What is the period of the function f(x) = cos 2x?
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The rocket will reach its maximum height after 7.438 seconds.

An equation shows the relationship between numbers and variables in an expression.

Let y represent the height of the rocket x seconds after its launch.

Given that:

y = -16x² + 238x + 81

The height of the rocket is maximum when the rate of change is zero. Hence:

The rocket reaches it maximum at dy/dx = 0

dy/dx = -32x + 238

-32x + 238 = 0

32x = 238

x = 7.438

The rocket height would be maximum at 7.438 seconds.

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The graph of the system of inequality is plotted and attached

In mathematics,  the term inequality refers to a relationship between two expressions or values that is not equal to each other.

Therefore, inequality emerges from a lack of balance.

The graph of the inequality is represented by two horizontal lines one is a dashed line and the other is a solid line

y < 8

This is a dashed line at point y = 8, the dashed line is because the inequality does not have the "equal to".

Also the shading is below the line since it is less than

y ≥ 3

This is a solid line at point y = 3, the solid line is because the inequality have the "equal to". as in greater than or equal to.

Also the shading is above the line since it is greater than symbol.

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Answer:

6,004.024

Step-by-step explanation:

Answer:

The number 0.000380 converted to standard form is 3.80 x 10 -4 Note that we do not remove the trailing 0 because it was originally to the right of the decimal and is therefore a significant figure. Additional Resources See the Scientific Notation Calculator to add, subtract, multiply and divide numbers in scientific notation or E notation.

Step-by-step explanation:

Answer: Simple 75 peanuts for $3.50

Step-by-step explanation:

The equation of the line that is perpendicular to y = -2x + 1​ will be y = (1/2)x + 1.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

y = -2x + 1​

The slope(m) intercept form of a line is given as,

y = mx + c

By comparing,

Slope m = -2

The product of the slopes of the two perpendicular lines is -1.

Slope of perpendicular line (m') x -2 = -1

m' = 1/2

Put m' = 1/2 and (4,3) into y = m'x + C.

3 = (1/2)4 + C

C = 1

Thus, line will be y = (1/2)x + 1

Hence "y = (1/2)x + 1 will be the equation for the line that is perpendicular to y = -2x + 1.".

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The volume of the figure is has been determined to be 597.632 cubic centimeters.

The volume of a figure is the amount of substance that it can conveniently contain considering its dimensions. Each figure has a given formula to determine its volume.

Considering the figure in the question, divide it into two parts.

So that,

i. volume of the first part = length x width x height

                                      = 16.25 x 5.8 x 4.6

                                      = 433.55

The volume of the first part is 433.55 cubic cm.

ii. volume of the second part = length x width x height

                                            = (16.25 - 10.1) x 5.8 x 4.6

                                            = 6.15 x 5.8 x 4.6

                                            = 164.082

volume of the second part is 164.082

iii. Total volume of the figure = 433.55 + 164.082

                                           = 597.632 cubic centimeters

The total volume has been determined to be 597.632 cubic centimeters.

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The inequality that describes Mr. Clarke's problem is x < 450/3.

This means that the cost of each camera must be less than $450/3, or $150.  This inequality means that Mr. Clarke can spend up to $450 on the cameras, but the amount he spends on each camera must be less than $450 divided by 3, or $150. To calculate this, we take the total budget of $450 and divide it by the number of cameras, which is 3. To solve this, we can use the formula x < 450/3. We can calculate the maximum amount Mr. Clarke can spend on each camera by multiplying 450 by 1/3, resulting in $150. Therefore, Mr. Clarke can spend a maximum of $150 on each camera in order to stay within his budget of $450.

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The results generated in the map phase are combined in the _reduce_ phase.

In maps, the "reduced phase" refers to a technique used to remove the phase ambiguity present in interferometric synthetic aperture radar (InSAR) data. InSAR uses radar to measure the distance between a satellite or aircraft and the ground and can be used to create detailed maps of changes in the surface of the earth over time.

However, because InSAR data is collected using radar waves, which are sensitive to the phase of the signal, the data can be affected by phase ambiguities. The reduced phase technique is used to remove these ambiguities and create more accurate maps.

Therefore, The results generated in the map phase are combined in the _reduce_ phase.

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For the given regular polygon with the angle sum of 10x + 4, the value of x = 143.6

They are referred to as regular polygons if the interior angles and sides are all equal. Equilateral triangles, squares, and other shapes are examples of regular polygons. Along with the sides being congruent, regular polygons also have congruent angles. They are equiangular, according to that.

We know that sum of interior angles of a regular polygon is

( n − 2 ) × 180°, where n is sides

For the given question

( 10 − 2 ) × 180°

= 8 × 180°

= 1440°

Given that

10x + 4 = 1440°

10x = 1436

x =  1436/10

x =  143.6

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Answer:

2 & 4 :)

Step-by-step explanation:

The probability for the first digit of a random number of a data set to be greater than 7 is 0.097.

Here we are given a probability distribution table regarding Benford's law where all the probabilities about the occurrence of the first digit of a data set are given. As we can see that digit 1 has the highest probability with number 9, the least.

Here we need to find the probability that a randomly selected number, has a first digit greater than 7.

Here we don't have to think about Benford's law since the data already has given us the required distribution.

Hence P(D > 7) = P(D = 8) + P(D = 9)

= 0.051 + 0.046

= 0.097

Hence the probability for the first digit to be greater than 7 is 0.097.

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Correct Question

(Image Attached)

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2} \implies {\Large \begin{array}{llll} \cfrac{3}{ 2 } \end{array}}}}[/tex]

Given the figure below, the value of x is  1.4 and z is 5.85 according to vertical angles rule.

Vertical angles, also known as vertically opposite angles, are formed when two lines intersect. Angles that are vertically opposite to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles; that is, they add up to 180 degrees.

For instance, if two lines intersect and form an angle, say X=45°, then its opposite angle is also 45°. And the angle next to angle X will be 180 - 45 = 135°. As we know vertical angles of intersection are equal:

63 = (15x + 42)

15x = 21

x = 1.4

For 20z, we know that opposite angle is 20z too

and all angles add upto 360°

So,

63 + 63 + 20z + 20z = 360

126 + 40z = 360

40z = 234

z = 5.85

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In Exercises 23-26 and In Exercises 27-36 , the trigonometric function by memory and by constructing an appropriate triangle for the given special angle are mentioned below

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

1. Exercises 23-26

23. (a) cos 60° = 0.5

24. (a) cot 45° = 0.7071

25. (a) sin 45° =  0.7071

26. (a) sin 60° = 0.8660

(b) cos 30° = 0.8660

(b) cos 45° =  0.7071

(b) cos 30° = 0.8660

(b) tan 45° = 1

27. (a) sin 10° = 0.9958

28. (a) tan 23.5° = 0.4348

29. (a) sin 16.35° = 0.2815

(c) tan 60° = 1.732

(c) cosec 45° = 1.4142

(c) tan 30° = 0.5773

(c) sec 30° = 1.1547

2.  Exercises 27-36

(b) cos 80° = 0.1736

(b) cot 66.5° = 0.4348

(b) cosec 16.35° = 3.5523

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Answer:

9 years

Step-by-step explanation:

Losing 15 % means 85% remains

  so multiply each year's value by .85 to find the current value

       after 'n'  years it will be  24300 * .85^n

when will it be 5600 ?

    5600 = 24300 * .85^n

     5600/24300  = .85^n  

             now you need to take the log of both sides and solve for 'n'  years

  log ( 5600/24300) / log(.85) = n = 9.031 = ~~ 9 years

The number 96 into simplest radical form is 4√6.

In the given question we have to simplify the number into simplest radical form.

The given number is 96.

To simplify and obtain the radical form of square roots, we will first identify every element below the square root.

The square factor for 96 is 16.

Now we can factor 96 as 16 * 6.

The radicals are not in their least complicated form, as should be evident.

When we pay close attention now and subtract the square root of 16 * 6.

As √16 = 4 is the starting point, which leads to 4√6.

Currently, all radicals have been upgraded.

Never again will the extreme have any square factors.

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The complete question is:

Simplify the number into simplest radical form. Use the factor tree to help determine the factors 96.

Use the factor tree, the simplest radical form of 64 is 8.

Lets Simplify the number 64 into the simplest radical form.

To solve this, we can use a factor tree.

First, we will start with the number 64. We can break this down into two groups of two numbers, one being 4 and the other being 16.

Next, we can break down the 4 into two groups of two numbers, one being 2 and the other being 2.

Finally, we can break down the 16 into two groups of two numbers, one being 4 and the other being 4.

Now we have our factors, 2, 2, 4, and 4. We can use these factors to simplify the number 64 into its simplest radical form.

The formula for the radical form of a number is √(a × b × c × d).

In this case, our a, b, c, and d values are 2, 2, 4, and 4 respectively.

Therefore, our simplified radical form of 64 is √(2 × 2 × 4 × 4) = √64 = 8.

This means that the simplest radical form of 64 is 8.

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number of minibuses required = 7

Division is the process of dividing some object into a number of parts. It is opposite to the multiplication process. In mathematics, the number that is divided by other number is called dividend and the other number is called divisor.

given, number of tourists = 169

each minibus can accommodate 26 passengers.

number of minibuses required for the total 169 tourists.

will be 169/26 = 6.5 = 7

they need to hire total 7 minibuses for a tour around Tokyo.

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D. y-2 cos(2x) + 4 is not a solution to the differential equation y" + 4y = 0.

The differential equation y" + 4y = 0 is a second-order, homogeneous linear differential equation with constant coefficients. The general solution to this type of differential equation is of the form y = e^(rt) where r is a root of the characteristic equation r² + 4 = 0. The roots of this equation are r = +/- √(4) = +/- 2i, which are both imaginary. Therefore, the general solution to the differential equation is y = c1cos(2x) + c2*sin(2x), where c1 and c2 are arbitrary constants.

Option D. y - 2 cos(2x) + 4 is not a solution to this differential equation because it doesn't have the same form as the general solution. It is a combination of a constant term, cosine and sine function but the general solution only contains sine and cosine function.

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Answer;

-2.8m

Step-by-step explanation;

It's just adding m terms, and yes it's adding decimals but you can do it in your head if your good at arithmetic if not your calculator is there to help you out dw

so -5.1m+2.3m is

Answer: -2.8

Step-by-step explanation:

it the answer

Answer:

c.-a²-a-35

Step-by-step explanation:

a(4-a)-5(a+7)

=4a-a²-5a-35

=a²-a-35

Answer:

g(3) = 11

Step-by-step explanation:

g(n) = n^2 +2

g(3) = 3^2 +2

g(3) = 9 + 2

g(3) = 11

To simplify a radical expression, you can use a few different techniques. One common technique is to factor the expression under the radical sign (the radicand) as much as possible.

Another technique you can use is to use the properties of radicals. For example, you can use the product property of radicals to combine like terms under the radical sign

You can also use the quotient property of radicals to divide out a factor under the radical sign. Finally, some radicals are unsimplifiable by these methods. You can approximate a value of radical or try to get it in a form of fraction with radical.

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Answer: To find the midpoint of a line segment, you can average the x-coordinates of the endpoints and average the y-coordinates of the endpoints.

The x-coordinates of the endpoints are -1 and -9, so the average of the x-coordinates is (-1 + (-9))/2 = -5

The y-coordinates of the endpoints are 3 and -7, so the average of the y-coordinates is (3 + (-7))/2 = -2

So the midpoint of the segment with endpoints (-1, 3) and (-9, -7) is (-5, -2)

Step-by-step explanation:

Answer:

D. IT shows it is Exponential function i believe

Step-by-step explanation:

For HL congruence, two triangles need to have the same corresponding angles and corresponding sides. This means that the angles in one triangle must match the angles in the other triangle, and the side lengths must match respectively.

HL congruence is a type of congruence between two triangles, which states that two triangles are congruent if they have the same corresponding angles and corresponding sides. The angles of one triangle must be equivalent to the angles of the other triangle, and the side lengths must match.

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Answer:

2

Step-by-step explanation:

i got 100

Answer:

no

Step-by-step explanation:

the X corrdinate ( the first part of the ordered pair) has multiple repeating 0's.The numbers in the X cant repeat or its not a funtion

The value of cosec B if A and B are complementary is 15/7

Two angles are called complementary when their measures add to 90 degrees. Since A+B = 90°, then A and B are complementary. Examples of complementary angles are 45 and 45, 30 and 60, 20 and 70 e.t.c

If sec A is 15/7

sec A= 1/cos A

therefore cos A = 7/15

if cos A = 7/15 , then from law of complementary angles

cos A = sin (90-A)

and 90-A = B

therefore cos A = sinB

if cos A = 7/15, then;

sin B = 7/15

then sinB = 1/cosec B

cosec B = 15/7

therefore the value of cosec B = 15/7

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1. The ratio of the surface area to volume of the cube = 3/ 5

2. The ratio of the surface area to volume of the cuboid = 113/ 62

Surface area and volume of a figure.

The surface area of a given figure is the area of the total external boundary of the figure. While the volume of a figure is the quantity of substance that can fill up the figure.

To solve the question, we have;

1. The surface area of a cube = 6a

where: a = length x length

              = 10 * 10

            a = 100 square centimeters

So that;

surface area of the cube = 6*100

                               = 600 sq cm

ii. Volume of a cube = l^3

                        = 10^3

volume of the cube = 1000 cubic centimeters

iii. The ratio of its surface area to volume = 600/ 1000

                                        = 6/ 10 = 3/ 5

2. The surface area of a cuboid = 2a + 2b + 2c

                = 2(a + b + c)

where a = b = c = length * width

a = length x width

  = 4*2

a = 8 sq. m

b = length x width

  = 6.2 x 4

b = 24.8 sq. m

c = length x width

      6.2 x 2

c = 12.4 sq. m

Surface area of the cuboid = 2(8 + 24.8 + 12.4)

                      = 90.4 sq. m

ii. volume of a cuboid = length x width x height

                             = 6.2 x 4 x 2

                             = 49.6 cubic meters

iii. The ratio of surface area to volume of the cuboid = 90.4/ 49.6

                                                 = 113/ 62

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The fourth ordered pair using the two

sequences is ( 7/3 ,106) .

The first sequence is constructed by first multiplying the terms by 2 and then adding one-third starting from zero. So, sequence starts from 0.

First term of first sequence, a₁ = 0

a₂ = (2x0) + 1/3 = 1/3

a₃ = (2x1/3) + 1/3 = 2/3 + 1/3 = 1

a₄ = (2x1) + 1/3 = 2 + 1/3 = 7/3

Hence, the sequence is 0, 1/3, 1, 7/3, ...

The second sequence is constructed by first adding one half in terms and then multiplying by 4. The sequence starts from 1 ,

a₁ = 1

a₂ = (1 +1/2) × 4 = (3/2)4 = 6

a₃ = (6+1/2) x 4 = 13/2 x 4 = 26

a₄ = (26 + 1/2)× 4 = 53/2 x 4 = 106

Hence, the sequence is 1, 6, 26, se106, ...

Therefore, the fourth terms of the two sequences are the following, 7/3 and 106.

So, required ordered pairs is ( 7/3, 106).

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