1

1/4 and 8/1 turn into 2

y = 2 + 1

Add 2 to 1

y = 3

Let's solve for equation 3:

y = 1/4 (12) + 1

Multiply number in parenthesis

y = 1/4 * 12/1 + 1

1/4 and 12/1 turn into 3

y = 3 + 1

Add 3 to 1

y = 4

So the table of values would be:

x--------------y

4--------------2

8--------------3

12-------------4

look at the graph

3 0

2 years ago