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3 years ago

-4 + (-1) on a number line

Mathematics

2 answers:

satela [25.4K]3 years ago

6 0

Answer:

-5

Step-by-step explanation:

Note- Since these are negative numbers, when you add, you will be farther to a positive number.

-4 + -1 = -5.

It is like adding, so your answer is -5. Hope this helps!

katrin2010 [14]3 years ago

5 0

Answer:

-5

Step-by-step explanation:

+-=-

-4-1=-5

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Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

Which measures of central tendency would be affected if the outlier 11 was added to the following set 27,20,34,37,21,42,39

MrRa [10]

Answer:

Median will not be affected by the outlier.

Step-by-step explanation:

With the outlier, the mean will be dragged way down. The median will likely be about the same. Mean is non-resistant to outliers, median is resistant.

Hope this helps!

5 0

2 years ago

Y=x^2+bx+c;(-2,3)

Maksim231197 [3]

<h3>Answer: b = 4 and c = 7.</h3>

===============================================

Explanation:

Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.

The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.

Plug those three values into the vertex form below

y = a(x-h)^2 + k

y = 1(x-(-2))^2 + 3

y = (x+2)^2 + 3

Then expand everything out and simplify

y = x^2+4x+4 + 3

y = x^2+4x+7

We see that b = 4 and c = 7.

8 0

2 years ago

if you spend d dinars for g identical pair of glasses a friend claims that d if you increase g and increases if you increase d e

trasher [3.6K]

No, d depends on g my friend

3 0

2 years ago

Which of the following expressions contain a coefficient of 4? Choose the TWO correct answers.

lara [203]

Answer:

C and D

Step-by-step explanation:

A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.

3 0

2 years ago

Read 2 more answers