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The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

-3.9

Step-by-step explanation:

hope it helps have a nice day

Answer:-3.9

Step-by-step explanation:

Answer:

CS M=2/3 , KP M=2/3

Step-by-step explanation:

Neither because, they have the same slope but CS is negative so, the slopes are in a line.

Answer:

1 459.25 feet (1459 feet 3 inches)

The rate of the rowing team in clam water and the rate of current is 8 km/hour and 9 km/hour respectively.

Given information:

Distance traveled in clam water = 16 km

Time Taken = 2 hour

Rate in Clam water = Distance/Time = 16/2 = 8 km/hour

Distance traveled against the current = 18 km

Time Taken = 2 hour

Rate of current = Distance/Time = 18/2 = 9 km/hour

Hence, The rate of the rowing team in clam water and the rate of current is 8 km/hour and 9 km/hour respectively.

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Answer: 55

Step-by-step explanation:

Angle VWX and the 55 degree angle are vertical angles.

Answer: 55

Step-by-step explanation:90-31= 59

59-4=55

The statement "the integers and the natural numbers have the same cardinality" is false.

To understand why, let's first define what we mean by "cardinality." Cardinality refers to the size or quantity of a set, often represented by a number called its cardinal number.

Natural numbers are a set of counting numbers starting from 1, and they go on infinitely. So, the cardinality of natural numbers is infinite.

On the other hand, integers include both positive and negative numbers, including 0. The integers also go on infinitely in both directions. Thus, the cardinality of the integers is also infinite, but it is a different type of infinity than the natural numbers.

We can prove that the cardinality of the integers is greater than the cardinality of the natural numbers using a technique called Cantor's diagonal argument. This argument shows that we can always construct a new integer that is not included in the set of natural numbers, and therefore, the two sets have different cardinalities.

In summary, while both the integers and natural numbers are infinite sets, they do not have the same cardinality. The cardinality of the integers is greater than the cardinality of the natural numbers.

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Answer: -3

Step-by-step explanation:

A discount is the amount of money that is removed from the original price. The original price of the dishwasher is  $438.

A discount is the amount of money that is removed from the original price of a commodity when it is being sold.

We know that the commodity is being sold that a price of $361.35 but the discount is 17.5% and we are to obtain the original price of the commodity.

Let the original price be x

x - 17.5/100x = 361.35

82.5x/100 =  361.35

x =  361.35 * 100/82.5

x =  $438

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The 95% confidence interval for the average apple weight is (119.14, 125.86).

An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.

Let, n = 49

x = 122.5 

σ = 12

To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;

⇒ (x ± 1.96*σ/√n)

⇒ (122.5 ± 1.96*12/√49)

⇒ (119.14, 125.86)

Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).

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First, find the cost of how much fence Mary needs per side.

10 * 5 = 50

10 * 5 = 50

6 * 5 = 30

6 * 5 = 30

Second, add all together.

50 + 50 + 30 + 30 = 160

Therefore, the total cost of the fence will be $160.

Best of Luck!

The dynamic range for a 9-bit magnitude PCM code is 3072 dB.

The dynamic range for a 9-bit magnitude PCM code is the difference between the maximum and minimum representable amplitude levels, which is calculated using the formula:

Dynamic range = (2^n - 1) * 6dB

where n is the number of bits used to represent each sample in the PCM code.

For a 9-bit magnitude PCM code, n = 9, so the dynamic range is:

Dynamic range = (2^9 - 1) * 6dB = (512 - 1) * 6dB = 3072dB

So, a 9-bit magnitude PCM code has a dynamic range of 3072dB.

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Answer:

Define the variable: The variable is the cost of one jar of jelly

Equation to be solved: Refer to Step by Step

One jar of jelly cost: 1.60

Step-by-step explanation:

total bread cost: 9.87

total peanut butter cost: 8.97

total jelly cost: x

so 23.64 - (9.87 + 8.97) = x

simplified: 23.64 - 18.84 = x

even more simplified: 4.80 = x

so 3 jars of jelly is 4.80

so divide

4.80 divided by 3 = 1.6

so one jar of jelly costs 1.6

The situation that describes a similar but not congruent triangle is a dilation, as the side lengths are different but the angle measures are constant.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The definitions for similar and congruent triangles are given as follows:

For the dilation, due to the multiplication of the side lengths by the scale factor, the side lengths are modified, meaning that the original triangle and the dilated triangle are not congruent.

The angle measures, conversely, remain constant, meaning that the original triangle and the dilated triangle are similar.

This problem is incomplete, hence a simple example was given of a case in which triangles are similar but not congruent.

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The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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Answer:

It's 96

Step-by-step explanation:

-The left and right rectangles
5*4=20

(5*4)*2=40


-Triangle (front and back)
8*3/2=12

(8*3)/2*2=24


-Bottom Triangle (base)

8*4=32


-Area
=40+24+32
=96

Answer: 96 in^2

Step-by-step explanation: I took the quiz and got it right!! Hope this helps you, have a beautiful day!! :)

The length of the side BC is 12 units.

Two triangles are said to be similar if the ratio of their corresponding sides are in equal proportion and corresponding angles are also equal.

Given that, a right triangle ABC with altitude BD drawn to hypotenuse AC. and AC = 24 and DC = 6,

BD is the altitude, hence, it breaks Δ ABC into two similar triangles:

Therefore, Δ ABD ~ Δ BCD

Hence, The ratios of corresponding sides:

AD/BD = BD/DC ⇒ BD² = AD*DC ⇒ BD² = (24 - 6)*6 ⇒ BD² = 108

Also,

BC² = BD² + DC² ⇒ BC² = 108 + 6² = 144

BC = √144

BC = 12

Hence, the required length is 12 units.

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Answer:

x=0

Step-by-step explanation:

it is a straight line on the y axis making x=0

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The equation of a line can be written as:

y = mx + b

Where m is the slope and b is the y-intercept.

For the word problem, the slope is -10 and the intercept is 50, thus the equation is:

y = -10x + 50

If x is the number of weeks, then y decreases by 10 when x increases by 1. We expect that the value of y goes from 50 down to 40, 30, 20, etc.

The example of the friend is that he started with

Answer:

Evaluate 2/2-1/2. 22−12 2 2 - 1 2. Combine the numerators over the common denominator. 2−12 2 - 1 2. Subtract 1 1 from 2 2 . 12 1 2.

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

.

4

2

Answer:

x = 4, -4

Step-by-step explanation:

You can do this by simply pressing the calculator OR by simplify

4x^2 - 64 = 0

(2x)^2 - 8^2 = 0

(2x - 8)(2x + 8) = 0

∴ 2x - 8 = 0 or 2x + 8 = 0

x = 4 or x = -4

Answer:  Change = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

Use the way that kids use i.e trial and error method .

Solution:-

The set given by

\(\\ \rm\longmapsto \left\{32+n,\dfrac{n}{8},\sqrt{n+225}\right\}\)

Lets understand

Come to 2nd one.

Come to third one

Lets think

Nearest squares to 225 are 196 and 289

We can't take 196 as we have to take a positive one other wise it will come in terms of i.

Take 289

\(\\ \rm\longmapsto n+225=289\)

\(\\ \rm\longmapsto n=289-225=64\)

Its divisible by 8 .

Rewrite the set

\(\\ \rm\longmapsto \left\{64+32,\dfrac{64}{8},\sqrt{225+64}\right\}\)

\(\\ \rm\longmapsto \left\{96,8,\sqrt{289}\right\}\)

\(\\ \rm\longmapsto \left\{96,8,17\right\}\)

Hence n=64

Answer:

-5/6

Step-by-step explanation:

Using the slope formula we can easily find the slope

m=(y2-y1)/(x2-x1)

m=(-1-4)/(10-4)

m=-5/6