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2 years ago

What is the vertex of the function f(x) = 12 + 3x + ?

Mathematics

1 answer:

goldfiish [28.3K]2 years ago

6 0

Answer:

(2,1)

Explanation: f(x)=3x^(2)-12x+13

a=3

h=2

k=1

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How to solve derivative of (sin3x)/x using first principle

Leona [35]

$\dfrac{d}{dx}(\dfrac{\sin(3x)}{x})$

First we must apply the Quotient rule that states,

$(\dfrac{f}{g})'=\dfrac{f'g-g'f}{g^2}$

This means that our derivative becomes,

$\dfrac{\dfrac{d}{dx}(\sin(3x))x-\dfrac{d}{dx}(x)\sin(3x)}{x^2}$

Now we need to calculate $\dfrac{d}{dx}(\sin(3x))$ and $\dfrac{d}{dx}(x)$

$\dfrac{d}{dx}(\sin(3x))=\cos(3x)\cdot3$

$\dfrac{d}{dx}(x)=1$

From here the new equation looks like,

$\dfrac{3x\cos(3x)-\sin(3x)}{x^2}$

And that is the final result.

Hope this helps.

r3t40

7 0

2 years ago

Read 2 more answers

Tony has a bucket filled with green, blue, yellow, and red markers. He removes 3 markers from the bucket, with replacement. Sele

Margaret [11]

Answer:

Options A), B), C), D)

Step-by-step explanation:

There are 4 colors of markers.

Take out three "with replacement" markers.

As there is replacement, then the number of markers in the cube does not change in each trial.

A) There is a chance that when you get the three markers always get the same color.

B) It is likely to get a marker of each color

C) If 3 markers are taken it is likely to get the same amount of green and blue markers. For example, if there are 3 markers obtainable: blue, green, yellow. Then the number of blues and yellows is the same.

D) If 3 markers are taken it is likely to obtain the same amount of red and yellow markers. For example, if there are 3 markers you could obtain: red, yellow, blue. Then the number of reds and yellows is the same.

E) It is impossible for this to happen, because if only 3 markers of two different colors are taken, then there will always be 2 markers of one color and only one marker of another color:

green, green, yellow

blue, blue, green

blue, red, red .....

So the first 4 results are possible. Only the last result is impossible to obtain

5 0

2 years ago

A researcher believes that there is a difference in how cautious male stray cats and female stray cats are when approaching peop

Anika [276]

Answer:

The null hypothesis is that there is no difference in the mean number of male and female cats

H₀; μ₂ - μ₁ = 0

Step-by-step explanation:

The given parameters are;

The given percentage of male stray cat population = 50%

The given percentage of female stray cat population = 50%

The number of areas the researcher visits, n = 15

The number of stray male cats he finds = 11

The kind of test to be performed = Sign test

The significance level, α = 0.05

A) Therefore the null hypothesis is H₀; μ₂ - μ₁ = 0

The alternative hypothesis is Hₐ; μ₂ - μ₁ ≠ 0.

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2 years ago

Mariyah bought 5 yards of fabric and a spool of thread for $22.75. If the spool of thread cost

Tems11 [23]

Answer:

$4.25

Step-by-step explanation:

Subtract the cost of the spool of thread from the total price:

22.75 - 1.50

= 21.25

Then, divide this by 5 to find the cost of fabric per yard:

= 4.25

So, the cost of the fabric per yard is $4.25

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2 years ago

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Which of the following inequalities is equivalent to -31 + 12s <3s + 15 ?

Travka [436]

Answer:

-31+12s

Step-by-step explanation:

3 0

2 years ago