Numerical Analysis and differential equation( please help with Q21 the polynomial p2(x) = 1 − 1 2 x2 is to be used to approximate f (x) = cos x in [−1 2 , 1 2 ]. find a bound for the maximum error)

Answers

Answer 1

The maximum error between the polynomial approximation p2(x) = 1 - (1/2)x² and the function f(x) = cos(x) over the interval [-1/2, 1/2] is less than or equal to 0.031818.

To find a bound for the maximum error between the polynomial approximation and the function in question, we can utilize the error bound formula for polynomial interpolation known as the Weierstrass approximation theorem.

The Weierstrass approximation theorem states that if a function f(x) is continuous on a closed interval [a, b], then for any positive value ε, there exists a polynomial P(x) such that |f(x) - P(x)| < ε for all x in [a, b].

In this case, we want to approximate the function f(x) = cos(x) using the polynomial p2(x) = 1 - (1/2)x^2 over the interval [-1/2, 1/2]. We need to determine a bound for the maximum error, which we'll call E.

To find the bound, we can use the fact that the maximum error occurs at the extrema (endpoints) of the interval. Let's evaluate the error at the endpoints:

For x = -1/2:

E1 = |f(-1/2) - p2(-1/2)| = |cos(-1/2) - (1 - 1/2(-1/2)²)|

For x = 1/2:

E2 = |f(1/2) - p2(1/2)| = |cos(1/2) - (1 - 1/2(1/2)²)|

To find a bound for the maximum error, we need to find the larger value between E1 and E2:

E = max(E1, E2)

To determine the value of E, we can evaluate the expressions for E1 and E2 using a calculator or software:

E1 ≈ 0.006739

E2 ≈ 0.031818

Hence, the bound for the maximum error, E, is approximately 0.031818.

Therefore, the maximum error between the polynomial approximation p2(x) = 1 - (1/2)x² and the function f(x) = cos(x) over the interval [-1/2, 1/2] is less than or equal to 0.031818.

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Related Questions

Please help me with this questions please please ASAP ASAP please ASAP help please please ASAP please I'm begging you please please ASAP

Answers

Answer:

32

Step-by-step explanation:

The shapes are the same except for the direction so i think it would be 32

Answer:

32°

Step-by-step explanation:

quadrilateral ABCD is similar to quadrilateral WXYZ

Corresponding angles of similar polygons are congruent. We are told the two quadrilaterals are similar, so the pairs of corresponding angles are congruent.

You know angles are corresponding according to the statement of similarity is written.

quadrilateral ABCD is similar to quadrilateral WXYZ

The vertices are listed in the same order in both polygons showing which angles are corresponding.

<A corresponds to <W

m<W = m<A = 32°

Answer: 32°

Help I don’t know this you dont have to explain:]

Answers

The total cost next year will be: $10,613.10

Solving:

The total cost of this year

Simply just add up everything that has been given which wouold give you 10,405

The total cost of next year

multiply the total cost of this year by 1.02 to find what the cost would be with a 2% increase which should give you 10,613.1

A point on the terminal side of angle 0 is given. Find the exact value of the indicated trigonometric function of 0. (9,12) Find csc 0.

Answers

Given a point on the terminal side of an angle, (9, 12), we can find the exact value of the cosecant (csc) of the angle. The exact value of csc(θ) is 13/9.

To find the exact value of csc(θ), we need to use the given point (9, 12) on the terminal side of angle θ.

The cosecant function (csc) is defined as the reciprocal of the sine function (sin). Since the sine of an angle is given by the ratio of the opposite side to the hypotenuse in a right triangle, we can determine the value of csc(θ) by calculating the ratio of the hypotenuse to the opposite side.

In this case, the coordinates of the point (9, 12) represent the lengths of the sides of a right triangle. The opposite side is 12 and the hypotenuse is the length of the hypotenuse is the distance from the origin (0, 0) to the point (9, 12), which can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we find that the hypotenuse is √(9^2 + 12^2) = √(81 + 144) = √225 = 15.

Therefore, the exact value of csc(θ) is the reciprocal of the sine of the angle θ, which is 13/9.

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The school playing field is 300 meters. Our coach wants us to run three kilometers, how many times will we need to run around the field.

Answers

Answer:

10 times

Step-by-step explanation:

1km=1000m

3*1000=3000m

3000/300=10

you will need to run 10 times around the field

1. Using the .05 level of significance, run a z- test given the following:
n = 74, p = 5/74 Po = 10%
A. The computed z value 0.91 is greater than the critical value -1.96.
B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.
C. The computed z value -0.91 is lesser than the critical value -1.96.
D. Based on the evidence on hand that the computed z statistic 0.91 lies inside the rejection region, we cannot reject the null hypothesis.

Answers

We can see that the computed z value lies inside the non-rejection region. Hence, we cannot reject the null hypothesis based on the evidence on hand.Therefore, the correct option is B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.

The given values for the problem are: n = 74, p = 5/74, Po = 10%.

The significance level is given by alpha = 0.05 (given in the problem).

The null hypothesis and alternate hypothesis are as follows:H0: p = 0.10 Ha: p < 0.10.

The formula to calculate the z-statistic is given by:z = [tex](p - Po) / √[(Po(1 - Po))/n].[/tex]

Substituting the given values,z = [tex](5/74 - 0.10) / √[(0.10(0.90))/74] = -0.9138.[/tex]

Using the standard normal distribution table, the critical value for z at alpha = 0.05 for a left-tailed test is -1.645.

The computed z value is -0.9138 and the critical value at alpha = 0.05 is -1.645.

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Jim's Co. has set a requirement on stock items of a turnover ratio of 2.6 per year. It is examining three stocked items, A, B and C, which have to be bought in large amounts. As a result of the purchasing requirements, the maximum stock for A is $1,000, for B $1,200 and for C $2,500. If the average stock is assumed to be one-half the maximum stock, what would be the required annual sales of each of these items?

Answers

The required annual sales for stocked items A, B, and C would be $1,300, $1,560, and $3,250, respectively.

To calculate the required annual sales for each stocked item, we need to consider the turnover ratio and the maximum stock level. The turnover ratio indicates how many times the stock is sold and replaced within a year.

Given that the turnover ratio requirement is 2.6 per year, we can calculate the required annual sales for each item by multiplying the turnover ratio with the maximum stock level.

For item A, the maximum stock level is $1,000, and the required annual sales would be 2.6 times $1,000, which equals $2,600.

Similarly, for item B, the maximum stock level is $1,200, and the required annual sales would be 2.6 times $1,200, which equals $3,120.

For item C, with a maximum stock level of $2,500, the required annual sales would be 2.6 times $2,500, which equals $6,500.

However, since the average stock is assumed to be one-half the maximum stock, we need to adjust the required annual sales accordingly. The average stock for each item would be $500 for A, $600 for B, and $1,250 for C. Therefore, the required annual sales for A would be $2,600 minus $500, which equals $1,300. For B, it would be $3,120 minus $600, which equals $1,560. And for C, it would be $6,500 minus $1,250, which equals $3,250.

In summary, the required annual sales for items A, B, and C would be $1,300, $1,560, and $3,250, respectively.

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Find the sum of the Interior angle measures of a convex 11-gon (an eleven-sided polygon).

Answers

Answer:

1620 degrees.

Step-by-step explanation:

In a polygon the number of sides = the number of angles.

Each external angle = 360 / 11 = 32 8/11 degrees.

Each internal angle = 180 - 32 8/11 = 147 3/11 degrees

So sum = 147 3/11 * 11

= 1617 + 3

= 1620 degrees.

Answer:

It's 1620°

Hope it helps

Step-by-step explanation:

Hint:>

( The sum of the interior angle (S),

The the sides of the polygon (n).)

Then use this formula :

S=180°(n-2)

= 180°(11-2)

= 180°(9)

= 1620°

rewrite y=(0.9)t−4 in the form y=a(1 r)t or y=a(1−r)t to determine whether it represents exponential growth or exponential decay. round a and r to the nearest hundredth if necessary.

Answers

The equation y = (0.9)t - 4 can be rewritten in the form y = a(1 - r)t, where a = -4 and r = 0.1. This represents exponential decay.

In the equation y = (0.9)t - 4, the term (0.9)t represents the exponential part, where the base is 0.9. By rewriting it in the form y = a(1 - r)t, we can identify the values of "a" and "r" that correspond to the given equation.

In this case, "a" is the initial value, which is -4. The negative value indicates a downward shift or decrease from the initial value. The term (1 - r) represents the remaining portion after each time interval. By comparing the given equation to the general form, we find that r = 0.1, which signifies a decay rate of 10%.

Overall, the equation y = (0.9)t - 4 represents exponential decay because the value of "r" is less than 1 (0.1) and "a" is negative (-4). This indicates a decreasing trend as time (t) increases.

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on for the hyperbola with write an equation for the hyperbola given characteristics.

4. foci (0, 6), (0, 4); length of transverse
axis 8 units

Answers

Answer:

Step-by-step explanation:

Jamie was surveying students about their use of the new science lab in a school. Which question in the survey is a statistical question?

Answers

Complete Question is:

Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?

A.) How qualified is the trainer at the computer lab?

B.) Where is the computer lab located in the school?

C.) What is the number of learning stations at the computer lab?

D.) How many class projects did you complete using the computer lab?

Answer:

D.) How many class projects did you complete using the computer lab?

The answer is D because the question is directly related to the use of their new computer lab and the number of projects the students have completed in the computer lab. This is directly related to the survey since it is carried out for the students using computer lab.

NO LINKS!!! PLEASE HELP!!

Answers

Answer:

stay calm

Step-by-step explanation:

stay calm

11. Which set of ordered pairs represents y as a function of x?
A. {(-4,-3), (-4,-2), (-3,-3), (-3,-2)}
B. {(2.0), (4,0), (4,2), (6, 2)}
C. {(6,-2), (6.0), (6,2), (6,4)}
D. {(0, 0), (2, -4), (4, -8), (6,-12)}

Answers

Answer is C. {(6,-2), (6.0), (6,2), (6,4)}

Step-by-step explanation:

Your welcome

The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?



x7 + 5x6 – 6x4 – 30x3 + 9x + 45


x – 5


x + 5


x7 + 5x6 + 6x4 + 30x3 + 9x + 45

Answers

Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

[tex]f(x)=x^4+5x^3-3x-15[/tex]

[tex]q(x) = (x^3-3)[/tex]

We need to find the polynomial. We know that, Euclid division lemma states that

[tex]f(x)=q(x)\times g(x)+r(x)[/tex]

Where

f(x) is dividend

g(x) is the poynomial

q(x) is quotient

r(x) is remainder

So,

[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]

So, the polynomial is (x+5).

 

Answer: its C

Step-by-step explanation: i just took the test

What is the difference between binomial distribution and Bernulli distribution.

Answers

The key difference is that the Bernoulli distribution models a single trial, while the binomial distribution models multiple trials and focuses on the number of successes in those trials. The binomial distribution is an extension of the Bernoulli distribution to multiple trials.

The main difference between the binomial distribution and the Bernoulli distribution lies in the number of trials involved.

Bernoulli Distribution:

The Bernoulli distribution is a discrete probability distribution that models a single trial or experiment with two possible outcomes: success or failure. It is characterised by a single parameter, often denoted as p, which represents the probability of success. The outcome of each trial is independent of other trials, and it is represented by a random variable that takes the value 1 for success and 0 for failure.

Binomial Distribution:

The binomial distribution is also a discrete probability distribution that models multiple independent Bernoulli trials or experiments. Each trial is identical, and it has two possible outcomes: success or failure, just like the Bernoulli distribution. However, the binomial distribution considers the number of successes (k) in a fixed number of trials (n). It is characterised by two parameters: the probability of success (p) and the number of trials (n).

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STRESSING‼️ PLEASE HELP❗️❗️

Answers

Answer: 3.14

Explanation:
The formula for area is A = pi*r^2
Plug in your values A = 3.14*1^2
And your answer is 3.14

Hope this helps ;)

use a double- or half-angle formula to solve the equation in the interval [0, 2). (enter your answers as a comma-separated list.) tan 2 − sin() = 0

Answers

The solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])` where `k` is an integer and `cos(x) = 1-2sin²(x/2)`

Given, `tan(2x)-sin(x)=0`.We can use the half-angle formula to solve this equation in the interval `[0, 2)` and obtain the solutions. The half-angle formula for tangent is: `tan(θ/2)= sin(θ)/(1+cos(θ))`The half-angle formula for sine is: `sin(θ/2)=±√[(1-cos(θ))/2]`Using the half-angle formula for tangent:`tan(2x)-sin(x)=0`Substituting `sin(x)` in terms of `tan(θ/2)`, we get:`tan(2x)-2tan(x/2)/(1+tan²(x/2))=0`Multiplying both sides by `1+tan²(x/2)`, we get:`tan(2x)(1+tan²(x/2))-2tan(x/2)=0`Simplifying this equation further using the double-angle formula for tangent:`(2tan(x/2)/(1-tan²(x/2)))(1+(2tan²(x/2))/(1-tan²(x/2))) - 2tan(x/2) = 0`

Multiplying both sides by `(1-tan²(x/2))`, we get:`2tan(x/2)(1+tan²(x/2)) - 2tan²(x/2) - (1-tan²(x/2))(2tan²(x/2)) = 0`Simplifying this equation, we get:`tan⁴(x/2) - 3tan²(x/2) + 1 = 0`This is a quadratic equation in `tan²(x/2)`.Solving this quadratic equation, we get:`tan²(x/2) = (3±√5)/2`Taking square root of both sides, we get:`tan(x/2) = ±√[(3±√5)/2]`We know that, `tan(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval. Therefore, we take the positive square root. We get:`tan(x/2) = √[(3+√5)/2]`Using the formula for sine, we get:`sin(x/2) = ±√[(1-cos(x))/2]`We know that, `sin(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval.

Therefore, we take the positive square root. We get:`sin(x/2) = √[(1-cos(x))/2]`Therefore, the solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])`where `k` is an integer and `cos(x) = 1-2sin²(x/2)`

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Carry out the indicated operations. Express your results in rectangular form for those cases in which the trigonometric functions are readily evaluated without tables or a calculator.

8(cos 17+ isin 170) x 7(cos 42° + isin 439)

Answers

The product of 8(cos 17° + i sin 170°) and 7(cos 42° + i sin 439°) can be expressed as -336 + 94i.

To find the product of two complex numbers, we multiply their magnitudes and add their angles. Let's break down the given complex numbers. The first complex number, 8(cos 17° + i sin 170°), has a magnitude of 8 and an angle of 17°. The second complex number, 7(cos 42° + i sin 439°), has a magnitude of 7 and an angle of 42°.

To find the product, we multiply the magnitudes: 8 * 7 = 56. To determine the angle, we add the angles: 17° + 42° = 59°. Now we have the complex number 56(cos 59° + i sin θ). However, we need to convert the angle to the standard range of 0° to 360°. In this case, 59° is already within that range.

Therefore, the product of the given complex numbers is 56(cos 59° + i sin θ), where θ is the angle in the standard range. To evaluate this expression, we can use trigonometric identities to find the cosine and sine of 59°, or use a calculator. The result is approximately -336 + 94i, which represents the product in rectangular form.

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6. A cylinder has a volume of 500 cm3 and a diameter of 18 cm. Which of the following
is the closest to the height of the cylinder?
a) 1 cm
b) 2 cm
c) 4 cm
d) 8 cm​

Answers

Well, h≈1.96 cm. Choose b. since it’s the closest to 2.

Select all the representations that are appropriate for comparing bite strength to weight for different carnivores. 1. Scatter plot 2. Box plot 3. Histogram 4. Table 5. Dot plot

Answers

Scatter plot

Box plot

Dot plot

To compare bite strength to weight for different carnivores, scatter plot, box plot, and dot plot are appropriate representations.

Scatter plot: A scatter plot can show the relationship between bite strength and weight by plotting each carnivore as a data point. The x-axis can represent weight, the y-axis can represent bite strength, and each point on the plot represents a different carnivore. This allows for visualizing the overall trend or pattern between the two variables.

Box plot: A box plot can display the distribution of bite strength and weight for different carnivores. It provides information about the median, quartiles, and any outliers in the data. By comparing the box plots for different carnivores, we can assess the variations in bite strength relative to weight.

Histogram: A histogram is not appropriate in this case because it represents the distribution of a single variable, such as bite strength or weight, and does not directly compare the two variables.

Table: A table can present the bite strength and weight data for different carnivores, but it does not provide a visual comparison or representation of the relationship between the two variables.

Dot plot: A dot plot can show the individual data points of bite strength and weight for each carnivore. Each dot represents a carnivore, and by comparing the position and density of dots, we can observe the relationship between bite strength and weight.

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find the value of x and y, special right triangles

Answers

Answer:

25 and 135

Step-by-step explanation:

you see that the small square equals 90

Let Z = {] ² | c=b}. ER}. Prove that Z is a subspace of R2x2. for some beR Prove that Y is not a subspace of R2×2,

Answers

To prove that Z = {[b² | c=b] | b, c ∈ ℝ} is a subspace of ℝ²x², we need to show that Z satisfies the three properties of a subspace.

To prove that Y = {A ∈ ℝ²x² | A is an upper triangular matrix} is not a subspace of ℝ²x², we only need to show that it fails to satisfy one of the three properties.

For Z to be a subspace of ℝ²x², it needs to satisfy closure under addition, closure under scalar multiplication, and contain the zero vector.

1. Closure under addition: Let A = [b₁² | c₁=b₁] and B = [b₂² | c₂=b₂] be two matrices in Z. Their sum, A + B, is [b₁² + b₂² | c₁ + c₂ = b₁ + b₂]. Since b₁ + b₂ is a real number, A + B is also in Z. Hence, Z is closed under addition.

2. Closure under scalar multiplication: Let A = [b² | c=b] be a matrix in Z, and k be a scalar. The scalar multiple kA is [k(b²) | k(c) = kb]. Since kb is a real number, kA is also in Z. Therefore, Z is closed under scalar multiplication.

3. Contains the zero vector: The zero vector in ℝ²x² is the matrix [0 0 | 0 = 0]. This matrix satisfies the condition c = b, so it is in Z.

Thus, Z satisfies all the properties and is a subspace of ℝ²x².

For Y to be a subspace of ℝ²x², it needs to satisfy the three properties mentioned earlier. However, Y fails to satisfy closure under addition since the sum of two upper triangular matrices may not always be an upper triangular matrix. Hence, Y is not a subspace of ℝ²x².

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Find the equilibrium vector for the transition matrix. 0.70 0.10 0.20 0.10 0.75 0.15 0.10 0.35 0.55 The equilibrium vector is __ (Type an integer or simplified fraction for each matrix element.)

Answers

The equilibrium vector for the transition matrix is [0.4, 0.2667, 0.3333].

The transition matrix given is:

0.70 0.10 0.20 0.10 0.75 0.15 0.10 0.35 0.55

'To find the equilibrium vector, we need to multiply the transition matrix by a vector of constants that would make the equation valid. The value of this vector of constants is given by:

(P-I)x = 0

Where P is the transition matrix and I is the identity matrix. The value of x is the equilibrium vector.

Let's write the augmented matrix:

(P-I|0) = 0.70-1 0.10 0.20 0.10 0.75-1 0.15 0.10 0.35 0.55-1

After subtracting the identity matrix from the transition matrix, we get the augmented matrix.

Using the Gauss-Jordan elimination method, we get 1 -0.08 -0.4-0.12 1 -0.28-0.18 -0.12 1

After row reducing the augmented matrix, we get the following equations:

x1 - 0.08x2 - 0.4x3 = 0-0.12

x1 + x2 - 0.28x3 = 0-0.18x1 - 0.12

x2 + x3 = 0

Solving these equations, we get

x1 = 1.2

x2 = 0.8

x3 = 2.

Using x1, x2, and x3 values, we can determine the equilibrium vector:

x = [1.2/3, 0.8/3, 2/3]

Simplifying the vector, we get the equilibrium vector as:

x = [0.4, 0.2667, 0.3333]

Thus, the equilibrium vector is [0.4, 0.2667, 0.3333].

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If f(x) = x is changed to g(x) = -f(x + 3) + 2, how is the graph transformed?

Answers

Answer:

f(x) is flipped, and each point is moved 3 units to the left and 2 units up

Step-by-step explanation:

If z = 7, what is the value of the equation? ( only write the numeric value for the answer)

4z + 5 = ?

Answers

Answer

4z+5=

4*7+5=33

33

Step-by-step explanation:

A private ship carries two types of cargo: large crates and extra-large crates. Each type of crate weighs a specific amount.

On Saturday the ship carried 400 large crates and 275 extra-large crates weighing 18,800 tons.

On Sunday, the ship carried 190 large crates and 335 extra large crates, weighing 16,100 tons.

How much does an extra-large crate weigh in tons?
F 25 tons
G 32 tons
H 30 tons
J 24 tons

Answers

Answer:

G. 32

Step-by-step explanation:

32 x 335 = 10720

16,100 - 10720 = 5380/190 = 28.3157894737

275 x 32 = 8800

18,800 - 8800 = 10,000/400 = 25 (This is the closer).

30 x 335 = 10,050

16,100 - 10,050 = 6050/190  = 31.8421052632

30 x 275 = 8250

18,800 - 8250 = 10550/400 = 26.375 (Same reason why it does't work)

25 x 335 = 8375

16,100 - 8375 = 7725/190 = 40.6578947368

25 x 275 = 6875

18,800 - 6875 = 11925/400 = 29.8125

24 x 335 = 8040

16,100 - 8040 = 8060/190 = 42.4210526316

24 x 275 = 6600

18,800 - 6600 = 12200/400 = 30.5

I need help desperately question in picture

Answers

Answer:

25.3

Character minimum

Which of the following equations represents a line that is perpendicular toy = -2x+4 and passes through the point, (4, 2)?
A. y=-3x +2
B. y - x
O C. y - 3x+4
O D. y = -2x

Answers

The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Simplify the following expression. COSX + Sinx - tanx

Answers

The expression COSX + Sinx - tanx can be simplified by combining trigonometric identities.

We can use the trigonometric identities to simplify each term in the expression:

COSX + Sinx:

We know that sin(x) = cos(π/2 - x). Therefore, we can rewrite Sinx as Cos(π/2 - x):

COSX + Cos(π/2 - x)

tanx:

We know that tanx = sinx / cosx. Therefore, we can rewrite tanx as sinx/cosx:

sinx / cosx

Now, let's combine the terms:

COSX + Cos(π/2 - x) - sinx / cosx

Using the sum-to-product formula for cosine (Cos(A + B) = CosA * CosB - SinA * SinB), we can rewrite the expression as:

CosX * Cos(π/2) - SinX * Sin(π/2) - sinx / cosx

Since Cos(π/2) = 0 and Sin(π/2) = 1, the expression simplifies to:

0 - 1 - sinx / cosx = -1 - sinx / cosx

Therefore, the simplified expression is -1 - sinx / cosx.

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right triangle abc is inscribled in a circle . the shortest height of the triasngle is h

Answers

In a right triangle ABC that is inscribed in a circle, the shortest height of the triangle is the altitude drawn from the right angle to the hypotenuse. This height, denoted as 'h', is perpendicular to the hypotenuse and divides it into two segments.

The altitude is also the shortest distance between the hypotenuse and the opposite vertex (the vertex not on the hypotenuse). The property of a right triangle inscribed in a circle is that the hypotenuse is the diameter of the circle, and the other two sides are radii of the circle.

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To observe a session of the state senate, 18 students are visiting the state capitol. They will tour the capital in groups with x chaperones.
Complete the table. How many students will be in each group if x = 9?

Answers

Answer:9

Step-by-step explanation:

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