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3 years ago

Find the sum of the geometric series 1 - 4/5 + (4/5)² - (4/5)³ + ... - (4/5)²⁹

Mathematics

1 answer:

masha68 [24]3 years ago

3 0

Answer:

Step-by-step explanation:

Given,

1st term (a) = 1

Common ratio (r) = -4/5

last term (l) = - $(4/5)^{29}$

Now,

Sum (S) = (lr- a)/(r - 1) =[(4/5)³° - 1]/(-9/5)

= -0.99876206/-1.8

= 0.5548678111

Sorry bro couldn't get answer in fraction.

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Which of the following functions is graphed below?

jenyasd209 [6]

Answer:

Step-by-step explanation: Hope that helps

3 0

3 years ago

Please help!!

Mamont248 [21]

Answer:

(Q.1) No solution

(Q.2) True

(Q.3) x = 4 - 2y

(Q.4) True

========================================

Step-by-step explanation:

(Q.1) As shown in the first attached figure.

By graphing. x + 2y = 8 & x + 2y = -4

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

===================================================

(Q.2) As shown in the second attached figure.

By graphing the system of inequalities y> -3x+2 & y<2x+1

The Shaded area represents the solution of the system of inequalities

And the point (4,2) is inside the shaded area

So, The ordered pair (4,2) is a solution to the system of inequalities.

====================================================

(Q.3)  solving the system { x+2y=4 & 2x+2y=6 } by substitution

From the first equation x + 2y = 4

we will find x in terms of y then plug it into the second equation

So, x + 2y = 4 ⇒ x = 4 - 2y

=====================================================

(Q.4) As shown in the third attached figure.

By graphing. 2x + 4y = 8 & x + 2y = 6

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

7 0

3 years ago

Read 2 more answers

Find the slope of the line that goes through the given points.

lesya692 [45]

Answer:

Step-by-step explanation:

the formula to calculate slope is

m=( y2-y1)/(x2-x1)

here,

(9,2)= x1 ,y1

(10,6)= x2 ,y2

putting the values in formula , we get

m= (6-2)/(10-9)

=4/1

= 4

8 0

3 years ago

Read 2 more answers

15 POINTS ANSWER ASAP, SHOW WORK

forsale [732]

Answer:

$V=97.6\ in^3$

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=4/2=2\ in$ ---> the radius is half the diameter

$h=8\ in$

substitute

$V=\pi (2)^{2}(8)\\\\V=32\pi\ in^3$

step 2

Find the volume of the cone

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$r=2\ in$ ---> the radius is the same that the radius of the cylinder

$h=0.70\ in$

substitute

$V=\frac{1}{3}\pi (2)^{2} (0.70)\\\\V=0.93\pi\ in^3$

step 3

Find the volume of the plastic object

we know that

The volume of the plastic object is equal to the volume of the cylinder minus the volume of the cone

$V=32\pi-0.93\pi=31.07\pi\ in^3$

assume

$\pi=3.1416$

$V=31.07(3.1416)=97.6\ in^3$

8 0

3 years ago

Amy runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?

lapo4ka [179]

That would be (4/6) of 45 minutes, or 180/6 minutes, or 30 minutes.

You could also find her rate: 6 miles / 45 minutes, or 8 miles / 60 minutes.

Write an equation of ratios:

8 mi 4 mi
---------- = ------------
60 min x

Solving for x: 8x = 240; x = 30 minutes

7 0

4 years ago