can anybody help me with this problem in math ? asap .

The terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

In this question,

The function is f(x) = \(\frac{sin(x)}{1-x}\)

The general form of Maclaurin series is

\(\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......\)

To find the Maclaurin series, let us split the terms as

\(f(x)=sin(x)(\frac{1}{1-x} )\) ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

\(f^{iv}(x)\) = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

\(f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....\)

⇒ \(f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....\)

Now, consider \(f(x) = (1-x)^{-1}\)

Then, the derivatives of f(x) with respect to x, we get

\(f'(x) = (1-x)^{-2}, f'(0) = 1\)

\(f''(x) = 2(1-x)^{-3}, f''(0) = 2\)

\(f'''(x) = 6(1-x)^{-4}, f'''(0) = 6\)

\(f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24\)

Maclaurin series for (1-x)^-1 becomes,

\(f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....\)

⇒ \(f(x)=1+x+x^{2} +x^{3} +......\)

Thus the Maclaurin series for \(f(x)=sin(x)(\frac{1}{1-x} )\) is

⇒ \(f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)\)

⇒ \(f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....\)

⇒ \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\)

Hence we can conclude that the terms through degree four of the Maclaurin series is \(f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....\).

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Answer:

9 and 10

Step-by-step explanation:

The sqaure root of 85 is 9.21954445729.

9.21954445729 is greater than 9 but less than 10, meaning it falls in between them.

Therefore, the roots of the polynomial equation \(x^4 - x^3 = 4x^2 + 4x\) are infinite, and it is not possible to find them precisely using a graphing calculator or a system of equations.

To find the roots of the polynomial equation \(x^4 - x^3 = 4x^2 + 4x\), we can utilize a graphing calculator and a system of equations. Here's how you can proceed: Rewrite the equation to bring all terms to one side:

\(x^4 - x^3 - 4x^2 - 4x = 0\)

Enter the equation into a graphing calculator or any equation-solving software. Look for the x-intercepts or roots of the equation on the graphing calculator. These are the values of x where the graph intersects the x-axis. Alternatively, we can solve the equation using a system of equations. Let's set up the system:

Consider the original equation:\(x^4 - x^3 = 4x^2 + 4x.\)

Rearrange the equation to bring all terms to one side:

\(x^4 - x^3 - 4x^2 - 4x = 0\)

Introduce a new variable, y, to create a system of equations:

\(x^4 - x^3 - 4x^2 - 4x = 0 (Equation 1)\)

\(y = x^4 - x^3 - 4x^2 - 4x (Equation 2)\)

Now, we can solve this system of equations by eliminating y. Subtract Equation 2 from Equation 1:

0 = 0

The result is always true, indicating that there is an infinite number of solutions. This suggests that the equation has infinitely many roots.

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Option D, 4x + 12y, is not an equivalent expression.

The given expression is x + 2x + 12y + x. To simplify the expression, we can combine the like terms.

The terms x and 2x are like terms because they have the same variable raised to the same power. Combining these two terms, we get 3x.

Similarly, the last x can also be combined with the previous terms, so the final expression becomes 3x + 12y. Therefore, option D, 4x + 12y, is not an equivalent expression.

Option A, x^2 + 2x + 12y, is not equivalent either because it contains a squared term that is not present in the original expression. Option B, 16xy, is not equivalent as it contains a product of two variables, which is not present in the original expression.

Option C, 2x^3 + 12y, is also not equivalent as it contains a term with a variable raised to a power greater than one, which is not present in the original expression.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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The two linear constraints to maximize Niki's income are 1. x + y ≤ 12 (total number of hours worked constraint) and 2. 2x + y ≤ 16 (preparation time constraint)

Let x represent the number of hours per week Niki works at Job I, and let y represent the number of hours per week she works at Job II. The total number of hours Niki works should not exceed 12, so the constraint is x + y ≤ 12.

For every hour Niki works at Job I, she needs 2 hours of preparation time, and for every hour at Job II, she needs 1 hour of preparation time. The total number of hours for preparation should not exceed 16, so the constraint is 2x + y ≤ 16.

Since Niki wants to maximize her income, we need to formulate the objective function. She earns $40 per hour at Job I, so her income from Job I is 40x. Similarly, she earns $30 per hour at Job II, so her income from Job II is 30y. The objective is to maximize her total income, which is the sum of her income from both jobs: 40x + 30y.

In summary, the linear constraints to maximize Niki's income are:

1. x + y ≤ 12 (total number of hours worked constraint)

2. 2x + y ≤ 16 (preparation time constraint)

The objective function to maximize is:

Maximize 40x + 30y (total income)

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Use the Law of Sines to solve the triangle. The correct option among the given options is B C = 85°, a = 5.76, b = 8.69, where c ≈ 10.38.

To solve the triangle using the Law of Sines, we can use the formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's analyze each option one by one:

A) C = 85°, a = 7.76, b = 10.69

To solve this triangle, we can use the Law of Sines as follows:

a/sin(A) = b/sin(B) = c/sin(C)

7.76/sin(35°) = 10.69/sin(60°) = c/sin(85°)

Using this equation, we can solve for c:

c = (7.76 * sin(85°)) / sin(35°) c ≈ 13.99

Therefore, the answer is not C = 85°, a = 7.76, b = 10.69.

Now let's check the other options:

B) C = 85°, a = 8.76, b = 10.69

Using the same formula, we can calculate c:

c = (8.76 * sin(85°)) / sin(35°) c ≈ 15.77

Therefore, the answer is not C = 85°, a = 8.76, b = 10.69.

C) C = 85°, a = 8.69, b = 9.69

Using the same formula, we can calculate c:

c = (8.69 * sin(85°)) / sin(35°) c ≈ 15.56

Therefore, the answer is not C = 85°, a = 8.69, b = 9.69.

The correct option among the given options is B C = 85°, a = 5.76, b = 8.69, where c ≈ 10.38.

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In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.

If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:

Total number of People = 1000

Chances of winning the lottery = 1%

How many people would win 10 dollar lottery = 1000 * 1%

= 1000 * 0.01

= 10 People.

So there are chances that 10 out of 1000 people will win the lottery.

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Answer:

I WILL SAY THE 2 ONE

Step-by-step explanation:

Answer:

1 round of wire = 25m

5 rounds of wire = 5×25m

                            = 125m

1m = 100cm

125m = 12500cm

Answer: y = 6; x = 12

Step-by-step explanation:

3x - 30 = y

Change this into an equation where x and y are in the same side.

3x - 30 = y

Subtract y from both sides

3x - y - 30 = 0

Add 30 to both sides

3x - y = 30

7y - 6 = 3x

Do the same thing I did to the first equation

7y - 6 = 3x

Subtract 3x from both sides

-3x + 7y - 6 = 0

Add 6 to both sides

-3x + 7y = 6

We can now use the system of elimination to find x and y.

3x - y = 30

-3x + 7y = 6

After adding both equations, you get:

6y = 36

Divide 6 from both sides

y = 6

Since we now know y, we can solve for x.

3x - 30 = y

Substitute y for 6

3x - 30 = 6

Add 30 to both sides

3x = 36

Divide both sides by 3

x = 12

Hope this helped!

Answer:

\(x = 12.y = 6\)

Step-by-step explanation:

Restructuring

[3x - 30 = y

-3x - 6 =7y

\( \frac{ - 36}{ - 6} = \frac{ - 6y}{6} \)

y=6

Sub 6 in equ II

7(6)-6=3x

\( \frac{36}{3} = \frac{3x}{3} \)

x=12

The correct decision for this hypothesis test is to reject the null hypothesis, indicating that younger participants have significantly lower vocabulary scores than older participants.

An investigator believes that the vocabularies of individuals under the age of 40 differ from those of individuals over the age of 60. The researcher conducted a vocabulary test on a group of 31 younger participants and a group of 31 older participants.

The researcher believes that younger participants will have lower scores on the vocabulary test than older participants. Stat Crunch output for the hypothesis test with a 0.10 significance level is given below:

The null hypothesis for this test is that the mean scores of younger and older individuals are equal, whereas the alternative hypothesis is that the mean scores of younger and older individuals are not equal.

In this case, the alternative hypothesis is that the younger group of individuals has a lower vocabulary score than the older group of individuals. Since the p-value is less than 0.10, the null hypothesis is rejected. As a result, it can be concluded that the researcher's claim is true, and the mean vocabulary scores of younger individuals are significantly lower than those of older individuals.

Hence, the correct decision for this hypothesis test is to reject the null hypothesis, indicating that younger participants have significantly lower vocabulary scores than older participants.

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Answer:B

Step-by-step explanation:100% correct

Option B

Step-by-step explanation:

Hence , Eli spent $1.84 on oranges to buy 4 bags of oranges .

It is given that a grocery store sells a bag of 6 oranges for $2.76.

Using unitary method ,

The bag of 6 oranges cost =  $2.76

Each bag of oranges costs = 2.76/6

                                              = $0.46

Next we need to find out how many Eli spent on oranges.

$0.46 amount spent on to buy = 1 bag of orange

$1.84  amount spent on to buy = 1.84 /0.46

                                                     = 4  bags of oranges.

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If  Shushu adds 8 new cards to her collection each month, and Vivak adds 13 new cards each month. The number of months  they have the same number of baseball cards is 10 months.

Let m  represent the number of months they will both have the same number of cards.

First step is to formulate an equation

210 +8 × m  = 160 +13 × m

Rearrange

8m - 13m =160 -210

-5m = -50

Divide both side by -5m

m = -50/ -5

m = 10 months

Therefore the number of months is 10 months.

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Answer:

Was it from goldenglare? Cuz that was disgusting

Answer:

i'm with u cause i saw something inappropriate earlier

Step-by-step explanation:

The derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹ * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

To find the derivative of the given function g(x), we can apply the product rule and the chain rule. Let's break down the function into its constituent parts: f(x) = (x² - x + 1\()^1^0\) and h(x) = (tan(x))³.

Using the product rule, the derivative of g(x) can be calculated as g'(x) = f'(x) * h(x) + f(x) * h'(x).

First, let's find f'(x). We have f(x) = (x² - x + 1\()^1^0\), which is a composite function. Applying the chain rule, f'(x) = 10(x² - x + 1\()^9\) * (2x - 1).

Next, let's determine h'(x). We have h(x) = (tan(x))³. Applying the chain rule, h'(x) = 3(tan(x))² * sec²(x).

Now, we substitute these derivatives back into the product rule formula:

g'(x) = f'(x) * h(x) + f(x) * h'(x)

       = 10(x² - x + 1)² * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\)* (tan(x))² * sec²(x).

In summary, the derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹  * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

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Answer:

B

Step-by-step explanation:

We can graph the line using the y and x-intercepts. To find the y-intercept, we substitute x = 0 into y = -2x - 2 so the y-intercept is (0, -2). To find the x-intercept, we substitute y = 0 into y = -2x - 2 so the x-intercept is (-1, 0). The line that goes through both of these points is line B.

Answer:

B.

Step-by-step explanation:

Here's a picture of me graphing it:

Sorry for dark mode :/

The probability of exactly one successes in five trials  is 0.20

From the question, we have the following parameters that can be used in our computation:

The probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n -x)

Where

n = 5

p = 5%

x = 1

Substitute the known values in the above equation, so, we have the following representation

P(1) = 5C1 * (5%)^1 * (1 - 5%)^(5 -1)

Evaluate

P(1) = 0.20

HEnce, the probability value is 0.20

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Answer:

i think its 5 i think i dont know havent done this since 6th grade

Answer:

Step-by-step explanation:

go to school

Answer:

x = -4

Step-by-step explanation:

Subtract 17 on both sides to get 6x = -24 then divide 6 to both sides to get your answer of x = -4

First, you need to get 6x by itself. So you would subtract 17 from both sides. After that you should have 6x= -24.Then you need to get x by itself. You divide 6 from both sides. The answer is x= -4.

Hope this helps!!

The value of sin 315° = -√2/2, cos 9π/4 = √2/2 , tan (-135) = 1°

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant , cosine , cotangent , secant , sine , and tangent .

We can use the following trigonometric identities to find the values ​​of sin, cos, and sun:

sin(x) = sin(x 360°)

cos(x) = cos(x 360°)

tan(x) = tan(x 180°)

Using these identities, we can convert  angles to equivalent angles in the first quadrant, where the values ​​of sin, cos, and sun are known.

sin (315°)

We can convert 315° to the corresponding angle in the first quadrant by subtracting 360°:

315° - 360° = -45°

Since sin(x) = sin(x 360°), we have:

sin(315°) = sin(-45°)

We know that sin(-θ) = -sin(θ), so:

sin(-45°) = -sin(45°)

We also know that sin (45°) = √2/2, so:

sin(315°) = -√2/2

Therefore, the power of 315  is equal to -√2/2.

cos(9π/4)

We can convert 9π/4 to the corresponding angle in the first quadrant by subtracting 2π:

9π/4 – 2π = π/4

Since cos(x) = cos(x 360°), we have:

cos(9π/4) = cos(π/4)

We know that cos(π/4) = √2/2, so:

cos(9π/4) = √2/2

Therefore, cos 9π/4 is equal to √2/2.

tan(-135°)

We can convert -135° to the corresponding angle in the second quadrant by adding 180°:

-135°- 180° = 45°

Since tan(x) = tan(x 180°), we have:

We know that tan(45°) = 1, so:

reddish brown (-135°) = 1

Therefore tan (-135°) equals 1.

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According to the Pythagoras theorem, the value of the other leg is, 15.7 cm

Pythagoras theorem:

Pythagoras theorem defines that  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.

Here we need to find the measure of the other leg and round off it to nearest tenth.

Though the given question, we know that the value of

Hypotenuse = 16 cm

one leg = 3cm,

Then let us consider the length of the other leg as x.

So, according to the Pythagoras theorem,

It can be calculated as,

=> hypotenuse² = one leg² + other leg²

=> 16² = 3² + x²

=> 256 = 9 + x²

Here we need the value of x, so it can be rewritten as,

=> 247 = x²

=> x = √247

When we take square root for 247, then we get the value of x as,

=> x = 15.716

When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.

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Answer:y=3x-2

Step-by-step explanation:

Following Vectors are given , the answer for (A) is said to kept in inverse cosine i.e. also known as arccosine. Orthogonal means at a right angles to the vectors.

(a) To find the angle between the vectors ~u = (1, 1, 1) and ~v = (0, 3, 0), we can use the dot product and the formula: cos(∅) = \(\frac{(~u . ~v) }{ (|~u| x |~v|)}\) The dot product of ~u and ~v is (~u • ~v) = 1(0)+ 1(3)+ 1(0) = 3, and the magnitudes are |~u| = \(\sqrt{(1^2 + 1^2 + 1^2) }\)= \(\sqrt{3}\)and |~v| = \(\sqrt{(0^2 + 3^2 + 0^2) }\)= 3. Plugging these values into the formula, we have: cos(∅) =  \(\frac{3}{3\sqrt{3} }\)= \(\frac{1}{\sqrt{3} }\). Therefore, the angle between ~u and ~v is given by ∅  = acos\(\frac{1}{\sqrt{3} }\)

(b) To find |4~u - ~v| + |2w~ + ~v|, we first compute each term separately.

|4~u - ~v| = |4(1, 1, 1) - (0, 3, 0)| = |(4, 4, 4) - (0, 3, 0)| = |(4, 1, 4)| = \(\sqrt{(4^2 + 1^2 + 4^2)}\)) = \(\sqrt{33}\) .  

∴|2w~ + ~v| = |2(0, 1, -2) + (0, 3, 0)| = |(0, 2, -4) + (0, 3, 0)| = |(0, 5, -4)| = \(\sqrt{ (5^2 + (-4)^2)}\) = \(\sqrt{41}\)

Thus, the expression becomes \(\sqrt{33}+ \sqrt{41}\)

(c) To find the vector projection of ~u onto ~v, we can use the formula: proj~v(~u) = ((~u • ~v) / |~v|^2) * ~v. Using the dot product and magnitudes calculated earlier: proj~v(~u) =( \(\frac{(~u .~v) }{|~v|^2)}\))~v = (3 / 9)  (0, 3, 0) = (0, 1, 0). Therefore, the vector projection of ~u onto ~v is (0, 1, 0).

(d) To find a unit vector orthogonal to both ~v and w~, we can take the cross product of ~v and w~: ~v x w~ = (0, 3, 0) x (0, 1, -2) = (6, 0, 3). To obtain a unit vector, we divide this result by its magnitude:

unit vector = \(\frac{(6, 0, 3) }{|(6, 0, 3)| }\)= \(\frac{(6, 0, 3) }{\sqrt(6^2 + 0^2 + 3^2)}\)  = \(\frac{(6, 0, 3)}{ \sqrt(45)}\) = (\(\frac{2}{\sqrt45}\) , 0, \(\frac{1}{\sqrt5}\)). Therefore, a unit vector orthogonal to both ~v and w~ is (\(\frac{2}{\sqrt5}\), 0, \(\frac{1}{\sqrt5}\)).

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Answer:

the answer is D

Step-by-step explanation:

I don't have an explanation for you but I did my research and I'm positive D is the correct answer

hope this helps :)