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Advocard [28]
3 years ago
6

Help me with 11 and 12 please

Mathematics
1 answer:
djverab [1.8K]3 years ago
4 0
We can not see the rest of 12
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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of
Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is (-1)^{k+1}(\frac{1}{2^{k}}).

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as (-1)^{k+1}(\frac{1}{2^{k}}).

where k is from 1 to 10.

By the given expression sequence will be \frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......

In this sequence first term "a" = \frac{1}{2}

and common ratio in each successive term to the previous term is 'r' = \frac{\frac{(-1)}{4}}{\frac{1}{2} }

r = -\frac{1}{2}

Since the sequence is infinite and the formula to calculate the sum is represented by

S=\frac{a}{1-r} [Here r is less than 1]

S=\frac{\frac{1}{2} }{1+\frac{1}{2}}

S=\frac{\frac{1}{2}}{\frac{3}{2} }

S = \frac{1}{3}

Now we are sure that the sum of infinite terms is \frac{1}{3}.

Therefore, sum of 10 terms will not exceed \frac{1}{3}

Now sum of first two terms = \frac{1}{2}-\frac{1}{4}=\frac{1}{4}

Now we are sure that sum of first 10 terms lie between \frac{1}{4} and \frac{1}{3}

Since \frac{1}{2}>\frac{1}{3}

Therefore, Sum of first 10 terms will lie between \frac{1}{4} and \frac{1}{2}.

Option D will be the answer.

3 0
3 years ago
It's a PEMDAS question
monitta

[3 * (2 + 4)] - 4

  • Solve inside the brackets first.
  • Solve the parentheses inside the brackets, (2 + 4).

[3 * (6)] - 4

  • Now solve 3 * 6.

18 - 4

  • 18 - 4 = 14, so your answer is:
<h3>14</h3>
4 0
3 years ago
Read 2 more answers
Smallest number that can be made from 5 7 9 4
Vinil7 [7]

Answer:

Step-by-step explanation:

you want your largest digits to be in the units , tens, hundred, and then thousands

4,579

5 0
2 years ago
NEED HELP EMERGENCY ‼️
cestrela7 [59]

Answer:

A. Reflect across the y-axis

Step-by-step explanation:

if the negative sign was outside the radical then it would've been a reflection on the x-axis.

6 0
3 years ago
Read 2 more answers
A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it
makvit [3.9K]

Answer:

The length of the hallway is 10 m.

Step-by-step explanation:

Given:

Time taken to cover 1 km = 2.5 hours

Distance covered in 2.5 hours = 1 km

Therefore, speed of robot = \frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h

Now, speed is constant.

Now, time taken to cover the length of hallway = 90 s

Speed of the robot = 0.4 km/h

Converting 0.4 km/h to m/s, we multiply by the factor \frac{5}{18}. This gives,

0.4\times \frac{5}{18}=\frac{1}{9}\ m/s

Now, distance of the hallway is equal to the product of speed and time. So,

Distance of hallway = Speed \times Time

Distance of hallway = \frac{1}{9}\times 90=\frac{90}{9}=10\ m

Therefore, the length of the hallway is 10 m.

5 0
3 years ago
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