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kykrilka [37]
3 years ago
6

23. According to one of Tolkien's essays, there were 144 elves originally created by the gods in Middle-Earth. If their numbers

tripled every century after that, how many elves were there 1000 years after the creation of Middle-Earth?
A) 432,000 elves
B) 59,049,000 elves
C) 432 elves
D) 8,503,056 elves
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0

Answer:

D

Step-by-step explanation:

elves in 1000 years = elves now x (rate of increase)^time

elves increase every century. there are ten years in a century. thus time = 1000/100 = 10 years

144 x (3)^10 =  8,503,056 elves

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A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strengt
ss7ja [257]

Answer:

Mean = 3640

Mode = 4100

Median = 3830.

Step-by-step explanation:

We are given the following data in the question:

Strength of casts (in psi):

3970,4100,3100,3200,2950,3830,4100,4050,3460

Formula:

Mean = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observations}}

\displaystyle\frac{3970+4100+3100+ 3200+ 2950+ 3830+4100+ 4050+ 3460}{9} = \displaystyle\frac{32760} {9} = 3640

Mode is the entry with most frequency. Thus, for the given sample mode = 4100.

Median

Since n = 9 is odd,

Formula:

Median = \displaystyle\frac{n+1}{2}th~term

Data in ascending order:

2950,3100,3200,3460,3830,3970,4050,4100,4100

Median = 5th term = 3830.

7 0
3 years ago
Check whether the function yequalsStartFraction cosine 2 x Over x EndFraction is a solution of x y prime plus yequalsnegative 2
Jobisdone [24]

The question is:

Check whether the function:

y = [cos(2x)]/x

is a solution of

xy' + y = -2sin(2x)

with the initial condition y(π/4) = 0

Answer:

To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.

Let us do that.

y = [cos(2x)]/x

y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]

Now,

xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x

= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)

= -2sin(2x)

Which is the right hand side of the differential equation.

Hence, y is a solution to the differential equation.

6 0
4 years ago
60 points
DIA [1.3K]

Answer:

2 is C. , 3 is C. , 4 is D.  

Step-by-step explanation:

2

Square roots are not polynomials

3

The highest degree of one term in the polynomial is 4

4

Terms are separated by (+) or (-) signs. If you count them up there are 4

7 0
3 years ago
Read 2 more answers
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igor_vitrenko [27]

Answer:

1   1/2

Step-by-step explanation:

Took the same thing

4 0
3 years ago
Change the value of n some more, and observe how the lengths of the sides of the image change. Once you've settled on a value fo
Anettt [7]

Answer:

n=3.5 a=1.41 units  a'=4.95 units b3 units b'10.5 units c2.24 units c'=7.83 units

Step-by-step explanation:

This answer assumes that n = 3.5. The ratio of each side length on  to the corresponding side length on  is equal to 3.5. For example, a′ = 3.5a. The ratio is equal to the scale factor, n.

4 0
3 years ago
Read 2 more answers
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