compute the equation of the tangent line to y = sin(x 2 ) at x = π/6

Answer:  Simplify the expression.

12x+6

Step-by-step explanation:

your answer is 12x+6

The natural length of the spring is approximately 3.97 cm.

The natural length (in cm) of the spring can be found by the following steps:

Given that 2.4 J of work is needed to stretch a spring from 15 cm to 19 cm  and 4 J is needed to stretch it from 19 cm to 23 cm.

We know that the work done in stretching a spring is given by the formula;

W = ½ k (x₂² - x₁²)

Where,W = work done

k = spring constant

x₁ = initial length of spring

x₂ = final length of spring

Let the natural length of the spring be x₀.

Then,

2.4 = ½ k (19² - 15²)

Also,4 = ½ k (23² - 19²)

Expanding and solving for k gives:

k = 20

Next, using the value of k in any of the equations to solve for x₀,

x₀² - 15² = (2 × 2.4) ÷ 20

x₀² = 15² + (2 × 2.4) ÷ 20

x₀² = 15.72

x₀ = √15.72

x₀ ≈ 3.97

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The variety of nonrandom sampling that takes proportions into consideration is: c) quota

Quota sampling is the variety of nonrandom sampling that takes proportions into consideration. In quota sampling, the researcher selects a specific number of participants from each subgroup of the population based on their proportion in the overall population. This ensures that the sample represents the different subgroups in the population proportionately.

In quota sampling, the researcher selects participants based on specific characteristics or proportions to ensure that the sample represents the target population accurately. The researcher sets quotas for different groups or segments based on known proportions or desired representation in the population.

For example, if a population consists of 60% males and 40% females, a quota sample might be designed to include the same proportions of males and females. The researcher would continue to select participants from each group until the quotas are met.

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the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

To solve this problem, we need to count the number of squares of each size that contain the black center square.

There is only one square of size\($5\times 5$\), which is the entire grid and obviously contains the black center square.

For squares of size\($4\times 4$\), there are \($4$\)possible squares that contain the black center square (one for each corner).

For squares of size\($3\times 3$,\) there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).

For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).

For squares of size \($1\times 1$\), there is only one possible square that contains the black center square (the center square itself).

Therefore, the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

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There are 11 squares containing the black center square in the 5x5 grid.

To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).

So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.

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Answer:

  0.92

Step-by-step explanation:

Each year, the value declines. This eliminates choices A and D.

The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...

  0.92 . . . . the third listed choice

a. There are 2 cycles in the graph.
b. The period of the graph is 360 degrees.
c. The amplitude of the graph is 2.


a. To determine the number of cycles in the graph, we need to count the number of complete repetitions of the pattern. In this case, there are 2 complete repetitions, so there are 2 cycles.

b. The period of a sine graph is the distance it takes to complete one full cycle. In this graph, one full cycle is completed in 360 degrees, so the period is 360 degrees.

c. The amplitude of a sine graph is the distance from the midline to the maximum or minimum point of the graph. In this case, the amplitude is 2 units. y = 2 sin θ.

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Answer:

0ption C is your answer

Step-by-step explanation:

by using Pythagoras law

x²=8²+15²

x²=289

x=√289=17

Answer:

The polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

Step-by-step explanation:

To convert the rectangular coordinates (0, 6√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = tan^(-1)(y/x)

Substituting the given values, we get:

r = √(0^2 + (6√3)^2) = 6√3

θ = tan^(-1)((6√3)/0) = π/2

However, note that the angle θ is not well-defined since x=0. We can specify that the point lies on the positive y-axis, which corresponds to θ = π/2 radians.

Thus, the polar form of the rectangular coordinates (0, 6√3) is:

r = 6√3

θ = π/2

To express the angle θ in terms of θo, where 0 ≤ θo < 27 and in radians, we can write:

θ = π/2 = (π/54) × 54 ≈ (0.0292) × 54 ≈ 1.58 radians

Therefore, the polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

Step-by-step explanation:

we use the point's coordinates to find the missing y-interception :

9 = 3×1 + b

9 = 3 + b

b = 6

so,

y = 3x + 6

Answer:

21.6 liters

Step-by-step explanation:

40 drops make up a volume of 10 mL

Therefore, the volume of 1 drop of water = 10mL/40 = 1/4 mL= 0.25mL

Since the tap loses 1 drop of water in 1 sec, it loses 0.25mL of water in 1 second

60 seconds make up 1 second so volume of water lost in 1 minute = 0.25 x 60 = 15 mL

60 minutes make up 1 hour so volume of water lost in 1 hour = 15 x 60 = 900 mL

24 hours make up a day so volume of water lost in 1 day = 900 x 24 = 21,600 mL

Since 1000 mL make up 1 liter, divide by 1000 to get volume in liters

Volume of water lost in 1 day = 21600/1000 = 21.6 liters

Can be done as one equation

V lost in one day = 0.25 x 3600 x 24 mL = 21600 mL = 21.6 L

Answer:

Hover for more information. In the given question, the accepted value is 350 grams; the experimental value is 342 grams. Therefore, the percentage error is % = % = 2.286% (to three decimal places). ... Therefore, the percentage error is 0.02286 x 100% = 2.286%.

The percentage error in selecting the random box is 2.285 %

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the total amount of bag of cereal be = 350 grams

The box selected at random had a weight of = 342 grams

The percentage error is calculated by the formula

Percentage Error =
( ( Original Value - Observed Value ) / Original Value ) x 100

So , the equation is

Percentage Error =
( ( Total weight of bag of cereal - Observed weight ) / Total weight ) x 100

Percentage Error = ( ( 350 - 342 ) / 350 ) x 100

                             = ( 8 / 350 ) x 100

                             = 0.02285 x 100

                             = 2.285 %

Therefore , the percentage error in selecting the random box is 2.285 %

Hence , the percentage error in selecting the random box is 2.285 %

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The sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

Given: The sample of seven infants was selected randomly and the weights are: {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6} (in pounds)

What is a sample?

A sample can be defined as a part of something big or a whole. It can be some of the elements from a given set of elements.

For example: Let us consider the set of natural numbers. The set of natural numbers has an infinite number of elements in it. We choose some numbers from the set, say {2, 7, 9, 10, 99, 200, 234}. These chosen numbers are known as samples from the set of natural numbers.

What is the sample mean?

The sample mean is the average value of the samples or it is the mean of all the elements which exist in the given sample.

The sample mean is denoted by x⁻ which is pronounced as x bar.

The formula to calculate sample mean (x⁻) is:

Sample Mean (x⁻) = Summation of all the elements in the sample / Total number of elements in the sample.

x⁻ = ∑xₙ / n

where,

∑xₙ = Summation of all the elements in the sample

n = Total number of elements in the sample

x⁻ = Sample mean

Now let's solve the given question:

The given sample is {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6}

The summation of the elements in the sample is:

∑xₙ = 9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6

∑xₙ = 52.9

The total number of elements in the sample is:

n = 7

Therefore, the sample mean (x⁻) is:

x⁻ = ∑xₙ / n

x⁻ = 52.9 / 7

x⁻ = 7.5571 ≈ 7.6

Hence the sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

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Disclaimer: The question is incomplete. The complete question is mentioned below:
Question: A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

Answer:

c

Step-by-step explanation:

$376.35 / 4 does equal to $94.0875 but when it comes to money, it should be rounded to the nearest cent being $94 and .08 cents.

Answer:

Try doing it yourself

Step-by-step explanation:

Answer:

it's pretty easy

Step-by-step explanation:

Answer:

228 cm

Step-by-step explanation:

the average is calculated as

average = \(\frac{sum}{count}\) , then

\(\frac{sum}{10}\) = 140 ( multiply both sides by 10 to clear the fraction )

sum = 1400

let the height of new pupil be x , then

\(\frac{sum+x}{11}\) = 148 ( multiply both sides by 11 )

sum + x = 1628 , that is

1400 + x = 1628 ( subtract 1400 from both sides )

x = 228

height of new pupil is 228 cm

Answer:

UV=25 units

Step-by-step explanation:

we know that

UW=UV+VW -----> by addition segment postulate

substitute the given values

4x+10=5x+5

solve for x

5x-4x=10-5

x=5

Find the value of UV

UV=5x

substitute the value of x

UV=5(5)=25 units

Answer:

338

explanation

no of students= 26

no of books read by each this year= 13

total books they have read although = 26×13= 338

\(\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m\)

Answer:

B

Step-by-step explanation:

We have a graph that models the value of a $20,000 car t years after it was purchased.

The value of the car is denoted with the y-axis in dollars and the time is denoted with the x-axis in years.

The question is: Which statement best describes why the value of the car is a function of the number of years since it was purchased.

The key element in this question is that we want to determine why the graph is a function.

Thus, we can eliminate C and D. A graph's rate of change and whether or not the graph touches 0 does not matter in determining whether or not a graph is a function.

So, we are left with two choices:

A) Each car value, y, is associated with exactly one time t.

B) Each time, t, is associated with exactly one car value, y.

Remember that for a relation/graph to a function, each input must match to exactly one output.

An input cannot repeat. Outputs can.

Therefore, we should be concerned with matching the input to exactly one output.

In this case, our input is the time t for the amount of years that passed.

And our output is the cost of the car.

Therefore, the correct answer is B.

Answer:

B

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

4.8 + 2.2 = 7

8.8 - 7 = 1.8

Answer:

  B.  6

Step-by-step explanation:

You want the 9th term of the arithmetic sequence with first term 30 and common difference -3.

The n-th term of an arithmetic sequence is given by ...

  an = a1 -d(n -1 . . . . . . . first term a1, common difference d

For the given first term and difference, the formula for the n-th term is ...

  an = 30 -3(n -1)

The 9th term is ...

  a9 = 30 -3(9 -1) = 30 -24

  a9 = 6

There are 6 logs in the 9th row.

__

Additional comment

Sometimes, the answer can be found quicker by simply listing the terms:

  30 27 24  21 18 15  12 9 6

The 9th row has 6 logs.

The frequency of this wave is 1 s⁻¹.

Since, We know that;

Frequency describes the number of waves that pass a fixed place in a given amount of time.

Given that;

A coiled spring with coils that are closely spaced then widely then closely then widely then closely, ending with a yellow line labeled 1 second.

We know that -

Frequency = 1 / Time period

f = 1/T

f = 1/1

f = 1 s⁻¹

Therefore, the frequency of this wave is 1 s⁻¹.

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the answer is x equal to 18

Answer:

m = 3/8

Step-by-step explanation:

ibdotn know if this is correct hit here s

The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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Answer:

2+10=12

3+9=12

4+8=12

5+7=12

6+6=12

Answer:

50x

Step-by-step explanation:

5x(7x + 3)

(7x + 3)= 10x

5x x 10x=50x