Simplify the expression completely.<br> (-3c-2d2e101-3)

The graph of this function is "M" shaped? f(x)=−3x4−7x3+6x2+5 Question 28 options: True False

Nana76 [90]

the answer of this question is 8 bro..........................................................

8 0

3 years ago

Consider the implicit differential equation <img src="https://tex.z-dn.net/?f=%2849%20y%5E%7B3%7D%20%2B%2045%20xy%29%20dx%20%2B%

BaLLatris [955]

We're looking for an integrating factor $\mu(x,y)=x^py^q$ such that

$\mu\underbrace{(49y^3+45xy)}_M\,\mathrm dx+\mu\underbrace{(98xy^2+50x^2)}_N\,\mathrm dy=0$

is exact, which would require that

$(\mu M)_y=(\mu N)_x$
$(49x^py^{q+3}+45x^{p+1}y^{q+1})_y=(98x^{p+1}y^{q+2}+50x^{p+2}y^q)_x$
$49(q+3)x^py^{q+2}+45(q+1)x^{p+1}y^q=98(p+1)x^py^{q+2}+50(p+2)x^{p+1}y^q$
$\implies\begin{cases}49(q+3)=98(p+1)\\45(q+1)=50(p+2)\end{cases}\implies p=\dfrac52,q=4$

You can verify that $(\mu M)_y=(\mu N)_x$ if you'd like. With the ODE now exact, we have a solution $F(x,y)=C$ such that

$F_x=\mu M$
$F=\displaystyle\int(49y^3+45xy)x^{5/2}y^4\,\mathrm dx$
$F=10x^{9/2}y^5+14x^{7/2}y^7+f(y)$

$F_y=\mu N$
$50x^{9/2}y^4+98x^{7/2}y^6+f'(y)=98x^{7/2}y^2+50x^{9/2}y^4$
$f'(y)=0$
$\implies f(y)=C$

and so the general solution is

$F(x,y)=10x^{9/2}y^5+14x^{7/2}y^7=C$

8 0

3 years ago

Subtract (5x+3)-(x+2)

Gemiola [76]

Answer:

C. 4x + 1.

Step-by-step explanation:

(5x+3)-(x+2) First remove the parentheses. Remember to distribute the negative over the second one:

= 5x + 3 - x - 2 Bring like terms together:

= 5x - x + 3 - 2 Simplify like terms:

= 4x +1.

8 0

3 years ago

4 ftA wire isneeded tosupport averticalpole 4 feettall. Thecable willbeanchoredto a stake3 feet fromthe baseof thepole. How3 ftA

Oxana [17]

SOLUTION

From the image in the question, we can see that it is a right triangle problem.

And we can use the Pythagoras theorem to solve for the length of cable wire needed.

Pythagoras theorem states that:

$\begin{gathered} \text{hypotenuse}^2=opposite^2+adjacent^2 \\ x^2=4^2+3^2 \end{gathered}$ $\begin{gathered} x^2=16+9 \\ x^2=25 \\ \text{Take the square roots of both sides:} \\ \sqrt[]{x^2}=\sqrt[]{25} \\ x=5ft \end{gathered}$

Final Answer:

A cable of length 5 feet is needed.

5 0

1 year ago

Se tienen dos libros: uno de 240 página y otro de 160 páginas. Si los 2 libros están formados por cuadernillos con el mismo núme

mafiozo [28]

Answer:

Book of 240 pages has 12 booklets in total

Book of 160 pages has 8 booklets in total.

Total booklets both the books have in total = 20

Step-by-step explanation:

Given - There are two books: one of 240 pages and the other of 160 pages. If the 2 books are made up of booklets with the same number of pages (between 16 and 28),

To find - How many booklets do the two books have in total?

Proof -

Given that, Number of pages of a booklet is between 16 and 28.

So, The number that lies between 16 and 28 will have to divide the number of pages of both the books.

(Because given that both the books are made up of booklet with the same number of pages)

By inspection, we get

The number of pages of a booklet = 20

because

240/20 = 12 and 160/20 = 8

∴ we get

1 booklet = 20 pages

i.e.

20 pages = 1 booklet

⇒1 page = $\frac{1}{20}booklet$

⇒240 pages = $\frac{240}{20}booklet$ = 12 booklet

So, we get

The book of 240 pages has 12 booklets in it.

Now,

1 page = $\frac{1}{20}booklet$

⇒160 pages = $\frac{160}{20}booklet$ = 8 booklet

So, we get

The book of 160 pages has 8 booklets in it.

∴ we get

Book of 240 pages has 12 booklets in total

Book of 160 pages has 8 booklets in total.

So, Total booklets both the books have = 12 + 8 = 20

4 0

3 years ago

Simplify the expression completely. (-3c-2d2e101-3)