Use the first five terms of the trigonometric series to approximate the value of [tex]sin\frac{\pi }{2}[/tex] to four decimal places.

a. 0.9878
b. 1.2345
c. 0.6578
d. 1.0000

Answer:

13

Step-by-step explanation:

Since you want 2 significant figures, you take the first 2 figures, and since there is a .9 after 12, you round up to 13.

Answer:

k = 3.

Step-by-step explanation:

At the given point x = -1 an f(x) = 1/2, so we have the equation:

1/2 = (2 - k)/(5(-1) + k)

(2 - k)/(k - 5) = 1/2

Cross multiplying:

2(2 - k) = k - 5

4 - 2k = k - 5

-2k - k = -5 -4

-3k = -9

k = 3.

9514 1404 393

Answer:

  (x, y, z) = (5, 11, 6)

Step-by-step explanation:

To solve this problem, you need to understand "row operations". The ones we're concerned with are multiplying a row by a scalar, and adding rows together.

You also need to understand what the solution looks like, and the usual way that is achieved. The solution will have the 3×3 matrix left of the vertical line be a diagonal of 1s (the identity matrix). Then the numbers to the right of the vertical line represent the solution.

__

In the following, we will use the notation [a]+b[c]⇒[d] to mean that row 'a' is added to the product of row 'c' and the scalar 'b' and that sum replaces row [d]. Multiplying a row by a scalar multiplies each element in the row by that scalar.

The first several operations look like this. Notice we have made the upper left 2×2 matrix an identity matrix. Steps will continue to take care of the 3rd column.

  [tex]\left[\begin{array}{ccc|c}1&1&1&22\\6&1&8&89\\-6&4&4&38\end{array}\right] \qquad\text{given}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&-5&2&-43\\0&5&12&127\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ 6[1]+[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ $-\frac{1}{5}$[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[1]-[2]$\rightarrow$[1]}[/tex]

Now, we normalize the third column.

  [tex]\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&1&6\end{array}\right] \qquad\text{$\frac{1}{14}$[3]$\rightarrow$[3]}\\\\\left[\begin{array}{ccc|c}1&0&0&5\\0&1&0&11\\0&0&1&6\end{array}\right] \qquad\text{$-\frac{7}{5}$[3]+1$\rightarrow$[1];\ $\frac{2}{5}$[3]+[2]$\rightarrow$[2]}[/tex]

This is the target of our row operations. It tells us the solution to the system of equations is ...

  (x, y, z) = (5, 11, 6)

_____

A number of online calculators and phone or tablet apps are available for putting a coefficient matrix into this "reduced row-echelon form." Many graphing calculators will do this, too.

In the end, this is not terribly different from ad hoc solution using "elimination" methods. That is precisely what we did when we created the zeros in the first two columns of row 3.

Answer:

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Step-by-step explanation:

f(x)=-4 cos (3x-pi)+2

The equation is in the form

f(x) = a cos (bx -c) +d  where |a| is the amplitude

period  is 2 pi /b

phase shift:  c/b

midline = d

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Answer:

angle c is 63

Step-by-step explanation:

Angles in a triangle add up to 180 therefore

70+47+x=180

x=180-117

=63°

I hope this helps

Answer:

x=24

Step-by-step explanation:

Answer:

BC = 24

Step-by-step explanation:

Since ∠ B and ∠ C are congruent the the triangle is isosceles with

AC = AB , that is

3x - 15 = x + 33 ( subtract x from both sides )

2x - 15 = 33 ( add 15 to both sides )

2x = 48 ( divide both sides by 2 )

x = 24

Then

BC = x = 24

Answer:

[tex]a = 2[/tex]

[tex]b = 2^{1/6}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

[tex]x = -2[/tex]

Required

Find a and b

We have:

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

Substitute -2 for x

[tex]\sqrt[3]{(-2)^{10}} = a^3 * \sqrt b[/tex]

[tex]\sqrt[3]{1024} = a^3 * \sqrt b[/tex]

Expand

[tex]\sqrt[3]{2^9 * 2} = a^3 * \sqrt b[/tex]

Split the exponents

[tex]2^{(9/3)} * 2^{(1/3)} = a^3 * \sqrt b[/tex]

[tex]2^{3} * 2^{1/3} = a^3 * \sqrt b[/tex]

By comparison:

[tex]a^3 = 2^3[/tex]

So;

[tex]a = 2[/tex]

and

[tex]\sqrt b = 2^{1/3}[/tex]

Take square roots of both sides

[tex]b = 2^{1/6}[/tex]

Answer: -8, -2

Step-by-step explanation: (the previous answers are ) 1. D 2. C 3. -8,-2 (for reference of order :))

Answer:

x=80 degrees

Step-by-step explanation:

We are given that

ABC is a right triangle

Therefore, angle B=90 degrees

Angle A=a+b=135 degrees

Angle C=c+d=55 degrees

Angle D=x

We have to find the value of x.

We know that

In quadrilateral

Sum of all angles of quadrilateral=360 degree

[tex]\angle A+\angle B+\angle C+\angle D=360^{\circ}[/tex]

[tex]135+90+55+x=360[/tex]

[tex]280+x=360[/tex]

[tex]x=360-280[/tex]

[tex]x=80[/tex]

x=80 degrees

Answer:

5%

Step-by-step explanation:

First, find the amount of tax:

5250 - 5000

= 250

Divide this by the original price of $5000 to find the percent of import tax:

250/5000

= 0.05

So, the percent of import tax is 5%

Answer: B. 74 cm

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit conversion and perimeter.

When there are multiple units in a question, then we should convert all units into one through converting factors.

Perimeter is the distance around a two-dimensional figure.

P = 2 (w + l)

1 cm = 10 mm

Solve:

140 mm = 14 cm

230 mm = 23 cm

P = 2 (w + l) ⇒ Given

P = 2 (14 + 23) ⇒ Substitute

P = 2 (37) ⇒ Addition

P = 74 cm ⇒ Simplify through muliplication

Hope this helps!! :)

Please let me know if you have any questions

The far left of the chart is the minimum(low) value of the box plot.

Answered by Gauthmath must click thanks and mark brainliest

Graph exists as an illustration of any object or a physical format by dots, lines, etc.

The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could also describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists in a particular case of the graph of an equation.

A function is defined as a connection between a set of inputs containing one output each. In simple words, a function exists as an association between inputs where each input is connected to exactly one output. Every function includes a domain and codomain or range. A function exists generally represented by f(x) where x is the input.

From the given figure,

Graph 1 exists a function.

Graph 2 exists a function.

Graph 3 doesn't exist as a function.

Graph 4 exists a function.

Graph 5 doesn't exist as a function.

Graph 6 doesn't exist as a function.

Hence, Graph exists as a representative of any object or a physical design by dots, lines, etc.

To learn more about graph refer to:

https://brainly.com/question/11803331

#SPJ2

Complete question is;

Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items were sold prior to the online launch date.

The equation below represents the number of belts sold, s, x days after its online launch. S = 3^(x)

The equation below represents the number of wallets sold, s, x days after its online launch. S = 4x + 15

Using graphing technology, complete the statements. After ___ days, the total number of belts sold will be the same as the total number of wallets sold. The number of belts and the number of wallets Mr. Matthew sold after this many days is ___

Answer:

Number of days = 3 days

Total belts and wallets after 3 days = 54

Step-by-step explanation:

We are told that the number of belts sold, s, x days after its online launch. S = 3^(x)

Also, we are told that the number of wallets sold, s, x days after its online launch. S = 4x + 15

Now, we want to find the Number of days that total number of belts sold will be the same as the total number of wallets sold using graphing technology.

The number of days will simply be the value of x where the two graphs meet.

I have drawn the graph of both equations.

From the attached graph, we can see that the x-value at where the both graph lines meet is approximately 3. I didn't take the negative solution because number of days cannot be negative.

Thus, x = 3

Putting x = 3 in;

S = 3^(x)

S = 3^(3)

S = 27

Similarly, Putting x = 3 in;

S = 4x + 15

We have;

S = 4(3) + 15

S = 12 + 15

S = 27

Thus,total number of belts and wallets sold after 3 days = 27 + 27 = 54

Answer: Rs 25,000

Step-by-step explanation:

Given

Retailer sold an electric iron to a customer at a loss of 10%

Suppose the Cost price of iron is [tex]x[/tex]

So, selling price is [tex]0.9x[/tex]

This price must be equal to [tex]25425[/tex]+ VAT

[tex]\Rightarrow 0.9x=25425-0.13(0.9x)\\\Rightarrow 0.9x+0.117x=25425\\\Rightarrow 1.017x=25425\\\Rightarrow x=\text{Rs }25,000[/tex]

Thus, the cost price is [tex]Rs.25,000[/tex]

Plugging the values into a table on desmos, it clearly follows an exponential equation as shown by the equation of best fit. Therefore, the relationship is exponential.

Answer:

324

Step-by-step explanation:

Each of the first 3 letters can be chosen from the 23 letters, {A, B, C, …, U, V, W}, so there are 23³ possible choices.

The first 2 digits can be any number from {0, 1, 2, …, 9}, so there are 10² choices.

The last digit cannot be 0 or 9, so you can select from {1, 2, 3, …, 8} which gives 8 choices.

Then the total number of PINs that you can make is

23³ × 10² × 8 = 9,733,600

Answer:

[tex] {f}^{ - 1}(0) = 6[/tex]

Step-by-step explanation:

When trying to solve for inverses, we are given a y value in place of an x value. Thus we are solving for the x value which the given y value corresponds to.

Answer:

6

Step-by-step explanation

Answer:

6

Step-by-step explanation:

plug in the 3

4(3-3)+5(3)-3^2

4(0)+15-9

0+15-9

15-9

6

Answer:

$17

Step-by-step explanation:

You reverse the operation, and you do 85 divided by 5, which is 17. Have an amazing day!!

Answer:

10^-5

10^-5 = 1/100,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{1}{100000}=\frac{1}{10^{5}}=10^{-5}\\\\\\\frac{1}{a^{m}}=a^{-m}[/tex]

Answer:

answer is in the attachment.

Answer:

option 3

Step-by-step explanation:

[tex](4 + 3) \sqrt[5]{x {}^{2}y } = 7 \sqrt[5]{ {x}^{2}y } [/tex]

Answer:

Step-by-step explanation:

[tex]4( \sqrt[5]{ {x}^{2}y } ) + 3( \sqrt[5]{ {x}^{2} y} )[/tex]

[tex](taking \: \sqrt[5]{ {x}^{2}y } \: as \: common \: then)[/tex]

[tex] = \sqrt[5]{ {x}^{2} y} (4 + 3)[/tex]

[tex] = \sqrt[5]{ {x}^{2} y} \times 7[/tex]

[tex] = 7 (\sqrt[5]{ {x}^{2}y } )(ans)[/tex]

Answer:

I think it's h(x)

Step-by-step explanation:

My knowledge

Hope it helps!

9514 1404 393

Answer:

  (c)  g(x)

Step-by-step explanation:

The initial temperature is -3, so you're looking for graphs that cross the y-axis at y = -3. The functions g(x) and h(x) do that.

The temperature rises 2 degrees per hour, so you're looking for a function that increases by 2 for each 1 unit to the right. Only the function g(x) does that.

The line g(x) represents the scenario.

Answer:

G is the midpoint of the side [tex]\overline {AB}[/tex] of triangle ΔOAB

Step-by-step explanation:

The vertices of the triangle ΔOAB are A(-15, 0), B(0, 8), and C(0, 0)

The coordinates of the point G =  (-7.5, 4)

The length from the point A to the point G, [tex]\overline {AG}[/tex] is given as follows;

[tex]\overline {AG} =\sqrt{(-7.5 - (-15))^2 + (4 - 0)^2} = \sqrt{7.5^2 + 4^2} = 8.5[/tex]

The length from the point A to the point B, [tex]\overline {AB}[/tex] is given as follows;

[tex]\overline {AB} =\sqrt{(-15 - 0)^2 + (8 - 0)^2} = \sqrt{15^2 + 8^2} = 17[/tex]

Therefore, the point G is the half way mark of [tex]\overline {AB}[/tex] = The midpoint of the side  [tex]\overline {AB}[/tex]

Answer:

[tex]l = 6w - - - - 1 \\ \\ 2l + 2w = 70 - - - - - 2 \\ \\ solving \: simultaneously \\ put \: l = 6w \: into \: 2 \\ 2(6w) + 2w = 70 \\ 12w + 2w = 70 \\ 14w = 70 \\ w = 5 \\ \\ l = 6w \\ l = 6(5) \\ l = 30[/tex]