Answer:
KL = 4.8
Step-by-step explanation:
In similar figures their corresponding parts have the same scale factor.
So CD : LM = 5 : 6
5KL = 24
KL = 24/5
KL = 4.8
Distribute to create an equivalent expression with the fewest symbols possible. 4(x - 2 y) =
1 answer:
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Answer: The angle of elevation would be 36.87 degrees (approximately)
Step-by-step explanation: Please refer to the attached diagram for details
The 30-foot ladder reaches a point in the building which is point A. The height at which the ladder touches the building is 18 feet (that is, the height of the building, line AC. The angle of elevation from the ground is at angle B, the angle which the ladder forms with the ground.
So we have a right angled triangle ABC, with two sides and a reference angle B. To find angle B, we shall apply the trigonometric ratio;
SinB = opposite/hypotenuse
SinB = 18/30
SinB = 0.6
By use of a calculator or table of values
B = 36.8698
Approximately, angle B = 36.87 degrees
Given that, the variable z is directly proportional to x.
So, we can set up an equation as following:
z = kx Where k is constant of variation.
When x= 13, z is 169.
Hence, next sep is to plug in these values in the above equation to get the value of k. Therefore,
169 = k * 13
Divided each sides by 13.
So, k = 13
By plug in k = 13 in the above equation we will get z = 13x.
Now we need to find the value of z when x = 19.
From the above equation we will get:
z = 13 * 19
z = 247
So, z = 247.
I hope this helps you!
Answer:
This series diverges.
Step-by-step explanation:
In order for the series to converge, i.e. it must hold that for any small
>0, there must exist
so that starting from that term of the series all of the following terms satisfy that
.
It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with , the other is constant with
, and the third one has terms that are approaching infinity.
Really, we can write this series like this:
If we denote the first series as , we will have that
.
The second series is denoted as and we have that
.
The third sub-series is a constant series and it holds that
.
Since those limits of sub-series are different, we can never find such so that every next term of the entire series is close to one number.
To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose , all those terms associated with the third sub-series will be out of this interval
.
Therefore, the observed series diverges.