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2 years ago

What’s this need help asap !

Mathematics

1 answer:

Vsevolod [243]2 years ago

5 0

I need points and i’m using this bc you didn’t even give an equation

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Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

4 0

2 years ago

If you roll a die three times how many different sequences are possible?

Rama09 [41]

216 sequences are possible

8 0

3 years ago

Which function is the inverse of f(x) equals negative 5X -4

nikitadnepr [17]

Answer:

f inverse x = -x+4/5

Step-by-step explanation:

5 0

3 years ago

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Evaluate 2 sin 60° + tan 45° + cos²60°

DerKrebs [107]

Answer:

1.25+√3 or 2.9821 to the nearest ten thousandth.

Step-by-step explanation:

sin 60 = √3/2, tan 45 = 1 and cos^2 60 = (1/2)^2 = 1/4

So we get 2 *√3/2 + 1 + 1/4

= √3 + 1.25

3 0

3 years ago

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Two consecutive positive integers have a product of 6. what are the integers

sergejj [24]

Hey there!

One way to do this is find all the factors of 6 and then see which pair fit the requirements.

The factors of 6 are 1, 2, 3, and 6. (Note: There can be negative factors, but I am going to leave them out since it is asking for positive integers.)

You can find them by asking if each number can go into 6.

1, 2, 3, and 6 all go into 6, while 4 and 5 do not.

The requirements we have is that they must be consecutive <u>and</u> have a product of 6.

Consecutive means right after one another.

The only numbers that fit this are 2 and 3.

2 x 3 = 6

Hope this helps!

6 0

2 years ago

Read 2 more answers