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2 years ago

9

You have 26 cards, each labeled with a letter of the alphabet. What is the probability of drawing a card that contains one of th

e letters in the word 'MATH'?

2 answers:

Sindrei [870]2 years ago

8 0

Answer: you were right it was 2/13 thanks i needed it for my test

Step-by-step explanation:

UNO [17]2 years ago

6 0

4/26 which simplified to 2/13

so 2/13 is the answer

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Find dy/dx for y= x^3 ln (cot x)

ICE Princess25 [194]

<h3>Answer</h3>

$\dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)$

<h3>Explanation</h3>

By the product rule $(d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)$ , we have

$\begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}$

By the chain rule:

$\begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}$

By the power rule:

$(x^3)' = 3x^2$

thus

$\begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}$

Nothing to do to simplify any further, other than factoring out $x^2$ .

4 0

3 years ago

Find the terminal point on the unit circle determined by 5pi/4 radians

zimovet [89]

The terminal point represented by P(x,y), is the coordinate where a certain point lies. Given is 5pi/4 radians - this will be our angle.

Evaluate the values of x and y using sin θ and cos θ

x = cos (5pi/4)
x = -√2/2

y = sin (5pi/4)
y = -√2/2

Therefore, (x,y) is (-√2/2, -√2/2)

7 0

2 years ago

What is 1/7 As a decimal?<br><br> Give your answer rounded to 2 decimal places.

PIT_PIT [208]

Answer:

0.14

Step-by-step explanation:

1/7 = 0.1428571429.......

round to two decimal places so se look at the 4 which is the second decimal place, and then we see that the number to the right of it is less than 5 and therefore we round down to 4 and not 5.

:) hope this helps, please mark as brainliest!

4 0

2 years ago

Pls help me with math ASAP

Vladimir79 [104]

C. Supplementary
This means their angles add up to 180° which is a straight line

3 0

2 years ago

Read 2 more answers

The polynomial given below has _____ root(s).2x2 + 5x + 2

Nastasia [14]

2x^2 + 5x + 2 = 0
(x + 2)(2x + 1) = 0
x = -2 x = - 1/2
Letter C

8 0

3 years ago