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3 years ago

If we replace y with x2cos x and solve for y', we can conclude that the derivative is

Mathematics

1 answer:

marusya05 [52]3 years ago

5 0

Y = x^2 cos x

y' = x^2 * -sin x + cos x * 2x

= 2x cos x - x^2 sin x

= x ( 2 cos x - x sin x)

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Please help!! x = 2 - 3 cos t, y = 1 + 4 sin t in rectangular form? thank you! :)

sukhopar [10]

Answer:

$\frac{(x-2)^2}{9}+\frac{(y-1)^2}{16}=1$

Step-by-step explanation:

$x=2-3\cos(t)$

$y=1+4\sin(t)$

Let's solve for $\cos(t)$ in the first equation and then solve for $\sin(t)$ in the second equation.

I will then use the following identity to get right of the parameter, $t$ :

$\cos^2(t)+\sin^2(t)=1$ (Pythagorean Identity).

Let's begin with $x=2-3\cos(t)$ .

Subtract 2 on both sides:

$x-2=-3\cos(t)$

Divide both sides by -3:

$\frac{x-2}{-3}=\cos(t)$

Now time for the second equation, $y=1+4\sin(t)$ .

Subtract 1 on both sides:

$y-1=4\sin(t)$

Divide both sides by 4:

$\frac{y-1}{4}=\sin(t)$

Now let's plug it into our Pythagorean Identity:

$\cos^2(t)+\sin^2(t)=1$

$\frac{x-2}{-3})^2+(\frac{y-1}{4})^2=1$

$\frac{(x-2)^2}{(-3)^2}+\frac{(y-1)^2}{4^2}=1$

$\frac{(x-2)^2}{9}+\frac{(y-1)^2}{16}=1$

5 0

3 years ago

Read 2 more answers

jamerra received a $3,00 car loan. she plans on paying off the loan in 2 years. at the end of 2 years, jamerra will have paid $4

leonid [27]

The rate of interest is 75 % per year

Solution:

Given that, Jamerra received a $3,00 car loan

she plans on paying off the loan in 2 years

Jamerra will have paid $450 in interest

Therefore, we get

Principal = $ 300

Number of years = 2

Simple Interest = $ 450

Rate of interest = ?

The simple interest is given by formula:

$simple\ Interest = \frac{p \times n \times r}{100}$

Where,

"p" is the principal and "n" is the number of years and "r" is the rate of Interest

Substituting the given values we get,

$450 = \frac{300 \times 2 \times r}{100}\\\\450 = 3 \times 2 \times r\\\\6r = 450\\\\r = \frac{450}{6}\\\\r = 75$

Thus rate of interest is 75 % per year

5 0

3 years ago

If the 50th and 51st terms of an arithmetic sequence are 140 and 142, find the 1st term

morpeh [17]

Answer:

The first term is 42.

Step-by-step explanation:

The common difference is 142 - 140 = 2 so we have

50th term = a1 + 2(50 -1) = 140 where a1 is the first term

a1 + 98 = 140

a1 = 140 - 98 = 42.

4 0

3 years ago

- 16 to the power of -3/4

vekshin1

The answer to -16^-3/4 is -8

3 0

2 years ago

Molly has five cupcakes jack has teo rhey combinde rhat what do they get

inessss [21]

They have seven cup cakes!

5 0

3 years ago

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