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2 years ago

Find dy/dx given that y = sin(cos(x))

Mathematics

1 answer:

bazaltina [42]2 years ago

5 0

Hi there!

$\large\boxed{-sin(x)cos(cos(x))}$

Use the chain rule:

f(g(x)) = f'(g(x)) · g'(x)

Thus:

dy/dx sin(x) = cos(x)

dy/dx cos(x) = -sin(x)

Use the chain rule format:

f(x) = sin(x)

g(x) = cos(x)

cos(cos(x)) · (-sin(x))

-sin(x)cos(cos(x))

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Determine the measure of each segment then indicate whether the statements are true or false

kupik [55]

Answer:

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

Step-by-step explanation:

Considering the graph

Given the vertices of the segment AB

A(-4, 4)

B(2, 5)

Finding the length of AB using the formula

$d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}$

$=\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}$

$=\sqrt{6^2+1}$

$=\sqrt{36+1}$

$=\sqrt{37}$

$d_{AB}\:=\sqrt{37}$

$d_{AB}=6.08$ units

Given the vertices of the segment JK

J(2, 2)

K(7, 2)

From the graph, it is clear that the length of JK = 5 units

$d_{JK}=5$ units

Given the vertices of the segment GH

G(-5, -2)

H(-2, -2)

Finding the length of GH using the formula

$d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}$

$=\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}$

$=\sqrt{3^2+0}$

$=\sqrt{3^2}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$d_{GH}\:=\:3$ units

Thus, from the calculations, it is clear that:

$d_{AB}=6.08$

$d_{JK}=5$

$d_{GH}\:=\:3$

Thus,

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

8 0

2 years ago

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomly selected ad

VMariaS [17]

Answer:

The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

323 blacks, 86% of blacks said that they would welcome a white person into their families. This means that $n = 323, p = 0.86$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.86 - 1.96\sqrt{\frac{0.86*0.14}{323}} = 0.8222$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.86 + 1.96\sqrt{\frac{0.86*0.14}{323}} = 0.8978$

The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).

5 0

3 years ago

What is greater, 2/5, 3/10, 1/2, or 1/10?

Pani-rosa [81]

2/5 = 40%
3/10= 30%
1/2= 50%
1/10= 10%

so it's 1/2

7 0

3 years ago

Read 2 more answers

I really need this thank you

a_sh-v [17]

slope intercept form: y=mx+b

y=2x-3

slope is also m

b is the y-intercept

answer:

slope is 2

y-intercept is -3

8 0

2 years ago

Lisa [10]

Answer:

what? what is this supposed to be?

4 0

2 years ago

Find dy/dx given that y = sin(cos(x))​

Find dy/dx given that y = sin(cos(x))