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3 years ago

Find the distance d(A,B) between points A and B.

Mathematics

1 answer:

Misha Larkins [42]3 years ago

7 0

Answer:

A(4,-5) ; B(4,3)

distance d(A,B) = $\sqrt{( 4 - 4)^{2} + (3 -(-5))^{2} }$ = 8

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If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

6 0

3 years ago

A letter is randomly chosen from the word EXCELLENT. Write each probability as a fraction, decimal, and a percent.

Sergio [31]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete. A complete question is in the form:

A letter is chosen at random from the letters of the word EXCELLENT. Find the probability that letter chosen is i) a vowel ii) a consonant.

Solution:

The total number of letters found in the word EXCELLENT = 9

i) The number of vowel letters found in the word EXCELLENT = {E, E, E} = 3

Hence, probability that letter chosen is a vowel = number of vowels / total number of letters = 3 / 9 = 1 / 3

probability that letter chosen is a vowel = 1/3 = 0.333 = 33.3%

ii) The number of consonant letters found in the word EXCELLENT = {X, C, L, L, N, T} = 6

Hence, probability that letter chosen is a consonant = number of consonant / total number of letters = 6 / 9 = 2 / 3

probability that letter chosen is a consonant = 2/3 = 0.667 = 66.7%

7 0

3 years ago

Help ill give brainliest

stellarik [79]

Answer:

$28.68

Step-by-step explanation:

57.24+64.08

121.32

150-121.32

6 0

3 years ago

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The secret number has 5 digits: 3, 9, 1, 6, 2

Sphinxa [80]

92631

thats the answerrrrrrrrrrrrrrrrrrrr

5 0

3 years ago

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An inflatable raft that you have jumped in to escape the monsters has 4500 cubic inches of air inside it when fully inflated. It

DedPeter [7]

Answer:

2628.48 cubic inches

Step-by-step explanation:

The inflatable raft has 4500 cubic inches of air inside it when fully inflated.

The inflatable raft loses air at a rate of a decrease 6.5% each day.

Now, we have to calculate the volume of air that will be left in the raft after 8 days.

Therefore, the volume of air left in the raft after 8 days will be $4500[1-\frac{6.5}{100} ]^{8} =2628.48$ cubic inches. (Answer)

8 0

3 years ago