3 It takes of an hour to paint g of a room.

Determine whether the sequence converges or diverges. If it converges, give the limit.

Arte-miy333 [17]

the sequence is geometric, with the common ratio being 1/6 (48 * 1/6 = 8

The formula for a geometric sequence is cr^n where "c" is a constant and "r" is the common ratio
=48(1/6)^n.

A geometric series converges only if the absolute value of the common ratio is < It diverges if the ratio is >or equal to 1.
the ratio is 1/6, so the sequence converges.

Now in this case, the limit seems to approach 0,
values can only keep getting smaller.
If the limit approaches 0, then the series will converge to a definite sum
S = c / (1 - are)
S = 48 / (1 - 1/6)
S = 57.6

series converges, has a limit of 0,
sum of 57.6.
hope this helps

6 0

3 years ago

Given the ordered pair P, determine the requested sin, cos, or tan of angle . P(4, 5) sin = (4√41)/41 (5√41)/41 4/5 5/4 what is

Viefleur [7K]

Ok One side would have a length of 4, another side would have a length of 5, and then we can use the Pythagorean Theorem to find the length of the hypotenuse. a^2 + b^2 = c^2 

a=4; b=5; 

4^2 + 5^2 = c^2 
16 + 25 = c^2 
41 = c^2 
c = √41 

Therefore, the hypotenuse has a length of √41. 

To find the sinθ, you take the opposite over the hypotenuse. 

Remember when you drew out the triangle? θ is the angle connected to the origin. The opposite side is b, which is 5. 

Your answer is 5/√41. 

This answer must be simplified since there is a radical in the denominator. To simplify, you can just multiply the numerator and the denominator by √41/√41 (since this is equivalent to 1). 

This gives you the answer

6 0

3 years ago

What statement is used to prove quadrilateral ABCD is a parallelogram

Nookie1986 [14]

Answer:

I believe D is the answer. (Triangles BPA and DPC are congruent.)

Angles BAD and ADC are not congruent.

Sides CD and DA are also not congruent

3 0

3 years ago

Read 2 more answers

Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it t

Dmitry [639]

Answer:

Levi's dad takes 1.67 hours to wash the car by himself

Step-by-step explanation:

* Lets explain how to solve the problem

- Levi takes 2.5 hours to wash his dad's car alone

- Levi and his dad take 1 hour to wash the dad's car together

∵ Levi takes 2.5 hours to wash the car alone

∴ The rate of Levi is 1/2.5 car/hr

∵ His dad takes x hours to wash the car alone

∴ The rate of his dad is 1/x car/hr

∵ They working together for 1 hour to wash the car

- The equation of the work is rate of Levi × t + rate of his dad × t = 1

∵ t is the time of working together

∵ t = 1 hour

∴ $\frac{1}{2.5}(1)+\frac{1}{x}(1)=1========\frac{1}{2.5}+\frac{1}{x}=1$

- Multiply both sides by 2.5x to cancel the denominators

∵ $\frac{1}{2.5}(2.5x)=x=====\frac{1}{x}(2.5x)=2.5$

∵ 1 × (2.5x) = 2.5x

∴ x + 2.5 = 2.5x

- Subtract x from both sides

∴ 2.5 = 1.5x

- Divide both sides by 1.5

∴ x = 5/3 ≅ 1.67

∵ x is the the time of his dad to wash the car alone

∴ Levi's dad takes 1.67 hours to wash the car by himself

3 0

3 years ago

Read 2 more answers

Flora has 33 flowers and she can pick 7 flowers a minute. Write an equation that shows how many flowers, F, that Flora will have

monitta

F=7M
33=M
Both answers will work

3 0

4 years ago