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3 years ago

Write the contrapositive of the conditional statement. If it is January, then there are 31 days this month.

Mathematics

2 answers:

guajiro [1.7K]3 years ago

8 0

Answer:

If there are not 31 days this month, then it is not January.

Step-by-step explanation:

Contrapositive of the conditional statement means switching the hypothesis and conclusion of a conditional statement and negating both.

Given statement is :

If it is January, then there are 31 days this month.

Its contrapositive will be :

If there are not 31 days this month, then it is not January.

kifflom [539]3 years ago

5 0

If there aren't 31 days this month, then it isn't January.

Hope this helps!

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3 years ago

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Answer:

2 1/2

Step-by-step explanation:

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2 years ago

Is (-a + b)² = a² - 2ab + b² right or wrong, and why?

antiseptic1488 [7]

Answer:

$\huge\boxed{\sf Right.}$

Step-by-step explanation:

$(-a+b)^2$

Let's apply the formula (x+y)² = x² + 2xy + y²

Here, x = -a and y = b

So,

= (-a)² + 2(-a)(b) + (b)²

= a² - 2ab + b²

Hence, it has been proved that (-a + b)² = a² - 2ab + b².

$\rule[225]{225}{2}$

Hope this helped!

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3 years ago

Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):