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4 years ago

Read the statement.

Mathematics

1 answer:

svp [43]4 years ago

8 0

Answer:

A and B

Step-by-step explanation:

Given

p -> Doubling the sides of a rectangle

q -> Area increases by factor of 4

From the question we understand that q depends on p.

This means that the original statement is option A which says p → q

The arrow from p to q indicates that if p is true then q is true.

Hence, option A is correct

Option B is also correct because it represents the inverse of (A) above.

I.e. if the sides of the triangle is not doubled, then the area won't increase by a factor of 4.

This in its actual sense represent negation or inverse statement.

Hence, options A and B answer the question while other options are incorrect.

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Solve the linear differential equation 2xy' + y = 2√x

77julia77 [94]

Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

$\frac{dy}{dx}+P(x)y=Q(x)$

For this case, we can rewrite the equation as:

$\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}$

Here $P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}$

To find the solution (y(x)), we can use the integration factor method:

$Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx$

Then $F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}$

So, we can find:

$y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C$

Suppose that $x\in \double R$ , then $\sqrt{|x|}=\sqrt{x}$ , and we find:

$y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}$

To check our solution is right or not, put your y(x) back to the ODE:

$y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}$

$2xy'=\frac{x-C}{\sqrt{x}}$

$2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}$

(it means your solution is right)

3 0

2 years ago

How many bucketloads would it take to bucket out the world’s oceans? Write your answer in scientific notation.

kodGreya [7K]

Answer: $7\times10^{19} buckets$

Step-by-step explanation:

Given: A cubic kilometer= $10^{15}$ cubic centimeters

The volume of world’s oceans= $1.4\times10^{9}$ cubic kilometers of water.

⇒ The volume of world’s oceans= $1.4\times10^{9}\times10^{15}$ cubic centimeters of water.

Volume of a bucket = 20,000 cubic centimeters of water.

The number of bucket-loads would it take to bucket out the world’s oceans

$n=\frac{\text{volume of ocean}}{\text{volume of bucket}}=\frac{1.4\times10^{9}\times10^{15}}{20000}$

$\Rightarrow\ n=\frac{1.4\times10^{9+15}}{0.2\times10^5}......[a^n\times a^m=a^{m+n}]\\\Rightarrow\ n=7\times10^{24-5}.....[\frac{a^m}{a^n}=a^{m-n}]\\\Rightyarrow\ n=7\times10^{19}$

hence, $7\times10^{19}$ bucketloads would it take to bucket out the world’s oceans.

5 0

3 years ago

When you multiply a mixed number by a fraction less than 1, will the answer be smaller?

mars1129 [50]

Answer:

no when you multiply anything it will always become bigger multiply means bigger

Step-by-step explanation:

8 0

3 years ago

(Name all sets to which each value belongs. Rational, irrational, whole or natural.

saw5 [17]

Answer:

Step-by-step explanation:

The natural numbers, whole numbers, and integers are all subsets of rational numbers. In other words, an irrational number is a number that can not be written as one integer over another.

Moderators i have not copied this ans

6 0

3 years ago

If the length of one leg of a right triangle is 16 and the length of the hypotenuse is 2 more than the length of the other leg,

Arturiano [62]

Let the length of one leg be x then another leg is (x+2)

According to Pythagoras theorem,
x^2 + (x+2)^2=16^2
=> x^2 + 2x - 126 =0
=>x= √(126 - 1) = 10.225
By sreedharchaya's formula

6 0

4 years ago