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3 years ago

List two numbers that have the same value as 34 divided 3

Mathematics

1 answer:

mel-nik [20]3 years ago

6 0

Answer:

89/8

99/9

Step-by-step explanation:

34/3 =11.33

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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

What is the surface area of this prism?

Zigmanuir [339]

Let's find the area of each shape that makes up the prism. Let's first start with the triangles.

There are two identical triangles on both ends of the prisms. They have a height of 12 and a base 18. Let's find the area of both of the triangles.
12×18=216
216 is the area of both triangles. Each triangle has an area of 108 though.
Let's find the area of the two rectangles.

There are two identical rectangles that are 30 m by 15 m. Let's find the area of both.
30×15=450×2=900
So, the area of both rectangles together is 900.
Let's find the area of the rectangle that acts as the base in the picture.

There's only one and it's 30 m by 18 m.
30×18=540
Let's add everything together.

540+900+216
1440+216
1656

So, the surface area is 1656 m².

7 0

3 years ago

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Yanka [14]

Answer:

ENQEU

Step-by-step explanation:

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3 years ago

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A spinner has 13 equal-sized sections marked 1 through 13. Find the probability. Enter your answer as a simplified fraction. You

grin007 [14]

Answer:

7/13

Step-by-step explanation:

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3 years ago

Identify the distance between points (−3,−6,7) and (−9,5,−4), and identify the midpoint of the segment for which these are the e

melisa1 [442]

Step-by-step explanation:

LET THE Point 1 A and point 2 is B

(AB) ^2=(-9-(-3))^2+ (5-(-6))^2+(-4-7)^2=278

AB=16.67 length unit

Midpoint

X=-9-3/2 =-6

Y=5-6/2=-0.5

Z=-4+7/2=-1.5

4 0

3 years ago

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List two numbers that have the same value as 34 divided 3​

List two numbers that have the same value as 34 divided 3