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3 years ago

What is the 77th derivative of y=sin(3x)?

1 answer:

8 0

With this, we have have a few things going on here. First notice the chain rule needed for 3x and then that d/dx sinx = cosx , d/dx cosx = -sin× , d/dx -sinx = - cos and finally
d/dx -cosx = sinx. In knowing these derivatives, you know that you need to take the derivative FOUR times to return it back to itself. Doing the 77th derivative makes you do taking the derivative in these 4 time "cycles" 19 times (bc 77/4 = 19.25) which leaves you with taking the derivative just ONCE more after the first 76 times. So the 77th derivative of sinx is cosx. That is not all though. Recognixe that you will also multiply it by 3 77times bc of chain rule, so the 77th derivative of sin (3x) is......: ( 3^77 × cos (3x) )

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What are the solutions of the quadratic equation?

KonstantinChe [14]

The quadratic equation:
4x^2 + 34x + 60 = 0
4x^2 + 24x + 10x + 60 = 0
4x(x + 6) + 10(x + 6)
(4x + 10) (x + 6)
x = - 6 , - 5/2
the answer is : c. -6, -5/2

hope this help

6 0

3 years ago

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The picture is the question, i need help, plz help!

Furkat [3]

You can set up a proportion to solve it.
6 15
------ = ------
270 x

270*15=4050
4050/6=675.

So the answer is B.
If you do not understand pls tell me.

3 0

3 years ago

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Hi. I need help with these See image for question Answer no 8 ,9 and 10

Nezavi [6.7K]

Answer:

8) 4 + 2q²/p² - 4r/p + r²/p²
9) (3/4, -9/4)
10) (3/8, 41/16)

Step-by-step explanation:

8. ============

Given

α and β are roots of px² + qx + r = 0

The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p

(2 + α²)(2 + β²) =
4 + 2(α² + β²) + (αβ)² =
4 + 2((α + β)² -2αβ) + (αβ)² =
4 + 2((-q/p)² - 2r/p) + (r/p)² =
4 + 2q²/p² - 4r/p + r²/p²

------------------------------

9. ============

Given function

y = 2x² - 3x - 1

The minimum point is reached at vertex

The vertex is:

x = -b/2a
x = -(-3)/2*2 = 3/4

The corresponding y-coordinate is:

y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4

So the point is:

(3/4, -9/4)

---------------

10. ============

Given function

y = 2 - 3x - 4x²

The maximum is reached at vertex

The vertex is:

x = -b/2a
x = -(-3)/2(-4) = -3/8

The corresponding y-coordinate is:

y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16

So the maximum point is:

(3/8, 41/16)

4 0

2 years ago

The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x + 12 = 48, where x

BARSIC [14]

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48 - First, subtract 12 from each side of the equation.

4x = 36 - Then, divide each side by 4 to get x by itself.

x = 9 - After dividing by 4, we are left with x = 9, so 1 ticket costs

$9.00

3 0

3 years ago

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Use the rational zero theorem to create a list of all possible rational zeroes of the function f(x) = 14x^7 - 4x^2 + 2

Bas_tet [7]

$f(x) = 14x^7 - 4x^2 + 2$

Use the rational zero theorem

In rational zero theorem, the rational zeros of the form +-p/q

where p is the factors of constant

and q is the factors of leading coefficient

$f(x) = 14x^7 - 4x^2 + 2$

In our f(x), constant is 2 and leading coefficient is 14

Factors of 2 are 1, 2

Factors of 14 are 1,2, 7, 14

Rational zeros of the form +-p/q are

$+-\frac{1,2}{1,2,7,14}$

Now we separate the factors

$+-\frac{1}{1}, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14},+-\frac{2}{1}, +-\frac{2}{2}, +-\frac{2}{7}, +-\frac{2}{14}$

$+-1, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14},+-2, +-1 , +-\frac{2}{7}, +-\frac{1}{2}$

We ignore the zeros that are repeating

$+-1, +-2, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14}, +-\frac{2}{7}$

Option A is correct

6 0

3 years ago

Read 2 more answers