1. Five more than three times a number is sixty- five.

Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a

NARA [144]

$x^3y^2+\sin(x\ln y)+e^{xy}=0$

Differentiate both sides, treating $y$ as a function of $x$ . Let's take it one term at a time.

Power, product and chain rules:

$\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}$

$=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}$

$=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}$

$=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)$

$=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}$

$=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)$

$=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}$

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

$3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0$

Isolate the derivative, and solve for it:

$\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}$

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by $y$ to get rid of that fraction in the denominator.

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}$

3 0

3 years ago

An isosceles triangle has an angle that measures 90°. Which other angles could be in that isosceles triangle? Choose all that ap

Inga [223]

Answer:

Step-by-step explanation:

If one angle = 90 degrees, then the other 2 added together must also = 90.

There is only 1 answer to this, since the triangle is isosceles..

x + x = 90 Combine

2x = 90 Divide by 2

x = 90/2

x = 45

So both acute angles = 45 degrees.

8 0

2 years ago

Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server p

nata0808 [166]

Answer:

The probability of the tip to be more than 200 is 0.1.

Step-by-step explanation:

As per the given data

Amount of tip Number

0-20 200

20-50 100

50-100 75

100-200 75

200+ 50

____________________

Total= 500

So what is the probability of tip to be more than 200 is given as

$P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}$

From the table the value is 50 for the tip to be more than 200 where as the total occurrences are 500 so substituting values:

$P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}\\P(200+)=\frac{50}{500}\\P(200+)=0.1$

So the probability of the tip to be more than 200 is 0.1.

5 0

3 years ago

Solve the above questions <br>don't spam

Bas_tet [7]

Answer:

10th question ka answer hai OK

7 0

3 years ago

Find the value of p in the figure below.

nirvana33 [79]

From the chord theorem we have:

$4\cdot4.5=6\cdot(2p-3)\\\\18=12p-18\\\\12p=18+18\\\\12p=36\qquad|:12\\\\\boxed{p=3}$

6 0

3 years ago