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Anettt [7]
3 years ago
13

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

Mathematics
1 answer:
nalin [4]3 years ago
7 0
First equation
a. 3x+5=65
b.3x=60     x=20



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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
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
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