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3 years ago

Find an equation of the tangent line to the curve y=arccos(x/2) at the point (1,4pi)

1 answer:

5 0

The derivative of inverse trigonometric identities follow a set of rules. 
For arc cos x, the dy/dx is equal to -1/ square root of (1 - x2).
In this case, we still have 1/2 x inside the angle quantity so we multiply the dy/dx above with 1/2. Hence, y' = is -1/ 2 square root of (1 - x2); x = 1, y' is infinity. this means the line is horizontal. The answer hence is y = 1.

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Plane R contains which of the following?

mars1129 [50]

The letter R is on the yellow section, which indicates the yellow area is plane R.

Now see what points and lines are on the yellow sections.

Point M, point R, line F are all in the yellow area. Point X and Y are at the intersection of the two planes, so could be part of both.

Based on the provided answers, the answer would be: Point M and line f.

4 0

3 years ago

Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. T

anyanavicka [17]

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

7 + 18 = 25 employees, which means that $N = 25$

7 over 50, which means that $k = 7$

10 dismissed, which means that $n = 10$

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055$

0.055 = 5.5% probability that exactly 5 employees were over 50.

5 0

2 years ago

Question 18.

DENIUS [597]

Answer: c

Step-by-step explanation:

sampling variability is the difference between the measured value of the random sample and the mean age of the population

3 0

3 years ago

The bakers made 25 each of lemon, apple, and

g100num [7]

Answer:

The answer is 600 pies

Step-by-step explanation:

25 times the 3 flavors is 75 pies per hour, multiplied by 8 is 600 pies

4 0

3 years ago

Read 2 more answers

Find the area of the shaded region. Round the the nearest tenth.

Brums [2.3K]

Answer:

226.084 sq.m.

Step-by-step explanation:

Radius of circle = 18.6 cm

Area of sector = $\frac{\theta}{360^{\circ} }\pi r^2$

Area of sector = $\frac{123}{360} \times 3.14 \times (18.6)^2$

Area of sector = $371.157 m^2$

Area of triangle = $\frac{1}{2} \times a \times b \times Sin x$

a = OA = radius = 18.6 cm

b = OB = radius = 18.6 cm

x =123 °

Substitute the values in the formula

Area of triangle = $\frac{1}{2} \times 18.6 \times 18.6 \times Sin 123$

Area of triangle = $145.073 m^2$

So, Area of shaded region = Area of sector - Area of triangle

= $371.157 m^2-145.073 m^2$

= $226.084 m^2$

Hence the area of the shaded region is 226.084 sq.m.

5 0

3 years ago