Given the points below, find

What is the sum of the first five terms of a geometric series with a1 =20 and r =1/4?

drek231 [11]

The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,

Sn = (a1(1−r^n) / (1−r)

Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625

Thus, the sum of the first four terms is 26.5625.

5 0

2 years ago

Which relation is a function?

xz_007 [3.2K]

Answer:

I see this

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

So the answer is none of these.

Please make sure you have the correct problem.

Step-by-step explanation:

A set of points is a function if you have all your x's are different. That is, all the x's must be distinct. There can be no value of x that appears more than once.

If you look at choice A, this is not a function because the first two points share the same x, which is -3.

Choice B is not a function because the first and last point share the same x, which is 6.

Choice C is not a function because the last two points share the same x, which is 3.

Choice D is not a function because the first and last choice share the same x, which is -3.

None of your choices show a function.

If you don't have that choice you might want to verify you written the problem correctly.

This is what I see:

"Which relation is a function?

A {(-3,4),(-3,8),(6,8)}

B {(6,4),(-3,8),(6,8)}

C {(-3,4),(3,-8),(3,8)}

D {(-3,4),(3,5),(-3,8)}"

7 0

3 years ago

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

Oliga [24]

Answer:

$\displaystyle 1)48.2 \: \: \text{sec}$

$\rm \displaystyle 2)3021.6 \: m$

Step-by-step explanation:

<h3>Question-1:</h3>

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

$\displaystyle - 4.9 {t}^{2} + 229t + 346 = 0$

to solve the equation can consider the quadratic formula given by

$\displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a}$

so let our a,b and c be -4.9,229 and 346 Thus substitute:

$\rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

remove parentheses:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

simplify square:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}$

simplify multiplication:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8}$

simplify Substraction:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8}$

by simplifying we acquire:

$\displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5$

since time can't be negative

$\displaystyle t = 48.2$

hence,

at 48.2 seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

$\displaystyle x _{ \text{max}} = \frac{ - b}{2a}$

let a and b be -4.9 and 229 respectively thus substitute:

$\displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)}$

simplify which yields:

$\displaystyle t _{ \text{max}} = 23.4$

now plug in the maximum t to the function:

$\rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346$

simplify:

$\rm \displaystyle h(23.4) = 3021.6$

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

5 0

2 years ago

If you change the sign of a point's x-coordinate,how does the location of the point change?

yuradex [85]

If you change the point's x-coordinate, the point will move either to the left or the right, depending on if the number you change is negative or positive.

4 0

3 years ago

Quadrilateral ABCD with vertices A(4, 3), B(4, -2), C(-4, -2) and D(-4, 3) is a rectangle, find the length of the diagonals.

marin [14]

Distance between two points P(x1,y1), Q(x2,y2):
D=sqrt((x2-x1)^2+(y2-y1)^2)

Polygons are generally named in order along the perimeter, so that for a rectangle ABCD, AC or BD are diagonals.
Here, we need the distance between points A(4,3) and C(-4,-2)
Applying the above formula for distance between two points,

D=sqrt((4-(-4))^2+(3-(-2))^2)=sqrt(8^2+5^2)=sqrt(64+25)=sqrt(89)

6 0

2 years ago