A model rocket is launched from ground level. It’s flight path is modeled by the following equation Y= -16t^2+160t where h is the height of the rocket above the ground in feet and t is the time after the launch in seconds. what is the rocket’s maximum height? when did the rocket reach the maximum height?

Answer:

  A.  440°, -280°

  B.  17π/6, -7π/6

Step-by-step explanation:

You want angles coterminal with the given angle, one with a positive sign, and one with a negative sign.

Adding an integer multiple of 360° = 2π radians to any angle will give the measure of a coterminal angle.

A positive coterminal angle is ...

  80° +360° = 440°

A negative coterminal angle is ...

  80° -360° = -280°

A positive coterminal angle is ...

  5π/6 +2π = 17π/6

A negative coterminal angle is ...

  5π/6 -2π = -7π/6

__

Additional comment

We have used the smallest multiples of 1 full rotation around the origin. You could choose others. For example, adding 3600° to the first angle will give 3680° as a positive angle coterminal with 80°.

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Answer:

  (B)  sin(60°) = 4/x

Step-by-step explanation:

You want an equation for finding the hypotenuse of a 30°-60°-90° triangle with the middle-length side being 4 units.

The trig relation between the side opposite and angle and the hypotenuse of the right triangle is ...

  Sin = Opposite/Hypotenuse

In this triangle, this relation means ...

  sin(60°) = 4/x . . . . . matches choice (B)

__

Additional comment

The middle-length side is opposite the middle length angle.

This is a "special" right triangle with sides in the ratios 1 : √3 : 2. The length x will be 4(2/√3) = (8/3)√3. It can be useful to remember the side length ratios for this triangle.

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The perimeter of the polygon which is a triangle is

72 units

The perimeter of the polygon is solved using the knowledge of tangents

This is applied as follows

perimeter of the triangle = GH + HL + GJ

GH = (4 + 32 - 15) = 21

HL = 15 + 4 = 19

GJ = 32

plugging in the values we have

perimeter of the triangle = 21 + 19 + 32

perimeter of the triangle = 72 units

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Answer: 0

Step-by-step explanation:

To solve the equation (x² + 3x)³ - 16(x² + 3x) - 36 = 0 using substitution, let's make a substitution:

Let u = x² + 3x.

Now, we can rewrite the equation in terms of u:

u³ - 16u - 36 = 0.

Let's solve this equation for u by factoring:

(u - 6)(u² + 6u + 6) = 0.

Now, we have two possible cases:

Case 1: u - 6 = 0.

This gives us u = 6.

Case 2: u² + 6u + 6 = 0.

To solve this quadratic equation, we can use the quadratic formula:

u = (-b ± √(b² - 4ac)) / (2a),

where a = 1, b = 6, and c = 6.

Plugging in these values, we get:

u = (-6 ± √(6² - 4(1)(6))) / (2(1)),

u = (-6 ± √(36 - 24)) / 2,

u = (-6 ± √12) / 2,

u = (-6 ± 2√3) / 2,

u = -3 ± √3.

Now that we have the possible values of u, let's substitute back to find the corresponding values of x:

Case 1: u = 6.

Since u = x² + 3x, we have x² + 3x = 6.

Rearranging, we get x² + 3x - 6 = 0.

Hope it helps!

I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .

We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .

We can go ahead and solve it, and get the following:

[tex]-81 = -\frac{b^{2}}{4}[/tex]

[tex]324 = b^2[/tex]

[tex]\pm{18} = b[/tex]

Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex]  or [tex]$f(x)=x^2-18x+118$[/tex] .

We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.

We have:

[tex]37 = x^2+18x+118[/tex]

[tex]0=x^2+18x+81[/tex]

[tex]0=(x+9)^2[/tex]

[tex]x+9=0\\x=-9[/tex]

Doing the same thing with the second equation, we get:

[tex]37 = x^2-18x+118[/tex]

[tex]0=x^2-18x+81[/tex]

[tex]0=(x-9)^2[/tex]

[tex]x-9=0\\x=9[/tex]

After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].

We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].

Conclusion:         [tex]h = -9, 9[/tex]

                            [tex]k=37[/tex]

The smallest subset containing 7.83 among the common subsets is Q.

We are given that;

The number 7.83

Now,

Subset of a given set is a set whose all elements are in the original set of which it is subset.

So if B is subset of A, then all elements of B are in A but it is not necessary that all elements of A are in B.

If B is subset of A, then A is superset of B.

The smallest subset containing the value 7.83 is the set of rational numbers. A rational number is a number that can be written as a fraction of two integers, such as 7.83 = 783/100. The set of rational numbers is denoted by Q and it is a subset of the set of real numbers R.

Therefore, by subsets the answer will be Q.

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The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

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

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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The solution to the proportional equation 5/8 = 8/a is a = 64/5 or a = 12.8.

To solve the proportional equation 5/8 = 8/a, we can cross-multiply.

Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.

We have:

5 × a = 8 × 8

5a = 64

To isolate the variable a, we divide both sides of the equation by 5:

a = 64/5

We may cross-multiply the proportional equation 5/8 = 8/a to find the solution.

Cross-multiplication is the process of multiplying the denominator of the second fraction by the first fraction's numerator, and vice versa.

We possess

5 × a = 8 × 8 5a = 64

We divide both sides of the equation by 5 to identify the variable a:

a = 64/5.

We may cross-multiply to find the solution to the proportional equation 5/8 = 8/a.

Cross-multiplication is the process of multiplying one fraction's numerator by another's denominator and vice versa.

There are:

5 × a = 8 × 8 5a

= 64

By multiplying both sides of the equation by 5, we may separate the variable a:

a = 64/5.

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Given statement solution is :- The slope (m) of the line is -2, and the y-intercept (b) is -5/4.

To find the y-intercept and slope of the line represented by the equation -8x - 4y = 5, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Let's begin by isolating the term with y:

-8x - 4y = 5

Subtract -8x from both sides:

-4y = 8x + 5

Next, divide both sides of the equation by -4 to solve for y:

y = (-8/4)x - (5/4)

Simplifying further:

y = -2x - 5/4

Now we can identify the slope and the y-intercept:

The slope (m) of the line is -2, and the y-intercept (b) is -5/4.

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The possible trigonometric ratios for the angle θ are given as follows:

A. [tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

B. [tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

The sine for the angle θ is given as follows:

sin(θ) = 2/3.

The identity relating the sine and the cosine is given as follows:

sin²(θ) + cos²(θ) = 1.

Hence the cosine of the angle is given as follows:

cos²(θ) = 1 - 4/9

cos²(θ) = 5/9

[tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex]

The tangent is given by the division of the sine by the cosine, hence it is calculated as follows:

[tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

(if the cosine is negative, the tangent is then negative, as the sine is positive).

The secant is the division of one by the cosine, that is, it is the inverse fraction of the cosine, hence:

[tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex]

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Answer:

[tex]\frac{3}{4}[/tex] or 75%

Step-by-step explanation:

There are 8 equal-sized sections, 6 being blue. 6/8 = 3/4 = 0.75 which is 75%. That is the probability that the spinner lands on blue.

answer is 45

400/9 = 44.44...

so with the extra employees you need another manager.

Answer:

40 managers

Step-by-step explanation:

If there is one manager for every 9 engineers, we can assume that each manager is responsible for a group of 9 engineers. To determine the number of managers in the company, we need to divide the total number of engineers by 9.

First, we need to determine the total number of engineers in the company. Since there is one manager for every 9 engineers, the ratio of engineers to managers is 9:1. This means that for every 10 people (9 engineers and 1 manager), there is 1 manager. So we can find the total number of groups of 10 people by dividing the total number of employees by 10:

400 employees / 10 = 40 groups of 10 people

This means that there are 40 groups of 10 employees (1 manager and 9 engineers) in the company. Since there is 1 manager in each group, the total number of managers in the company is equal to the number of groups:

Number of managers = Number of groups = 40

Answer:

y = (1)(1.004)^^(84)

y ≈ 1.610

Therefore, the balance of the investment account after 7 years, assuming an initial principal of 1 dollar, is approximately 1.610 dollars.

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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a)

The cost per unit decreasing by 0.00001 for production levels above 12,000.

Given,

From the graph it is clear that the graph passes through the points (12000,0.85) and (38000,0.59).

Now,

If a line passes through two points then the slope of the line is

m = y2 - y1 / x2 - x1

The rate of change in cost per unit for production levels above 12,000 is

m = 0.59 - 0.85 / 38000 - 12000

m = -0.00001

Here negative sign represents the decreasing rate. It means the cost per unit decreasing by 0.00001 for production levels above 12,000.

b)

The function for the domain over [12000, 38000] is :

y = -0.00001x + 0.97

The point slope form of a linear function is,

(y-y1) = m (x - x1)

m = slope.

The slope of the line over [12000, 38000] is -0.00001 and the point is (12000,0.85). So, the function for the domain over [12000, 38000] is

y-0.85 = -0.00001(x-12000)

y =  -0.00001x + 0.97

c)

The cost per unit at the production level of 19,000 is 0.78.

Substitute x=19000 in the above equation, to find the cost per unit at the production level of 19,000.

y = -0.00001(19000) + 0.97

y = 0.78

Thus the cost per unit at the production level of 19,000 is 0.78.

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The correct statement is that "Line p must be drawn in plane B."

If a new line, p, is drawn parallel to line /, the statement that is true is "Line p must be drawn in plane B."

To understand this, let's analyze the given information:

Planes A and B are shown.

Line m is shown in plane A.

Line n is shown in plane B.

Line / is the line that connects planes A and B.

When a new line, p, is drawn parallel to line /, it means that line p will also connect planes A and B. However, since line / itself is connecting planes A and B, line p must also lie in plane B to maintain its parallel relationship with line /. This is because parallel lines lie in the same plane.

This ensures that line p remains parallel to line / and maintains its connection between planes A and B.

It is important to note that line p being drawn in plane B does not necessarily imply that it intersects with line n. It simply means that line p lies within plane B and remains parallel to line /.

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Answer: Lara

Step-by-step explanation:

convert yards into feet

yards*3= feet

89 yards * 3 = 267 feet

Since 270 is greater than 267 Lara. Lara's distance is greater by 3 feet since 270-267 is 3

Answer:

21

Step-by-step explanation:

[tex]x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z[/tex]

Therefore, it's [tex]2z^5-7z[/tex].

10-10=69.420!!!!!!!!!!

no it dose not

your right whats the question

the answer is of the inequality is x>8

The values of the distance are;

1. 4. 49 feet

2. 7. 73 feet

We need to know the trigonometric identities and their ratios. We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Now, substitute the values, we have;

1. Adjacent = d

Hypotenuse = 12

Angle = 68 degrees

cos 68 = adjacent/hypotenuse

cos 68 = d/12

cross multiply the values, we get;

d = 4. 49 feet

2.

cos 25 = 7/x

cross multiply the values, we have;

x = 7/0. 9063

divide the values, we get;

x = 7. 73 feet

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(a) The inverse variation equation that relates to x and y is  y = -20/x.

(b) The value of y when x = 25 is -0.8 or -4/5

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

(a) To write the inverse variation equation that relates to x and y, we look for the constant k connecting x and y

From the questiuon,

To remove the proprotionality/Variation sign, we introduce a constant k

Given:

Substitute into equation 1 and solve for k

Hence, the equation is y = -20/x.

(b) To find the value of y when x = 25, we subtitute into the equation

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Answer:

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

Step-by-step explanation:

What is probability?

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.

To find which 2 books describe a pair of dependent events:

A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.

Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.

Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.

Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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The area of the decagon is 3077.68 square meters

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

A decagon with a side of 20 meters

This means that

a = 20

The area of the decagon is then calculated as

A = 2.5a² * √(5 + 2√5)

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

A = 2.5 * 20² * √(5 + 2√5)

Evaluate

A = 3077.68

Hence, the area of the decagon is 3077.68 square meters

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Complete question

A decagon with a side of 20 meters. What is the area?

The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Answer:

9:30

Step-by-step explanation:

Answer: y=4x+7

Step-by-step explanation:

-8x+2y=14

Convert to y=kx+b

2y=8x+14

y=4x+7

The size of angle EAD is 40°.

To find the size of angle EAD, we can use the information given in the diagram and apply some basic trigonometry principles. Let's go step by step.

First, we notice that triangle CDB is a right triangle since angle CDB is given as 90°. We also know that angle DCB is 40°. This means that angle CBD can be found by subtracting 40° from 90°:

angle CBD = 90° - 40° = 50°.

Since E is the midpoint of DB, we can conclude that angle CBE is also 50°, as it is vertically opposite to angle CBD.

Now, let's consider triangle ADE. We know that angle EAD is the angle we're trying to find. We can use the fact that the angles in a triangle add up to 180° to write the equation:

angle EAD + angle ADE + angle DEA = 180°.

Since E is the midpoint of DB, we can conclude that angle ADE is equal to angle CDE. Angle DEA is equal to angle CEA. Therefore, we can rewrite the equation as:

angle EAD + angle CDE + angle CEA = 180°.

We can substitute the values we know: angle CDE is 90° (since it's a right angle), and angle CEA is 50° (since it's vertically opposite to angle CEB).

angle EAD + 90° + 50° = 180°.

Simplifying the equation:

angle EAD = 180° - 90° - 50° = 40°.

Therefore, the size of angle EAD is 40°.

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