8.04 A

Graph each pair of parametric equations.
(2 points each)

x = 3 sin3t
y = 3 cos3t

A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.





x = 7 sin t + sin 7t
y = 7 cos t + cos 7t

A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.





x = 2t
y = t + 5, -2 ≤ t ≤ 3

A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.





x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4

A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.





x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π

A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.

The given conditions suggest a second-degree polynomial of form p(x) = ax^2 + bx + c. By solving the given conditions a = 5, b = -3, and c = 3, yielding the polynomial p(x) = 5x^2 - 3x + 3.

The question is asking for a second-degree polynomial, which can generally be written in the form p(x) = ax^2 + bx + c. Given that p(1) = 5, that means a + b + c = 5. The derivative of p(x), p'(x) = 2ax + b, and p'(1) = 7, so 2a + b = 7. The second derivative, p''(x) = 2a, and p''(1) = 10, so 2a = 10 or a = 5. We can substitute a = 5 into the first two equations to find the values of b and c. So, b = -3 and c = 3. Therefore, the original function is p(x) = 5x^2 - 3x + 3.

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Answer:

The Answer is Step 3. I took the test :)

The answer is 1/500 because it will always be the probability of the event occurring/total events

Sam's gas usage is a proportional relationship because he gets a constant 25 miles per gallon in both given scenarios.

Yes, this is a proportional relationship. To determine proportionality, we can calculate the gas mileage for each scenario. Gas mileage is calculated by dividing the number of miles driven by the number of gallons used. For the first scenario, the gas mileage is 50 miles / 2 gallons = 25 miles per gallon. In the second scenario, the gas mileage is 100 miles / 4 gallons = 25 miles per gallon. Since the gas mileage is the same in both cases, it indicates a proportional relationship.

Answer:

B. [tex]n(d-18)[/tex]

D. [tex]dn-18n[/tex]

Step-by-step explanation:

Let d represent the original price paid for the game.

We have been given that a local buys used video games. For each game bought, they will pay $18 less than the original price paid for the game.

The price of used video game would be original price minus 18. We can represent this information in an expression as:

[tex]d-18[/tex]

We have been given that Jordan sold n games, so the cost of n used games would be [tex]n(d-18)[/tex].

Using distributive property we will get,

[tex]n(d-18)=dn-18n[/tex]

Therefore, option B and D are correct choices.

The quadratic equation 7x^2 + 4x - 8 = 14 does not have any real solutions.

The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 7, b = 4, and c = -22. To find the solutions, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we get:

x = (-4 ± √(4² - 4(7)(-22))) / (2(7))

Simplifying further, we get:

x = (-4 ± √(16 - 616)) / 14

x = (-4 ± √(-600)) / 14

The expression inside the square root is negative, which means there are no real solutions to the equation.

Answer: 48.7 degrees

Step-by-step explanation:

Let [tex]\theta[/tex] is the angle between the his sight line form with the side of the hotel,

Since, the building is of 5-story and a men having height 6 feet is in the fifth-story.

Thus, the total length from the eyes of the man and foot of the building = 6 + 12 × 5 = 6 + 60 = 66 feet

Also, the distance of the statue from the foot of the building = 75 feet.

Then by the below diagram,

[tex]tan\theta = \frac{75}{60+6}[/tex]

[tex]tan\theta = \frac{75}{66}[/tex]

[tex]\theta=48.6522227803\approx 48.7\text{ degree}[/tex]

The 95 percent confidence interval is wider than the 90 percent confidence interval because the 95 percent level of confidence includes more of the distribution. This means there is a greater level of certainty that the true value of the population mean is contained within the interval.

The 90 percent confidence interval is (67.18, 68.82). The 95 percent confidence interval is (67.02, 68.98). The 95 percent confidence interval is wider. If you look at the graphs, because the area 0.95 is larger than the area 0.90, it makes sense that the 95 percent confidence interval is wider. For more certainty that the confidence interval actually does contain the true value of the population mean for all statistics exam scores, the confidence interval necessarily needs to be wider.

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The required rate of wingbeats per second is 92.

A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?

Rate of change is defined as the change in value with rest to the time is called rate of change.

given rate = 5520 wingsbeats a minute.
      now to convert it in seconds divide it by 60

= 5520/60
= 92 wingsbeats a second

Thus, The required rate wingbeats per second is 92.

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Answer:

The length of RO is 38.

Step-by-step explanation:

Given information: ROSE is trapezoid with median If MN = 24 and ES = 10.

Sufficient information is not given. This question can be solved if it is given that  [tex]RO\parallel ES[/tex].

According to the properties of trapezoid the length of the median is the average of length of parallel sides.

Let [tex]RO\parallel ES[/tex] and length of RO be x.

Since MN is median, therefore

[tex]MN=\frac{RO+ES}{2}[/tex]

[tex]24=\frac{x+10}{2}[/tex]

[tex]48=x+10[/tex]

[tex]x=38[/tex]

Therefore length of RO is 38.

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, evaluate the function for each value in the domain and find the minimum and maximum outputs. The range of the function is {4, 84}.

To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, we need to evaluate the function for each value in the domain and find the minimum and maximum outputs.

The range of the function is the set of all possible outputs. In this case, the minimum output is 4 and the maximum output is 84. Therefore, the range of the function is {4, 84}.

To find the common ratio of the given sequence, divide each term by the previous term. The common ratio is 0.75.

The given sequence is: 128, 96, 72, 54, ...

To find the common ratio, we need to determine the ratio between consecutive terms. We can do this by dividing each term by the previous term.

Ratio between the 2nd and 1st terms: 96/128 = 0.75

Ratio between the 3rd and 2nd terms: 72/96 = 0.75

Ratio between the 4th and 3rd terms: 54/72 = 0.75

Since the ratio is the same for all consecutive terms, we can conclude that the common ratio of this geometric sequence is 0.75.

The correct common ratio for the given sequence is [tex]\(\frac{3}{4}\) or 0.75.[/tex]

To find the common ratio of the sequence, we divide each term by the previous term and look for a consistent value:

1. For the second term, \(96\), divided by the first term, [tex]\(128\)[/tex], we get:

[tex]\[ \frac{96}{128} = \frac{3}{4} = 0.75 \][/tex]

2. For the third term, [tex]\(72\),[/tex] divided by the second term, [tex]\(96\),[/tex] we get:

[tex]\[ \frac{72}{96} = \frac{3}{4} = 0.75 \][/tex]

3. For the fourth term, [tex]\(54\),[/tex] divided by the third term, [tex]\(72\)[/tex], we get:

[tex]\[ \frac{54}{72} = \frac{3}{4} = 0.75 \][/tex]

Answer:

32 x^3 - y^3 + 42 x 2y + 11 xy^2 + 17

Answer:

the answer is d

Step-by-step explanation:

The vertex and the axis of symmetry are graphed incorrectly.

The final price that is paid for the jacket is:

                    $ 48

The actual cost of jacket was: $ 100

The cost of the jacket was reduced by 40%

This means that the after reduction of 40% the jacket will cost:

[tex]100-\dfrac{40}{100}\times 100\\\\\\=100-40\\\\=60[/tex]

This means that the cost of jacket after 40% reduction is: $ 60

Also, there was a coupon that contains 20% off.

This means that the jacket will actually cost:

[tex]60-\dfrac{20}{100}\times 60\\\\\\=60-12\\\\\\=48[/tex]

                    The final price of jacket is:

                              $ 48

Answer:

Option A. July-August.

Step-by-step explanation:

Phillips family spent each month on groceries. The amount of money in each month is shown in a graph.

Approximate amount in each month was spent :

March : $450

April  : $400

May  :  $400

June  :  $500

July  :  $300

August : $ 500

Sep.  :  $480

Oct. : $420

From the graph given, there is a greatest month to month increase in spending occur in July to August (from $300 to $500).

So Option a. July-August is the correct answer.

Answer:

Any rational root of f(x) is a factor of 9 divided by a factor of 12.

Step-by-step explanation:

Given:

f(x) = 12x³– 5x² + 6x + 9

Required; Rational root of f(x)

The rational root theorem states that: each rational solution

x = p⁄q, written in lowest terms so that p and q are relatively prime

Where

p = factors of the constant

q = factors of the lead coefficient.

Given that

f(x) = 12x³– 5x² + 6x + 9

The constant is 9

And the lead coefficient is 12

The factor of these two are

9; ±1 , ±3, ±9

12: ±1, ±2, ±3, ±4, ±6, ±12

Then the rational root of f(x) is

factor of 9 divided by a factor of 12.

Possible Rational Roots

= (±1 , ±3, ±9) / (±1, ±2, ±3, ±4, ±6, ±12)

The correct statement according to the rational root theorem is

The rational root of f(x) is

factor of 9 divided by a factor of 12

To find the common difference, subtract the first term from the last term and divide by the number of terms minus 1.

To find the common difference of an arithmetic sequence given the first and last term, you can use the formula: common difference = (last term - first term) / (number of terms - 1). First, subtract the first term from the last term. Then, subtract 1 from the number of terms. Finally, divide the result of the subtraction by the number of terms minus 1 to find the common difference.