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 
.
We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as .
where k is from 1 to 10.
By the given expression sequence will be 
In this sequence first term "a" = 
and common ratio in each successive term to the previous term is 'r' = 
r = 
Since the sequence is infinite and the formula to calculate the sum is represented by
[Here r is less than 1]
S = 
Now we are sure that the sum of infinite terms is .
Therefore, sum of 10 terms will not exceed
Now sum of first two terms = 
Now we are sure that sum of first 10 terms lie between 
and
Since 
Therefore, Sum of first 10 terms will lie between and .
Option D will be the answer.
X = 2. Here’s a link; https://www.tiger-algebra.com/drill/(7x-5)_5=14/
Answer:
Number lines can show what the distance is that you have traveled from one point to the other. You would be able to count on the number line.
Point B on the ground is 5 cm from point E at the entrance to Ollie's house.
Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
The complete question is as follows:
Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.
The objective of this information is:
- To find angle CAB and;
- Find the distance Ollie is from the entrance to his house when he first activates the sensor.
The diagrammatic representation of the information given is shown in the image attached below.
Using cosine rule to determine angle CAB, we have:
Here:
∠CAB = Sin⁻¹ (0.3451)
∠CAB = 20.19⁰
From the diagram attached;
- assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;
Then, we can say:
∠CBD = ∠GBF
∠GBF = (CAB + ACB)
(because the exterior angles of a Δ is the sum of the two interior angles.
∠GBF = 15° + 20.19°
∠GBF = 35.19°
Using the trigonometric function for the tangent of an angle.
BF = 2.55 m
Finally, the distance of Ollie║FE║ from the entrance of his bouse is:
= 5 - 2.55 m
= 2.45 m
Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
Learn more about exterior angles here:
20 beacause 120 divided by 6 equals 20 so 60x20=120
