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3 years ago

What is log base 7 of 252

Mathematics

1 answer:

rjkz [21]3 years ago

4 0

Answer:

2.84

Step-by-step explanation:

Recognize that 252 = 7*36

and so:

log base 7 of 252 = log base 7 of 36 + log base 7 of 7, or

log base 7 of 36 + 1

So the most you can simplify log base 7 of 252 is to write 1 + log base 7 of 36.

Or, if you want to use the change of base formula, you could do the following:

log 36

log base 7 of 36 = -------------- = 1.84

log 7

and so log base 7 of 252 would come out to

1 + log base 7 of 36 = 1 + 1.84 = 2.84

Check: does 7^2.84 = 252? YES. So we know that:

1 + log base 7 of 36 = 2.84

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sdas [7]

Answer:

B.) 8%

Step-by-step explanation:

Answer: B.) 8%

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3 years ago

Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $9

insens350 [35]

Answer:

The annual interest rate was 4%

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

0.08 = x

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

0.08 / 2 = 0.04 * 100 = 4%

7 0

3 years ago

Carlos and Mike work part time as salespeople for an electronics store. Carlos earns $7.25 per hour plus a $10 bonus. Mike earns

galina1969 [7]

Carlos and Mike earn same amount for 10 hours of part time work

Solution:

Let "x" be the number of hours worked by Carlos and mike

Given that,

Carlos earns $7.25 per hour plus a $10 bonus

Thus, total amount earned by Carlos for "x" hours is given by:

total earned = 7.25(number of hours) + $ 10

total earned = 7.25x + 10 ----- eqn 1

Mike earns $7.75 per hour plus a $5 bonus

Thus, total amount earned by Mike for "x" hours is given by:

total earned = 7.75(number of hours) + $ 5

total earned = 7.75x + 5 ------- eqn 2

To find number of hours, they earn same amount, equate eqn 1 and eqn 2

7.25x + 10 = 7.75x + 5

7.75x - 7.25x = 10 - 5

0.5x = 5

x = 10

Thus for 10 hours, they earn the same amount

3 0

3 years ago

Use logarithmic differentiation to find dy/dx

liq [111]

Answer:

dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

Step-by-step explanation:

y = (x^2 - 3)^sinx

ln y = ln (x^2 - 3)^sinx

ln y = sin x * ln (x^2 - 3)

1/y * dy/dx = sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x

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3 years ago

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hram777 [196]

Answer:

The perimeter is 7 dm

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c------> the length of the third side

case a)

1+c>3

c>2 dm

case b)

1+3> c

4 > c

rewrite

c<4 dm

The solution for c is the interval------> (2,4)

therefore

the value of c must be equal to

c=3 dm (because is an integer)

The perimeter is equal to

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7 0

3 years ago