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Leya [2.2K]
2 years ago
12

Use the Change of Base Formula to evaluate the expression. Then convert it to a logarithm in base 8. Round to the nearest thousa

ndth if necessary.
log4 8

0.667; log8 4.003

0.301; log8 1.870

1.5; log8 22.627

0.15; log8 1.366
Mathematics
1 answer:
Crazy boy [7]2 years ago
3 0

Answer

1.5; log8 22.627

Step-by-step explanation:

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Step 3a: Calculating the average rate
Alex73 [517]

9514 1404 393

Answer:

  a) average rate = (total distance)/(total time)

  b) Rave = 2·R1·R2/(R1 +R2)

  c) cheetah's average rate ≈ 50.91 mph

Step-by-step explanation:

a) Let AB represent the distance from A to B. Let t1 and t2 represent the travel times (in hours) on leg1 and leg2 of the trip, respectively. Then the distances traveled are...

  First leg distance: AB = 70·t1   ⇒   t1 = AB/70

  Second leg distance: AB = 40·t2   ⇒   t2 = AB/40

The average rate is the ratio of total distance to total time:

  average rate = (AB +AB)/(t1 +t2)

  average rate = 2AB/(AB/70 +AB/40) = 2/(1/70 +1/40) = 2(40)(70)/(70+40)

  average rate = 560/11 = 50 10/11 . . . mph

__

No equations are given, so we cannot compare what we wrote with the given equations. In each step of the solution, we have used the rules of algebra and equality.

b) For two rates over the same distance (as above), the average is their harmonic mean:

  average rate = 2r1·r2/(r1+r2)

__

c) The cheetah's average rate was 50 10/11 mph ≈ 50.91 mph.

4 0
3 years ago
Any gírl here<br>.<br>.<br>.<br>.<br>let's chàt​
Rufina [12.5K]

Answer:

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3 0
2 years ago
In the partial sequence …, 987, N, 2584, 4181, …, each new term is the sum of the two previous terms. Find the whole number valu
Alina [70]

Answer: 2584

Step-by-step explanation:

We can find N with 2584 and 4181.

4181 - 2584

= 1597

We can also check our answer by adding 1597 and 987

1597 + 987

= 2584

5 0
2 years ago
Prove the statement holds for all positive integers:<br><br> 2 + 4 + 6 + ... + 2n = n² + n
crimeas [40]

Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.

The relation 2+4+6+...+2n = n^2+n has to be proved.

If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2

Assume that the relation holds for any value of n.

2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)

= n^2 + n + 2n + 2

= n^2 + 2n + 1 + n + 1

= (n + 1)^2 + (n + 1)

This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.

<span>By mathematical induction the relation is true for any value of n.</span>

6 0
2 years ago
How do you solve this
love history [14]

Answer:

x=-2

Step-by-step explanation:

\frac{1}{6{x}^{2} }  =  \frac{1}{2x}  + \frac{7}{6 {x}^{2} }  \\  \frac{7}{6 {x}^{2} }  -  \frac{1}{6{x}^{2} }  +  \frac{1}{2 {x} }  = 0  \:  \:  \: \:  \:  ( -  \frac{1}{6 {x}^{2} } \: throughout) \\  \frac{6}{6 {x}^{2} }  +  \frac{1}{2x}  = 0  \:  \:  \:  \:  \: (simplify)\\ \frac{1}{ {x}^{2} }  +  \frac{1}{2x}  = 0 \\   \frac{2 {x}^{2} }{ {x}^{2} } +  \frac{2 {x}^{2} }{2x}  = 0 \:  \:  \:  \:  \: ( \times 2 {x}^{2} \:  throughout) \\ 2 + x = 0  \:  \:  \:  \:  \: (simplify)\\ x =  - 2

4 0
3 years ago
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