All categories

3 years ago

What is the least possible positive integer-value of n such that sqrt{18\cdot n \cdot 34}$ is an integer?

Mathematics

1 answer:

dusya [7]3 years ago

8 0

Answer:

n = 17. This means, √(18 x 17 x 34) = √(10404) = 102.

Step-by-step explanation:

An integer is a number that is not a fraction.

Given √(18 x n x 34), for the expression to be an integer, the product must be a perfect square. We are looking for n, the smallest number to multiply 18 x 34 to make it a perfect square. We have:

18 x 34 = 2 x 9 x 2 x 17 = 2 x 3 x 3 x 2 x 17 = 2² x 3² x 17.

From here, we see that we need to multiply an extra 17 to make it a perfect square, therefore n = 17. So we have:

√(18 x 17 x 34) = √(10404) = 102

You might be interested in

Which equations are true?

liberstina [14]

Answer:

B. D. E.

Step-by-step explanation:

A. False

${15}^{0} = 1$

B. True

$( {8}^{3} )( {8}^{6} ) = {8}^{(3 + 6)} = {8}^{9}$

C. False

${5}^{2} = 25$

D. True

$( {6}^{5} )^{3 } = {6}^{15}$

E. True

$\frac{ {3}^{7} }{ {3}^{9} } = {3}^{(7 - 9)} = {3}^{ - 2}$

3 0

3 years ago

What is another way to say 14 over 16 in fractions ( preferably in lowest number example 4 over 8 equals 1 over 2 both are halve

Degger [83]

Answer:

7/8

Step-by-step explanation:

The greatest common factor in each is two so you divide both the numerator and the denominator by two to simplify the fraction

4 0

3 years ago

A concrete mixing tub contains 34 liters of water and 22 liters of sand. Starting at the same time, water is added to the tub at

lubasha [3.4K]

Answer:

6 minutes

3 0

3 years ago

7) Mofor invests $3,101 in a savings account

Vika [28.1K]

Answer:

Step-by-step explanation:

$A = P(1+r/n)^{nt}$

A = final amount

P = initial amount

r = interest rate per time period

n = number of times compounded per time period

t = number of time period

A = 3932.82

r = what we want to find

n = 2

t = 6

$A = P(1+r/n)^{nt}\\3932.82 = 3101(1+r/2)^{12}$

divide both sides by 3101 to isolate the exponent and its parts

$3932.82/3101 = (1+r/2)^{12}$

put both sides to the power of (1/12) to help isolate the variable

$(3932.82/3101)^{1/12}= (1+r/2)$

subtract 1 from both sides to isolate the variable and its coefficient

$(3932.82/3101)^{1/12}-1= (r/2)$

multiply both sides by 2 to get r

$((3932.82/3101)^{1/12}-1) * 2= r$

r ≈ 0.04 = 4%

7 0

2 years ago

Please help me with this thank you

JulsSmile [24]

Answer:

I believe the answer to question (a) is 3085 ft and for (b) i think it's 238 ft

5 0

3 years ago

Read 2 more answers