find a cartesian equation for the curve. r = 8 sec()
Answers
The equation given, r = 8 sec(θ), is an equation in polar coordinates. To convert it to a cartesian equation, we can use the following relationships:
x = r cos(θ)
y = r sin(θ)
Substituting r = 8 sec(θ) into these equations, we get:
x = 8 sec(θ) cos(θ)
y = 8 sec(θ) sin(θ)
Next, we can use the identity sec²(θ) = 1/cos²(θ) to write sec(θ) in terms of cos(θ):
sec(θ) = 1/cos(θ)
Substituting this into our equations for x and y, we get:
x = 8/cos(θ)
y = 8 tan(θ)
Finally, we can eliminate θ by squaring both sides of the equation sec²(θ) = 1/cos²(θ) and using the trigonometric identity 1 + tan²(θ) = sec²(θ). This gives us:
cos²(θ) = 1/(1 + tan²(θ))
Substituting this into our equations for x and y, we get:
x = 8 cos(θ) / sqrt(1 + tan²(θ))
y = 8 sin(θ) / sqrt(1 + tan²(θ))
Simplifying further, we can write:
x² / 64 - y² / 64 = 1
This is the cartesian equation for the curve defined by r = 8 sec(θ). It is the equation of a hyperbola centered at the origin, with vertices at (8, 0) and (-8, 0), and asymptotes given by the lines y = ±x/8.
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Related Questions
30 Points. i fr need to pass this test i dont feel like taking it again my senior year
Answers
Answer:
3x^3+2x^2+2x+5
Step-by-step explanation:
The answer is A
C++ PLEASE,
The Fibonacci numbers are the numbers in the following integer sequence: 0, 1, 1, 2, 3, 5…
You can find the nth Fibonacci numbers by adding the last two digits before n.
Remember:
F (0) = 0 and F (1) =1
F(n)=F(n-1) +F(n-2) for n>1
Tasks
Write the first natural solution that you find to the problem (an inefficient algorithm) and implement it to find nth number of Fibonacci number F(n)
Write an efficient algorithm and implement it to find nth number of Fibonacci number F(n)
Record the time it takes to execute 120th Fibonacci number on both algorithms
Fill out the report sheet, compare and explain your results
Answers
The provided C++ code includes two algorithms to find the nth Fibonacci number: an inefficient recursive approach and an efficient iterative approach. The execution times for finding the 120th Fibonacci number can be compared to analyze the performance difference between the two algorithms.
Here's the C++ code to solve the Fibonacci number problem using both an inefficient and an efficient algorithm. We'll also measure the execution time for finding the 120th Fibonacci number using both approaches.
1. Inefficient Algorithm (Recursive Approach):```cpp
#include <iostream>
int fibonacci(int n) {
if (n <= 1)
return n;
else
return fibonacci(n - 1) + fibonacci(n - 2);
}
int main() {
int n = 120;
// Measure execution time
clock_t startTime = clock();
int result = fibonacci(n);
clock_t endTime = clock();
double elapsedTime = double(endTime - startTime) / CLOCKS_PER_SEC;
std::cout << "Fibonacci(" << n << ") = " << result << std::endl;
std::cout << "Execution time: " << elapsedTime << " seconds" << std::endl;
return 0;
}
```
2. Efficient Algorithm (Iterative Approach):```cpp
#include <iostream>
int fibonacci(int n) {
int prev = 0;
int curr = 1;
for (int i = 2; i <= n; i++) {
int temp = curr;
curr += prev;
prev = temp;
}
return curr;
}
int main() {
int n = 120;
// Measure execution time
clock_t startTime = clock();
int result = fibonacci(n);
clock_t endTime = clock();
double elapsedTime = double(endTime - startTime) / CLOCKS_PER_SEC;
std::cout << "Fibonacci(" << n << ") = " << result << std::endl;
std::cout << "Execution time: " << elapsedTime << " seconds" << std::endl;
return 0;
}
```
Note: Both algorithms assume the Fibonacci sequence starts with F(0) = 0 and F(1) = 1.
After executing the programs, you can compare the execution times and fill out the report sheet with the results.
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What are the x-intercepts of the quadratic function? parabola going down from the left and passing through the point negative 2 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 2 and 1 comma 0 a (0, −2) and (0, 1) b (0, −2) and (0, 2) c (−2, 0) and (2, 0) d (−2, 0) and (1, 0)
Answers
The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.
From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).
The correct answers are (d) (-2, 0) and (1, 0).
A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answers
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
lord someone please help :)
Answers
Other than one what are the perfect square factors of 792
Answers
So the perfect square factors of 792 are 4, 9, 36, 144, 484, and 1089.
The prime factorization of 792 by dividing it by its smallest prime factor repeatedly:
792 ÷ 2 = 396
396 ÷ 2 = 198
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
So the prime factorization of 792 is \(2^3 * 3^2 * 11.\)
To find the perfect square factors, we can look for pairs of factors where both factors have even exponents.
The factors of 792 are: 1, 2, 3, 4, 6, 8, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 132, 198, 264, 396, and 792.
The perfect square factors of 792 are:
\(2^2 = 4\\2^2 * 3^2 = 36\\2^2 * 11^2 = 484\\3^2 = 93^2 * 4^2 = 144\\3^2 * 11^2 = 1089\)
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please help I will give you any award
Answers
Answer:
218.57
Step-by-step explanation:
Since it is an isoceles triangle, the sides are 32, 32, and 14.
Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2, we can calculate the area.
(A+B+C)/2 = (32+32+14)/2=39.
A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.
Hope this helps have a great day :)
Check the picture below.
so let's find the height "h" of the triangle with base of 14.
\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)
find the domain of the graphed function:
Answers
Answer:
2<x<5
Hope this helps
Consider the exponential function with equation A = P(1+r)t
a. Name the independent and dependent variables.
b. What is the growth factor?
Answers
The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.
The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025
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2. One candle, in the shape of a right circular cylinder, has a
height of 7.5 inches and a radius of 2 inches. What is the
volume of the candle? Show your work and round your
answer to the nearest cubic inch.
Use 3.14 for pi
Answers
The volume of the candle is approximately 94 cubic inches.
What is circular cylinder?
A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.
The volume of a right circular cylinder is given by the formula:
V = πr²h
Where
V is the volumer is the radiush is the heightSubstituting the given values into the formula, we get:
V = 3.14 x 2² x 7.5
V = 3.14 x 4 x 7.5
V = 94.2
Rounding to the nearest cubic inch, we get:
V ≈ 94 cubic inches
Therefore, the volume of the candle is approximately 94 cubic inches.
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questions that require responses at fixed intervals along a scale of answers are called
Answers
Questions that require responses at fixed intervals along a scale of answers are called scale questions.
What are scale questions?Closed-ended questions, such as the Likert Scale, are one of the most popular methods for gauging public opinion. To gauge people's opinions, attitudes, and beliefs, they employ psychometric testing. Statements are used in the questions, and respondents are asked how much they agree or disagree with each assertion. Likert Scale questions typically have a scale from 0 to 10, while shorter scales are also conceivable.
Every sort of research has benefits and drawbacks, and this particular question type has both in spades. The fundamental benefit of Likert Scale questions is that they follow a standard way of data collection, making them simple to comprehend.
Hence, according to the definition questions that require responses at fixed intervals along a scale of answers are called scale questions.
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i need help please branliest to who gets it right
Answers
The kite is about 16.5 yards above the edge of the pond.
How to find the height of the kite?You are flying a dragon kite. It's connected to 36 yards string. The kite is directly above the end of the pond. The edge of the pond is 32 yards where the kite is tied to the ground.
Therefore, the height of the kite above the ground can be calculated as follows:
This situation form a right angle triangle. Hence, using Pythagoras's theorem,
Therefore,
h² = 36² - 32²
h² = 1296 - 1024
h = √272
h = 16.4924225025
Hence, the height of the kite is 16.5 yards.
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What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
Answers
Answer:
Emily your answer will be 9r9s9
Hope this helps you
Answer:
c
Step-by-step explanation:
took test on edge
since all components are 0, we conclude that curl(f) = 0 and, therefore, f is conservative. thus, a potential function f(x, y, z) exists for which fx(x, y, z) =
Answers
The potential function f(x,y,z) for which fx(x,y,z)= is zero, exists, and hence f is conservative.
Given that all components of curl(f) are zero, we can conclude that f is a conservative vector field. Therefore, a potential function f(x,y,z) exists such that the gradient of f, denoted by ∇f, is equal to f(x,y,z). As fx(x,y,z) = ∂f/∂x, it follows that ∂f/∂x = 0.
This implies that f does not depend on x, so we can take f(x,y,z) = g(y,z), where g is a function of y and z only. Similarly, we can show that ∂f/∂y = ∂g/∂y and ∂f/∂z = ∂g/∂z are zero, so g is a constant. Thus, f(x,y,z) = C, where C is a constant. Therefore, the potential function f(x,y,z) for which fx(x,y,z) = 0 is f(x,y,z) = C.
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A music store is having a clearance sale. All items are discounted by 15%. What is the sale price of a radio that regularly costs $20?
Answers
Answer:
17$
Step-by-step explanation:
Answer:
$17
Step-by-step explanation:
Since the discount is 15%, and 100% would be the full price, 100 - 15 = 85. You are paying 85% of the price. 20 * .85 = 17.
Malia is playing a target game with her friends. Each player throws a bean bag times toward a target on the ground. The distance between the bean bag and the target is recorded for each throw. The player with the lowest mean distance of all throws wins the game. The list shows the recorded distance, in , of Malia's first throws. , , , , , , Malia is the last player in the game. Her mean distance must be less than to win the game. What is the minimum distance, in , between the bean bag and the target that Malia needs on her last throw to win the game? Enter the answer in the box.
Answers
The minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.
How to determine distanceIn this target game, Malia needs to have the lowest mean distance of all throws to win. The mean distance is calculated by adding up all the distances and dividing by the number of throws.
First, we need to calculate the mean distance of Malia's first 7 throws.
Mean distance = (2 + 3 + 4 + 2 + 5 + 3 + 4) / 7 = 3.14
Now, we know that Malia's mean distance must be less than 3.14 to win the game. Let's call the distance of her last throw x.
The mean distance of all 8 throws will be: (2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8
To find the minimum distance that Malia needs on her last throw to win the game, we can set up an inequality:
(2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8 < 3.14
Multiplying both sides by 8 gives us:
2 + 3 + 4 + 2 + 5 + 3 + 4 + x < 25.12
Simplifying gives us:
x < 25.12 - 23
x < 2.12
Therefore, the minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.
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Ziplines Inc. enters into a contract to employ Scot as a manager for two years. If Ziplines breaches the contract, Scot has a duty to Group of answer choices find another job or receive no damages. rescind the contract with Ziplines. reduce the damages that Scot might otherwise suffer. act to punish Ziplines as an example to deter others from similar acts.
Answers
If Ziplines Inc. breaches the contract, Scot has a duty to Group of answer choices: find another job or receive no damages, rescind the contract with Ziplines, reduce the damages that Scot might otherwise suffer, and act to punish Ziplines as an example to deter others from similar acts.
Determine the Ziplines Inc. breaches?If Ziplines Inc. breaches the contract with Scot, Scot has the option to pursue different courses of action. The first option is to find another job or accept no damages, which means Scot can actively seek alternative employment without seeking compensation from Ziplines. This allows Scot to move on and secure a new position.
The second option is to rescind the contract with Ziplines. This means Scot can choose to terminate the contract altogether due to the breach, effectively nullifying the agreement between Scot and Ziplines.
The third option is to reduce the damages that Scot might otherwise suffer. In this case, Scot can take measures to minimize the negative impact caused by Ziplines' breach, such as mitigating financial losses or finding alternative sources of income.
The fourth option is to act to punish Ziplines as an example to deter others from similar acts. Scot can take legal action or pursue remedies to hold Ziplines accountable for the breach, aiming to discourage similar misconduct by setting an example for other companies.
Ultimately, Scot's course of action will depend on their individual circumstances, priorities, and the available legal remedies in the specific jurisdiction.
Therefore, In the event of a contract breach by Ziplines Inc., Scot is obligated to either seek alternative employment or forego damages, terminate the contract, minimize potential losses, or set an example by taking action against Ziplines.
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Can someone please help me with ASAP. I need to do this by tonight thx.
Which equation represents a parabola with focus (3,8)
A. y=1/4(x-3)^2-9
B. y= 4(x+3)^2-8
C. y=1/4(x-3)^2-10
D. 4(x+2)^2+7
also please don't be a bot or a person who says " I don't know" its not helpful
Answers
Answer: C
Step-by-step explanation:
If a parabola is given by \(a(x - h)^2 + k\), the focus is at the point \((h, k + 1/4a)\).
We know the focus is \((3, 8)\), so it should look like \(a(x - 3)^2 + k\). We can cross off B and D.
Let's check if A works: \(8 = -9 + 1/(4 \cdot \frac 14) = -8\). Obviously this is false, so we can cross off A.
Thus it's C by process of elimination.
im not good at this stuff
please help <3
:)
Answers
Answer:
1. 3.33
2. 8.75
3. 4.8
4. 2.5
Step-by-step explanation:
Pls solve this 15 points
Answers
Answer:
128
Step-by-step explanation:
1/3base area×height
helpppppppppppppppppppppppppppp
Answers
Answer:
pi 7^2 - 20
Step-by-step explanation:
area of the circle - area of the square
Find the lateral surface area of the figure.
Answers
The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.
The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated instead of the radius, we have to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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The mean is ? = 137.0 and the standard deviation is ? = 5.3.
Find the probability that X is between 134.4 and 140.1.
0.4069
0.6242
0.8138
1.0311
Answers
The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.
To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:
z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906
z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.
To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:
P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.
As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.
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If x=−4,y=−2,andz=12, solve the following:
zx
Answers
Answer: - 48 (edit: omg i didnt see the minus)
Step-by-step explanation: i mean, only z multiply x
z = 12
x = 4
zx
= z multiply x
= 12 x - 4
= - 48
^_____^
Answer:
-48
Step-by-step explanation:
zx=12(-4)=-48
Explain why two variables must both be quantitative in order to find the correlation between them
Answers
If the variables are not quantitative we cannot do the arithmetic required in the formulas for r.
What is a variable?A variable in mathematics is a symbol and placeholder for a changing quantity or any mathematical object.A variable can specifically represent a number, a vector, a matrix, a function, a function's argument, a set, or an element of a set.Quantitative order:
Quantitative methods emphasize objective measurements and statistical, mathematical, or numerical analysis of data gathered through polls, questionnaires, and surveys, as well as by manipulating pre-existing statistical data using computational techniques. Ordinal-level measurement data can be quantitative or qualitative. They can be arranged in ranked order, but differences between entries are meaningless. Measurement data at the interval level are quantitative. They can be arranged in any order, and meaningful differences between data entries can be calculated. We can't do the arithmetic required in the r formulas if the variables aren't quantitative.Therefore, if the variables are not quantitative we cannot do the arithmetic required in the formulas for r.
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Solve Similar Triangles (advanced)
Solve for X.
Answers
Given:
\(m\angle B=90^\circ, m\angle D=90^\circ, AB=x, BD=9, BC=1, DE=5\).
To find:
The value of x.
Solution:
In triangles ABC and ADE,
\(\angle B\cong \angle D\) (Right angles)
\(\angle A\cong \angle A\) (Common angles)
\(\Delta ABC\sim \Delta ADE\) (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,
\(\dfrac{AB}{AD}=\dfrac{BC}{DE}\)
\(\dfrac{x}{x+9}=\dfrac{1}{5}\)
On cross multiplication, we get
\(5x=x+9\)
\(5x-x=9\)
\(4x=9\)
\(x=\dfrac{9}{4}\)
\(x=2.25\)
Therefore, the value of x is 2.25 units.
You pick a card at random, put it back, and then pick another card at random.
1 2 3 4
What is the probability of picking a number greater than 1 and then picking a number greater
than 2?
Answers
Answer:75% percent chance of picking a card greater than 1 and a 50% chance of picking a card greater than 2
Step-by-step explanation:
please pick me as brainliest
Consider the following.
Answers
a) The perimeter of the figure is given as follows: 44 ft.
b) The area of the figure is given as follows: 24 ft².
How to obtain the perimeter and the area of the figure?The perimeter of the figure is obtained as the sum of the outer side lengths of the figure.
The side lengths are given as follows:
2 of 16 ft.2 of 6 ft.Hence the perimeter is of:
P = 2 x (16 + 6)
P = 44 ft.
The area of the figure is given as half the multiplication of the base of 16 ft by the height of 3 ft, hence:
A = 0.5 x 16 x 3
A = 24 ft².
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what is the equation of y=x^3 with the given transformations
Answers
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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1,346.275 round to the nearest whole number
Answers
Answer:
1,346
Step-by-step explanation: