Explain why the equation cos(x) = x has at least 1 solution

The Maclaurin series of  ln (1 + x³)  is

[tex]= x^3-\dfrac{1}{2}x^6+\frac{1}{3}x^9+\ldots \:[/tex]

The function is given in the question as

h(x) = ln (1 + x³)

Taylor (Maclaurin) series ofln (1 + x³) up to n = 3

A Maclaurin series is given by f(x),

[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]

[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]

We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

f⁽⁰⁾(x) = f(x) = ln (1 + x³)

Evaluate the function at the point: f(0)=0

1st derivative: f(1)(x)=(ln(x3+1))′=3x²/(x³+1)  

1st derivative at the given point: (f(0))′=0

2nd derivative: f(2)(x)=(f(1)(x))′=(3x²/(x³+1) )′=3x(2−x³)/(x⁶+2x³+1) 

Evaluate the 2nd derivative at the given point: (f(0))′′=0

3rd derivative: f(3)(x)=(f(2)(x))′= (3x(2−x³)/(x⁶+2x³+1) )′= 6(x⁶−7x³+1)x9+3x⁶+3x³+1

Evaluate the 3rd derivative at the given point: (f(0))′′′=6

Now, use the calculated values to get a polynomial:

f(x)≈0/0!x⁰+0/1!x¹+0/2!x²+6/3!x³+0/4/!x⁴+0/5!x⁵

Thus, the Maclaurin series of  ln (1 + x³)  is

[tex]= x^3-\dfrac{1}{2}x^6+\frac{1}{3}x^9+\ldots \:[/tex]

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Answer:

Step-by-step explanation:

We can use the Side-Side-Side (SSS) Theorem – Three pairs of corresponding sides are congruent in two triangles.

1.67 pounds flour we get per dollar.

Pound, avoirdupois weight unit equivalent to 16 ounces, 7,000 grains, or 0.45359237 kg, and troy and apothecaries' weight unit equal to 12 ounces, 5,760 grains, or 0.3732417216 kg The symbol lb comes from the Roman predecessor of the contemporary pound, the libra.

Given,

Cost for 2 pounds of flour = $ 1.20

Cost per pound of flour = $ 1.20 /2

                                       = $ 0.20

Now for 2 dollar we get flour = 2 pounds.

for 1 dollar we will get flour = 2/1.20 pounds

                                              = 1.6666 pounds

i.e. for 1 dollar we will get flour = 1.67 pounds.

So, 1.67 pounds flour we get per dollar.

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Answer: B) 2000

Step-by-step explanation:

Sale Price: The cost following a discount applied to the initial cost.

Cost Price: The cost price is what we pay to purchase a good.

Discount Price : A price that is lower than the usual price.

Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

So, The sale price is Rs 1600 after discount.

Discount =20%

Selling price of the skates = Rs 1600

Discount price = 100/80 × 1600= Rs 2000

Discount price = Rs 2000

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The solution to the inequality −18 ≤−3p, is shown in the graph in the attachment which is p ≤ 6.

To graph the solution of a given inequality, we have to first solve the inequality to determine what the solution will be.

Given the inequality, -18 ≤ -3p, solve to find p:

-18 ≤ -3p

Divide both sides by -3

-18/-3 ≥ -3p/-3 [the sign will change because we're dividing by a negative value]

6 ≥ p

It can be rewritten as p ≤ 6. The graph of this solution is a number line having a closed circle on point 6 that points towards the left.

See the diagram in the attachment which shows the solution of the inequality.

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The required proportion for the given case is 36/100 = x/150.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given statement is as below,

36% of 150

Suppose the required number is x.

Then, the equivalent form of the given statement is,

36% of 150 = x

=> 36% × 150 = x

=> 36/100 × 150 = x

=> 36/100 = x/150

Hence, the required proportion to to be used to solve the problem is 36/100 = x/150.

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Answer:

-3

Step-by-step explanation:

x - 3y = 4  Write in the slope intercept form.  Subtract x from both sides

-3y = -x + 4  Divide all the way through by -3

y = [tex]\frac{1}{3}[/tex] x - [tex]\frac{4}{3}[/tex]

The slope is the number before the x  ( 1/3 )

The perpendicular slope is the opposite reciprocal or -3

Answer:

70x

Step-by-step explanation:

multiply -10 and -7 for the coefficient

Answer: 70x

Step-by-step explanation:

Answer:

one and a third thats the amount of groups (mark me brainliest pls and ty <3) !

Answer: A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1.

Step-by-step explanation:

Answer:

170°

Step-by-step explanation:

180 - 10 = 170

It is a uniform rectilinear movement which is one in which an object moves in a straight line, in one only direction, with a constant speed.

When we spoke of constant speed we mean that the movement retains the same speed, that is; that the object does not move faster, or slower and always at the same speed.

We obtain the data, as specified by the exercise.

Data:

 V = 28 m/s

 T = 10 s

 D = ?

We have that the uniform motion formula is:

     [tex]\large\displaystyle\text{$\begin{gathered}\sf V=\dfrac{d}{t}, \to where \end{gathered}$}[/tex]

We solve the formula, to calculate the distance and we obtain.And we also substitute our data.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d=v*t} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d=28 \ \frac{m}{\not{s}}*10 \not{s} } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d=280 \ m } \end{gathered}$}}}[/tex]

Answer: -4.25

Step-by-step explanation:

subtract -6.75 from 2.5 and you have your answer. This works out because 2.5 and -2.5 cancel out and become 0.

The length and width of a rectangle are 36 and 30 yard respectively.

Its the sum of length of the sides used to made the given figure.

We are given that width of a rectangle is 6 yards less than the length. The perimeter is 132 yards.

Therefore, the perimeter = (2 x length)+(2 x width)

The length = 6 + w

Hence, we have;

132 = (2(6 + w))+(2w)

132 = 12 + 2w + 2w

132 = 12 + 4w

120 = 4w

w = 30

Length = 36 yard.

Thus, the length and width of a rectangle are 36 and 30 yard respectively.

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The linear depreciation function is: Depreciation = [tex]\frac{Cost-scrap value}{Estimated life span}[/tex],  (b) the value after five years is $11510 and (c) rate of depreciation is 11%

We should know that depreciation is a loss on a fixed asset over the accounting period that benefited from it.

The given parameters are

Cost of the asset (MSRP)= $25020

Scrap value = $14212

Estimated life span = 4 years

a.   Applying the depreciation model

Deprecation = [tex]\frac{Cost of asset - scrap value}{estimated life span}[/tex]

Depreciation = [tex]\frac{25020-14212}{4}[/tex]

depreciation = 10808/4

Dep. = $2702

(b) Note that the accumulated depreciation after 5 years is 2702*5

=$13510

The value of the car after 5 years is $(25020-13510)

=$11510

(c)  The rate of depreciation is determined by the model

% dep. = 1-[tex]\sqrt[n]{\frac{s}{c} }[/tex]

where n= number of years

s=scrap value

c cost of the asset

Applying the formular we have

% dep - 1-[tex]\sqrt[5]{\frac{14212}{25020} } = 1-\sqrt[5]{0.5680}[/tex]

% dep= 1-0.89

=0.11*100

=11%

In conclusion, the linear depreciation function is (Cost - Scrap value)÷Number of years, the value of the car 5 years from now is $11510 and the rate of depreciation is 11%

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Answer: $18/hour

12 x 1.5 = 18

[tex]\begin{array}{llll} ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \end{array} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6x^{-1}y^{-1}}{\left( xy^4 \right)^{\frac{1}{4}} }\implies \cfrac{6x^{-1}y^{-1}}{x^{\frac{1}{4}} y^{4\cdot \frac{1}{4}}}\implies \cfrac{6x^{-1}y^{-1}}{x^{\frac{1}{4}} y^1}\implies \cfrac{6x^{-1}y^{-1}x^{-\frac{1}{4}} y^{-1}}{1}[/tex]

[tex]6x^{-1}x^{-\frac{1}{4}}y^{-1} y^{-1}\implies 6x^{-1-\frac{1}{4}} y^{-1-1}\implies {\Large \begin{array}{llll} \underset{\textit{\small a}}{6} \stackrel{\textit{\small ~~ b}}{x^{-\frac{5}{4}}} \stackrel{\textit{\small ~~ c}}{y^{-2}} \end{array}}[/tex]

Answer:

Step-by-step explanation:

10-4=6

9-(x)=6

9-6=(x)

(x) = 3

The answer is 3

Answer:

Missing number = 3

Step-by-step explanation:

Forming the equation,

→ 10 - 4 = 9 - x

→ x = missing number

Now the value of x will be,

→ 10 - 4 = 9 - x

→ 6 = 9 - x

→ -x = 6 - 9

→ -x = -3

→ [ x = 3 ]

Hence, the value of x is 3.

Answer:

below

Step-by-step explanation:

5/6 th chance of NOT rolling a six EACH time (five rolls)  

(5/6)^5 = .402

Answer:

25.1 i think

Step-by-step explanation:

Answer:

25.1

Step-by-step explanation:

Conversion a mixed number 18 1/2 to an improper fraction: 18 1/2 = 18 1/

2= 18 · 2 + 1/2= 36 + 1/2 = 37/2 2. a) Multiply the whole number 18 by the denominator 2. Whole number 18 equally 18 * 2/2 = 36/2   Conversion a decimal number to a fraction: 6.6 = 66/10 = 33/5

The average cost per person when there are 4 people in the group is of:

$8.75.

The average cost per person represents the mean cost per person in the data-set.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, the average cost per person in this problem is obtained as the division of the total spending by four, as there are four people.

The total spending is obtained as follows:

Hence the numeric value of the total spending is of:

4 x (5 + 1.75) + 2 x 4 = $35.

Thus the average spending per person is of:

$35/4 = $8.75.

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Answer:

and the point F lies on the bottom face.

a) Construct a section of a parallelepiped by three given points E, F, G. Explain the construction of each of the segments (22 points).

b) Indicate the name (type) of the resulting polygon and shade its inner part (8 points).

1

Task 3.

An isosceles triangle ABC with base AB is given. From a point S lying outside the plane ABC, a perpendicular is dropped to point C.

a) Draw the linear angle of the dihedral angle SABC. Explain why this particular

first one

2x+43 = 180

.....

Answer:

x-4-16≥8

x≥28

Step-by-step explanation:

If you use x to begin with the unknown payment. then take away what you know was spent ($4,$16) and you have at least $8 left, x would have to be greater than or equal to 28

The statement that best describes a sequence of transformations in which the blue figure is the image of the red figure is given as follows:

A. Rotate 90° clockwise about the origin and then dilate with respect to the origin using a scale factor of 1/2.

The horizontal side lengths on the blue figure are given as follows:

8 - 4 = 6 - 2 = 4.

The vertical side lengths on the transformed red figure is of:

4 - 2 = 3 - 1 = 2.

Hence the scale factor of the dilation is given as follows:

2/4 = 1/2.

Which means that options C and D are not correct.

The rules for each rotation are given as follows:

On the second quadrant, of the blue figure, we have that:

On the first quadrant, of the red figure, we have that:

Hence the rotation was clockwise, and option A is correct.

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The animal which travel at a rate of 1.5 meters per minutes is ants.

The correct answer option is option D

Based on the given task content, it can be solved using fraction.

Speed refers to the rate of change of distance at a given time period.

Average speed = Total distance / Time taken

Turtle = Total distance / Time taken

= 6/5

= 1.2 meters per minutes

Snail = Total distance / Time taken

= 4/8

= 0.5 meters per minutes

Caterpillar = Total distance / Time taken

= 7/7

= 1 meters per minutes

Ant = Total distance / Time taken

= 12/8

= 1.5 meters per minutes

In conclusion, ant is the animal which has an average speed of 1.5 meters per minutes

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The final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

What is the interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.

We have,

F and H are sets of real numbers defined as follows.

F = { v l v < 4}

H = { v l v ≥ 7}

F is the set of all real numbers that are less than or equal to 4.  H is the set of real numbers greater than 7.

F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:

F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets.  Hence the answer is the empty set, Ø:

F ∩ H = Ø

F ∩ H = [7, 4]

F ∪ H = [-∞, ∞]

Hence, the final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

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The miles that Han will need to get to school is 2/3 miles

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in

From the information, after walking 1/4 mile from home, Han is 1/3 miles to the school.

The miles that she will need more to get to school will be:

= 1/3 × 2

= 2/3

The miles is 2/3 miles.

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Complete question

After walking 1/4 mile from home, han is 1/3 miles to the school. How many miles more will he need to get to school.

Answer:

749

Step-by-step explanation:

Malcolm should place the decimal point immediately after one (1) or before three (3) as follows: 8.25/6 = 1.375.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

As a general rule, the smaller the divisor (denominator) of a mathematical expression, the larger would be the quotient. This ultimately implies that, a quotient would be large when the divisor (denominator) of a mathematical expression is small.

On the other hand (conversely), a quotient would be small when the divisor (denominator) of a mathematical expression is large.

Based on Malcom's calculations, he forgot to place the decimal point in the following expression;

8.25/6 = 1375

Next, we would determine the maximum value of this quotient;

8.25/6 = 12/6

8.25/6 = 2

Therefore, the whole number part for this decimal number would be one (1) and as such, the decimal point must be placed immediately after 1 as follows;

8.25/6 = 1.375

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Complete Question;

Malcolm calculated how many liters of milk each team would get if 6 teams shared the milk equally. His work is shown above, but he forgot to place the decimal point in the quotient. Where should he place the decimal point? Use number sense to explain.

8.25/6 = 1375