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Anna [14]
3 years ago
6

The table shows a student's proof of the quotient rule for logarithms.

Mathematics
1 answer:
nikklg [1K]3 years ago
5 0

Answer:

The error is at step (3) .

The correct step (3) will be,

\log_{b}(\frac {b^{x}}{b^{y}})

= \log_{b}(b^{x - y})   [by using the laws of indices]

All other steps are correct.

Step-by-step explanation:

The error is at the step (3) , because the student has tried to prove the quotient rule of logarithms by using the property i.e., 'The quotient rule of logarithm' itself , i.e. ,by  assuming the property does hold before proving it. So, the proof is fallacious.

The correct step (3) will be,

\log_{b}(\frac {b^{x}}{b^{y}})

= \log_{b}(b^{x - y})   [by using the laws of indices]

All other steps are correct.

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At what rate did the rain fall?
Levart [38]

Answer:

2 cm per hour

Step-by-step explanation:

1 hour lines up with 2cm

2 hours line up with 4cm

3 hours line up with 6cm

6 0
2 years ago
Read 2 more answers
25 lb greater or less than 384 oz
NeTakaya
25 lbs would be greater than 384 oz because 384 divided by 16 (because 16 oz per lb) =24lbs
so 25lbs > 384 oz
7 0
3 years ago
Find the Prime Factorization of -165
Ghella [55]

Answer:

(-1)(11)(3)(5)

Step-by-step explanation:

First off:  -165 separates into the factors (-1) and (165).  Next, we divide 165 by 15, obtaining 15(11).

So far, we have (-1)(11)(15).

15 is still factorable.  We get:

(-1)(11)(3)(5), which is the desired prime factorization of -165.

6 0
3 years ago
Please explain, thank you
RoseWind [281]

Answer:

C. 2.

Step-by-step explanation:

The graph descends from the left  so the coefficient of the leading term is negative. It is also a cubic equation with zeros of -20, about 6.5 and about 13. so we can write the equation as below.  The last 2 values can only be guessed because the x axis only shows values which are multiples of 5.

f(x) = a(x + 20)(x - 6.5)(x - 13)   where a is  a negative constant.

(This is only an approximation).

By the Remainder theorem, when the expression is divided by (x + 10):

f(-10) = -20 so we have

-20 = a (-10 + 20)(-10-6.5)(-10 - 13)

(10)(-16.5)(-23)a = -20

a = -20 / (10)(-16.5)(-23)

a = -0.0053

When  the equation is divided by (x - 10) then f(10)  is the remainder so substituting we have as the remainder:

-0.0053(10+20)(10-6.5)(10 -13)

-0.0053 * 30 * 3.5 * -3

= 1.7 approximately.

Looks like the answer is 2.

3 0
3 years ago
Sam borrowed $2,000,000 for a
Daniel [21]

The total amount Sam will pay in all will be $2,400,000

<h3>Simple interest </h3>

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

Learn more on Simple interest here: brainly.com/question/16134508

#SPJ1

4 0
2 years ago
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