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erastovalidia [21]

3 years ago

15

What number and 12 have an average of 27?

1 answer:

artcher [175]3 years ago

6 0

Answer:

$\boxed{Number \: that \: give \: average \: of \: 27 \: with \: 12 \: is \: 42}$

Step-by-step explanation:

Let the number be 'x'

$= > \frac{x + 12}{2} = 27 \\ \\ = > x + 12 = 27 \times 2 \\ \\ = > x + 12 = 54 \\ \\ = > x = 54 - 12 \\ \\ = > x = 42$

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The vector wequalsaiplusbj is perpendicular to the line axplusbyequalsc and parallel to the line bxminusayequalsc. It is also tr

Likurg_2 [28]

Answer:

$\theta=45^{\circ}$

Step-by-step explanation:

We are given that the equation of lines

$x+\sqrt 3y=1$

$(1-\sqrt 3)x+(1+\sqrt 3)y=8$

According to question

The vector perpendicular to the lines is given by

$i+\sqrt 3j$ and $(1-\sqrt 3)i+(1+\sqrt 3)j$

Therefore, the angle between two vectors is given by

$cos\theta=\frac{a_1a_2+b_1b_2}{\sqrt{a^2_1+b^2_1}\sqrt{a^2_2+b^2_2}}$

Using the formula

$cos\theta=\frac{1(1-\sqrt 3)+\sqrt 3(1+\sqrt 3)}{2\times 2\sqrt 2}$

$cos\theta=\frac{1-\sqrt 3+\sqrt 3+3}{4\sqrt 2}=\frac{1}{\sqrt 2}$

$cos\theta=cos 45^{\circ}$

$\theta=45^{\circ}$

Hence, the acute angle between the lines is given by

$\theta=45^{\circ}$

3 0

3 years ago

Which of the following equations have complex roots?

Svetllana [295]

Answer: B

Step-by-step explanation:

We can rearrange the equation to get $x^2=-\frac{2}{3}$ , which clearly has complex roots.

7 0

2 years ago

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A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn Observe that, if n=0 or 1, the Bernoulli equation is line

aleksandr82 [10.1K]

It's unclear whether the ODE is

$xy'+y=4xy^2$

or

$xy+y'=4xy^2$

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$xy^{-2}y'+y^{-1}=4x$

then substitute $z=y^{-1}$ , so that $z'=-y^{-2}y'$ . Then

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If the second, then dividing through by $y^2$ gives

$xy^{-1}+y^{-2}y'=4x$

The same substitution as before gives

$xz-z'=4x\implies e^{-x^2/2}z'-xe^{-x^2/2}z=\left(e^{-x^2/2}z\right)'=-4xe^{-x^2/2}$

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$\implies z=4+Ce^{x^2/2}$

$\implies\boxed{y=\dfrac1{4+Ce^{x^2/2}}}$

5 0

3 years ago

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laila [671]

Answer:

Q

Step-by-step explanation:

5 0

4 years ago

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Effectus [21]

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3 years ago

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