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4 years ago

What two whole numbers is 29−−√ between?: 3 and 4 4 and 5 5 and 6 6 and 7

Mathematics

1 answer:

jolli1 [7]4 years ago

8 0

The two whole numbers are 5 and 6 ⇒ 3rd answer

Step-by-step explanation:

To prove that a square root number lies between which two consecutive integers do that

Find a square number less than the number under the root
Find a square number greater than the number under the root
Find the square root of the square numbers, they will be the two integers that the root lies between them

∵ The number is $\sqrt{29}$

- Find a square number less than 29

∵ 25 is a square number

∵ 25 is less than 29

- Find a square number greater than 29

∵ 36 is a square number

∵ 36 is greater than 29

∴ 25 < 29 < 36

- Take √ for each number

∴ $\sqrt{25}$ < $\sqrt{29}$ < $\sqrt{36}$

∵ $\sqrt{25}$ = 5

∵ $\sqrt{36}$ = 6

∴ 5 < $\sqrt{29}$ < 6

The two whole numbers are 5 and 6

Learn more:

You can learn more about the numbers in brainly.com/question/9621364

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Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

3 years ago

Determine whether the given set S is a subspace of the vector space V.A. V is the vector space of all real-valued functions defi

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Answer:

Check the explanation

Step-by-step explanation:

kindly check the attached image below to Determine whether the given set S is a subspace of the vector space (which is contained within a different vector space. So all the subspace is a kind of vector space in their own way, although it is also defined relative to some of the other larger vector space. The linear subspace is more often than not simply called a subspace whenever the situation serves to differentiate it from other types of subspaces.) V.A

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3 years ago

In the year 2003 a company made 8.8 million in profits. For each consecutive year after that their profits increased by 6%. How

yaroslaw [1]

Answer:

The company's profit in 2007 was 11.088 millions

Step-by-step explanation:

This is a compound interest problem where the initial amount is 8.8 million, the interest rate is 6% and the time period is 4 years and it gets compounded yearly. So we can use the compound interest formula, that is given by:

A = P*(1 + r/n)^(n*t)

Where A is the final amount, P is the initial amount, r is the rate, t is the total amount of time and n is the number of times it gets compounded in one year. We can now use all the values that were given to us to find out the profit of the company.

A = 8.8*(1 + (0.06))^(4) = 8.8*(1.06)^16

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So the company's profit in 2007 was 11.088 millions

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4 years ago

I-Ready

MAVERICK [17]

Answer: the answer is -2 1/3

Step-by-step explanation: it would be -2 1/3 because 5 + 2=7 and then add the 1/3 to make -7 1/3

5 0

3 years ago

Read 2 more answers

In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relat

Rus_ich [418]

Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.

What is Pythagoras Theorem?

The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.

The formula for Pythagoras Theorem is given by,

$h^{2}=a^{2} +b^{2}$

Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.

Each Subtraction in view of Pythagoras Theorem

It is is given that,

$d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }$

or $d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}$

Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.

Learn more about Pythagoras Theorem here:

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2 years ago