Consider the following first order differential equation: y = 3xy - 4 sec(y) (a) (7 points) Find the general solution to the differential equation. (b) (2 points) Find the particular solution when y(2) = 2
Answers
The general solution to the given first-order differential equation is y = ln|x| - 4 sec(y) / 3, where ln|x| represents the natural logarithm of the absolute value of x and particular solution is 2 = ln|2| - 4 sec(2) / 3.
To find the general solution, we start by isolating the variable y on one side of the equation. By rearranging the equation, we get y + 4 sec(y) / 3 = 3xy. Then, we divide both sides by 3x, which yields (y + 4 sec(y) / 3) / (3x) = 1. Finally, by integrating both sides with respect to x, we obtain the general solution: ∫ [(y + 4 sec(y) / 3) / (3x)] dx = ∫ 1 dx. Integrating the left side and simplifying, we arrive at y = ln|x| - 4 sec(y) / 3, as the general solution.
To find the particular solution when y(2) = 2, we substitute the given initial condition into the general solution. Plugging in y = 2 and x = 2, the equation becomes 2 = ln|2| - 4 sec(2) / 3. We can then solve this equation numerically or using numerical methods to find the value of x that satisfies the equation.
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Related Questions
GET BRAINLY IF ANSWET
Answers
Answer:
He is false
Step-by-step explanation:
Hey there!
The area of a shape is the total measurement of the inside of the shape
Meaning the parts I shaded in the screenshot
As you can see in the image, there is less area in shape B than shape A
Meaning, that the area has decreased
Now, Tom says that both area and perimeter has decreased
Lets check if the perimeter has decreased
If you look at it, the perimeter hasn't decreased at all
All that has happened was the shape getting a new form
The dimension are basically split
For example, if the top side of the square was 6 inches
Then the dimension after taking out a square from the shape would split
The top side of that square after is was split would be something along the ligns of 4 inches, and 2 inches and other dimensions like that
That is how I think of the perimeter and if it changes or not
But this explains why Tom is wrong
Since the perimeter is still the same
Tom is wrong
Find the size of each interior angle of a regular polygon of 15 sides.
Answers
Answer :
156°
Explanation :
Each triangle has an angle sum of 180 degrees.
The sum of the interior angles of the 15 sided polygon =
(n-2)180°
(n-2)180°
(15-2) × 180°
13 × 180 = 2340 °
Since the 15 sided polygon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of
2340° ÷ 15 = 156 °each
Find the area enclosed by the curve x 3t, y t and the y-axis. Step 1 The curve x = t2-3t, y = Vt intersects the y-axis when x = 0, which occurs when t = 0 and 3 3 H 3 '
Answers
The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.
We have been given parametric equations x = t^2 − 3t, y = √t
We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.
Consider x = 0
So, t^2 − 3t = 0
t(t - 3) = 0
t = 0 or t = 3
Let f(t) = t^2 − 3t and g(t) = t
Differentiate the curve f(t) with respect to t.
f'(t) = 2t - 3
NWe know that the formula to find the area under the curve.
A = ∫[a to b] g(t)f'(t) dt
here, a = 0 and b = 3
so, A = ∫[0 to 3] √t (2t - 3) dt
A = ∫[0 to 3] (2t√t - 3√t) dt
A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt
A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]
A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0
A = 4/5 3^(5/2) - 2 3^(3/2)
A = 6√3 /5
A = 2.08
Therefore, the area of the curve is 2.08 square units.
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An automobile and a truck start from rest at the same instant, with the car initially at some distance behind the track. The truck has constant acceleration 4.0ft/sec
2
and the car constant acceleration 6.0ft/sec
2
. The car overtakes the truck after the truck has moved 150ft. (a) How long does it take to overtake the truck? (b) How far was the ctar behind the truck initially? (c) What is the velocity of each vehicle when they are abreast? 485 A juggler performs in a room whose ceiling is 9ft above the level of his hands. He throws a ball vertically upward so that it just reaches the ceiling. (a) With what initial velocity does he throw the ball? (b) How many seconds are required for the ball to reach the ceiling? He throws a second ball upward, with the same initial velocity, at the instant the first ball touches the ceiling. (c) How long after the second ball is thrown do the two balls pass cach other? (d) When the balls nass, how far are they above the juggiers hands?
Answers
a). Solving for time (t): t = 150 ft / (v_car - v_truck)
b). Distance traveled by the car = v_car * t
c). The velocity of each vehicle when they are abreast is equal to the velocity of the car or the velocity of the truck.
(a) To calculate how long it takes for the car to overtake the truck, we need to consider their relative speeds and the distance traveled by the truck before being overtaken.
Let's assume the car's speed is v_car and the truck's speed is v_truck. Given that the truck has moved 150 ft before being overtaken, we can set up the following equation:
Distance traveled by the car = Distance traveled by the truck + 150 ft
Using the formula distance = speed × time, we can express this equation as:
v_car * t = v_truck * t + 150 ft
Since the car overtakes the truck, its speed is greater than the truck's speed (v_car > v_truck).
Solving for time (t):
t = 150 ft / (v_car - v_truck)
(b) To determine how far the car was initially behind the truck, we can substitute the value of time (t) obtained in part (a) into the equation for distance traveled by the car:
Distance traveled by the car = v_car * t
(c) When the car overtakes the truck and they are abreast, their velocities are the same. Therefore, the velocity of each vehicle when they are abreast is equal to the velocity of the car or the velocity of the truck.
485:
(a) To calculate the initial velocity with which the juggler throws the ball upward, we need to use the kinematic equation for vertical motion. Assuming upward as the positive direction, the equation is given by:
v_f = v_i + (-g) * t
where:
v_f is the final velocity (0 m/s when the ball reaches the ceiling),
v_i is the initial velocity (what we need to find),
g is the acceleration due to gravity (-9.8 m/s^2),
t is the time taken to reach the ceiling.
Since the final velocity is 0 m/s, we can rearrange the equation to solve for v_i:
0 = v_i - 9.8 m/s^2 * t
Since the ball just reaches the ceiling, the displacement is equal to the height of the ceiling (9 ft or approximately 2.7432 m). We can use the kinematic equation:
s = v_i * t + (1/2) * (-g) * t^2
Rearranging this equation to solve for t:
2.7432 m = v_i * t - 4.9 m/s^2 * t^2
(c) To determine how long after the second ball is thrown the two balls pass each other, we need to find the time at which the first ball reaches its maximum height and begins descending. This time is equal to half of the total time it takes for the first ball to reach the ceiling and fall back down.
(d) When the balls pass each other, the second ball is at the same height as the first ball when it was thrown. This height is equal to the height of the ceiling (9 ft or approximately 2.7432 m) above the juggler's hands.
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Which equation justifies why 73=3√7? (1 P
(73) - 7(6-0)-7
=7
O
O
° () .,(-4).
73
=7
(1)-(-)-
= 7
= 7
? (1 point)
Answers
Seven to the one third is the power all raised to the third of the power equals seven to the one of the third times three of power equals to seven.
What is power?Power is the amount that is the energy of to transferred or the converted per the unit.
Applying Power of a Power Property,
(X^a)^b= x^a×b
i.e. a power to the power, multiply by the exponents as
7^1/3 =√7
√7=7^1/3
We have given, seven to the one third power equals to the cube root of seven of
7^1/3=√7
√7= 7^1/3
Raise to the third power,
[7^1/3]^3
Applying the property ,
7^3/3=7^1 =7
i.e. seven to the one thirdly power all of the raised to the thirdly power equals to seven to the one of third times of three power equals to the seven.
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Solve the given differential equation. All solutions should be found. (7y6 + 2x³y) dx − (6xy³ + x6) dy = 0 NOTE: Do not enter an arbitrary constant. The solution in implicit form is = C where C is an arbitrary constant. =
Answers
Implicit solution for the differential equation is x^7y^6 + x^7y^2 - (1/8)x^8 + C = 0, where C is the arbitrary constant.
The given differential equation is not in a standard form, but we can check if it is exact by verifying if its partial derivatives satisfy the condition ∂M/∂y = ∂N/∂x, where M and N are the coefficients of dx and dy, respectively. In this case, M = 7y^6 + 2x^3y and N = -6xy^3 - x^6.
By computing the partial derivatives, we find ∂M/∂y = 42y^5 + 2x^3 and ∂N/∂x = -6y^3 - 6x^5. Since these derivatives are not equal, the equation is not exact.
To make the equation exact, we can introduce an integrating factor μ. By dividing the equation by μ and comparing the coefficients of dx and dy, we find that μ = 1/(x^7y^5) is an integrating factor.
Multiplying the entire equation by μ, we obtain (7y/x + 2x^2y^(-4)) dx - (6y^(-2) + x^(-7)) dy = 0.
Now, we recognize that this equation is a total derivative. Integrating both sides with respect to x and y, we obtain the implicit solution x^7y^6 + x^7y^2 - (1/8)x^8 + C = 0, where C is the arbitrary constant.
Hence, the solution to the given differential equation, in implicit form, is x^7y^6 + x^7y^2 - (1/8)x^8 + C = 0, where C represents the arbitrary constant.
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Complete this sentence. if the force of gravity ________, the weight of an object will _______________.
Answers
If the force of gravity increases, the weight of an object will increase.
a book store was selling 7 books for $39.55. online you could buy 3 books for $24.96. which place has a lower unit price
Answers
Answer:
the book store selling 7 books for $39.55 (the book store)
Step-by-step explanation:
we have to calculate what each book costs. to find out what each book costs, we have to use division...
so for the book store:
39.55 / 7 = 5.65 - this means that each book costs $5.65 by itself
for the online store:
24.96 / 3 = 8.32 - this means that each book costs $8.32 by itself
now we have to compare the prices... $5.65 costs less than $8.32, so the book store would have a lower unit price.
What is the solution set for the open sentence with the given replacement set? 2t−t=0, {1, 2, 3, 4}
Answers
The solution set for the open sentence \(2t - t = 0\), with the given replacement set \({1, 2, 3, 4}\) is \(2.\)
To find the solution set for the open sentence \(2t - t = 0\), using the replacement set \({1, 2, 3, 4},\) we substitute each value from the replacement set into the equation and solve for t.
Substituting 1:
\(2(1) - 1 = 1\)
The equation is not satisfied when t = 1.
Substituting 2:
\(2(2) - 2 = 2\)
The equation is satisfied when t = 2.
Substituting 3:
\(2(3) - 3 = 3\)
The equation is not satisfied when t = 3.
Substituting 4:
\(2(4) - 4 = 4\)
The equation is not satisfied when t = 4.
Therefore, the solution set for the open sentence \(2t - t = 0\), with the given replacement set \({1, 2, 3, 4}\) is \(2.\)
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The solution set for the open sentence 2t - t = 0 with the given replacement set {1, 2, 3, 4} is an empty set, indicating that there are no solutions in the replacement set for this equation.
The given open sentence is 2t - t = 0. We are asked to find the solution set for this equation using the replacement set {1, 2, 3, 4}.
To find the solution set, we substitute each value from the replacement set into the equation and check if it satisfies the equation. Let's go step by step:
1. Substitute 1 for t in the equation:
2(1) - 1 = 2 - 1 = 1. Since 1 is not equal to 0, 1 is not a solution.
2. Substitute 2 for t in the equation:
2(2) - 2 = 4 - 2 = 2. Since 2 is not equal to 0, 2 is not a solution.
3. Substitute 3 for t in the equation:
2(3) - 3 = 6 - 3 = 3. Since 3 is not equal to 0, 3 is not a solution.
4. Substitute 4 for t in the equation:
2(4) - 4 = 8 - 4 = 4. Since 4 is not equal to 0, 4 is not a solution.
After substituting all the values from the replacement set, we see that none of them satisfy the equation 2t - t = 0. Therefore, there is no solution in the replacement set {1, 2, 3, 4}.
In summary, the solution set for the open sentence 2t - t = 0 with the given replacement set {1, 2, 3, 4} is an empty set, indicating that there are no solutions in the replacement set for this equation.
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Writing the equation of a sine or cosine function given its graph:
Answers
A generic graph would be
\(A\cos \mleft(\frac{2\pi x}{p}+\varphi\mright)+D\)Where:
A = amplitude
p = period
φ = phase
D = middle line
First let's evaluate the period of the function, see that x = -1/4 we have y = 5, it will have again at x = 3/4.
The period is
\(\begin{gathered} p=\frac{3}{4}+\frac{1}{4} \\ \\ p=\frac{4}{4}=1 \end{gathered}\)Let's put it in our function already
\(\begin{gathered} A\cos \mleft(\frac{2\pi x}{p}+\varphi\mright)+D \\ \\ A\cos (2\pi x+\varphi)+D \end{gathered}\)To find out the amplitude, we take the max value, the minimum value (all in modulus) and take the average, the max value here is 5 and the minimum -3 (in modulus it's 3), the average is
\(A=\frac{5+3}{2}=\frac{8}{2}=4\)Therefore
\(4\cos (2\pi x+\varphi)+D\)And the D value will be the average too, of the maximum two, but here we don't use the modulus on negative values, therefore
\(D=\frac{5-3}{2}=\frac{2}{2}=1\)Hence.
\(4\cos (2\pi x+\varphi)+1\)We know that when x = 0 we have y = 1, then
\(\begin{gathered} y=4\cos (2\pi x+\varphi)+1 \\ \\ 1=4\cos (2\pi\cdot0+\varphi)+1 \\ \\ 4\cos (\varphi)=0 \\ \\ \cos (\varphi)=0 \end{gathered}\)When cos(φ) = 0? when φ = π/2 for example. Of course, there are other solutions but we just need one. Now we have all the parameters of our cosine
\(4\cos \mleft(2\pi x+\frac{\pi}{2}\mright)+1\)The final answer is:
\(4\cos \mleft(2\pi x+\frac{\pi}{2}\mright)+1\)HELP MEEEE !! I’m stuck
Answers
Answer:
10
Step-by-step explanation:
because it is what it is i just did the math
show all your working pleas
Answers
Answer:
800
Step-by-step explanation:
Formula:
P(1.05)ⁿ=AV
P(1.05)²=882
P=800
PLEASE ANSWER THE FOLLOWING QUESTION GIVEN THE CHOICES!!!
Answers
Answer: 3/52
Step-by-step explanation:
You want to pick a diamond jack, diamond queen or diamond king
There are only 3 of those so
P(DJ or DQ or DK) = 3/52 There are 3 of those out of 52 total
A smoothie recipe calls for 2 1\4 cups of frozen mango if the recipe serves two how many cups of frozen mango is needed the serve one
Answers
Answer: 1 1/8
Step-by-step explanation:
1/4 in half is equivalent to 1/8
Can someone explain how to do this?
thanksss <33
Answers
Answer:
True True False True
Step-by-step explanation:
You would substitute the value for x and the value for y into both equations and see if the sign holds true.
So for number 1:
x=3, y=-2;
y ≤ x -3
-2 ≤ x - 3
-2 ≤ -1
y ≥ -x - 2
-2 ≥ -3 - 2
-2 ≥ -5
Number 1 is true because the equations are true ^^
Do this for every problem so it would be:
1. True
2. True
3. False
4. True
Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
Answers
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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In ANOVA, which of the following is not affected by whether or not the population means are equal? between-samples estimate of o 2 within-samples estimate of o 2 None of these alternatives is correct.
Answers
In Analysis of variance, X (bar) is not affected by whether or not the population means are equal.
Analysis of variance is a statistical method for examining differences in means. It consists of a number of statistical models and the accompanying estimating techniques (such as the "variation" within and between groups). Ronald Fisher, a statistician, created Analysis of variance. The rule of total variance, on which the Analysis of variance is based, divides the observed variance in a given variable into components owing to various causes of variation.
ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the Analysis of variance is employed to determine whether two or more means differ from one another.
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what is the answer for this question
(0-1)(0+1)
Answers
Answer:
Step-by-step explanation:
-1
-8(8b-7)=-1-7b
How to solve
Answers
Answer: the answer is b=1
why (0.0) (3.4) (6.8) (6,12) not a function
Answers
Answer:
Step-by-step explanation:
Look at the first elements of the four points: {0, 3, 6, 6}. The element 6 appears twice and is associated with two different second elements: {8, 12}. That tells us immediately that this is not a function.
A company's prospectus includes:
A) The company's investment options.
B) The company's guaranteed return strategy.
C) The company's revenue and net worth.
D) The company's research
Answers
A company's prospectus includes: A) The company's investment options.
What is a company's prospectus?Company's prospectus can be defined as the document that entails detail information of a company investment option that are available for sales to potentials buyers or investors.
Examples of the investment options are:
BondsStocksMutual Funds etcTherefore the correct option is A.
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A company's prospectus is a formal legal document designed to provide information and full details about an investment offering for sale to the public.
A research analyst disputes a trade group's prediction that back-to-school spending will average $606.40 per family this year. She believes that average back-to-school spending will significantly differ from this amount. She decides to conduct a test on the basis of a random sample of 20 households with school-age children. She calculates the sample mean as $628.85. She also believes that back-to-school spending is normally distributed with a population standard deviation of $45. Use 5% significance.
Part 1
State the null hypothesis and the alternative hypothesis for testing that the average back-to-school spending differs from $606.40.
Part 2
State the critical value(s) for testing this hypothesis.
Part 3
Calculate the test statistic Z for testing this hypothesis
Part 4
State and support your conclusions
Answers
Based on the calculations we have rejected the null hypothesis .
Given,
Standard deviation = $ 45
Random sample = 20
Now,
Part 1
Set the null hypothesis and alternative hypothesis,
\(H_{0} : u = 0\\ H_{0} : u > 606.40\)
Part 2
The value of z critical signifies 5% level of significance .
\(Z_{0.05} = 1.65\)
According to critical value if z after calculation is greater than or equal to 1.65 we reject the null hypothesis .
Part 3
The value of Z can be calculated by the formula,
Z = X - µ/σ/√n
Substitute the values ,
Z = 628.85 - 606.40/45/√20
Z = 1.93
Part 4
From the above calculation the value of Z is greater than the critical value .
Thus we reject the null hypothesis .
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230 is what percent of 200? PLEASE HELP!!
Answers
Answer:
230 is what percent of 200?
The answer is 115
Help me with 1 please
Answers
Answer:
\(\huge\boxed{Mass = 11600\ kg}\)
Step-by-step explanation:
Given:
Density = ρ = 2900 kg/m³
Volume = V = 4 m³
Required:
Mass = m = ?
Formula:
Mass = Density × Volume
Solution:
Mass = 2900 * 4
Mass = 11600 kg
the answer is
mass=11600 kg
Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?
Answers
The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4
How to determine the solution of the inequality?From the question, we have the following parameters that can be used in our computation:
-2(3x + 6) ≥ 4(x + 7)
Divide both sides of the inequality by -2
So, we have the following representation
3x + 6 ≤ -2(x + 7)
Open the brackets
This gives
3x + 6 ≤ -2x - 14
Add 2x to both sides of the inequality
So, we have the following representations
5x + 6 ≤ -14
Subtract 6 from both sides of the inequality
So, we have the following representations
5x ≤ -20
Divide both side of the inequality
x ≤ -4
Hence, the solution is x ≤ -4
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A line passes through the points (8, –1) and (–4, 2).
Answers
Answer:
y=1/4x+1
Step-by-step explanation:
Goes zdown 3 and right 12 simplified to 1/4
Answer:
Your answer is: y = -1/4x + 1
Step-by-step explanation:
Hope this helped : )
a fair die is rolled times. what is the probability that a is obtained on at least one of the rolls? round your answer to three decimal places. (if necessary, consult a list of formulas.)
Answers
The probability of obtaining a 1 on at least one roll of a fair die rolled times is 0.421 (rounded to 3 decimal places).
Let E be the event of obtaining a 1 on at least one roll. We can find the probability of E using the complement rule:
P(E) = 1 - P(E')
where E' is the event of not obtaining a 1 on any of the rolls. Since the die is fair, the probability of obtaining any number on any roll is 1/6. Therefore, the probability of not obtaining a 1 on any roll is (5/6) for each roll.Using the multiplication rule for independent events, the probability of not obtaining a 1 on any of the rolls is:
(5/6) x (5/6) x (5/6) x ... x (5/6) (rolled times) = (5/6)^n
Therefore, the probability of obtaining a 1 on at least one roll is: P(E) = 1 - P(E') = 1 - (5/6)^n
We are given that the die is rolled times. Substituting n = into the formula above, we get:
P(E) = 1 - (5/6)^ = 1 - 0.3349 ≈ 0.421
Therefore, the probability of obtaining a 1 on at least one roll of a fair die rolled times is 0.421 (rounded to 3 decimal places).
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I WILL GIVE BRAINLY! PLEASE HELP! PLEASEEEEE!!
Bob walks up to a tank of water that can hold 75 gallons. When it is active, a drain empties water from the tank at a constant rate. When Bob first sees the tank, it contains 15 gallons of water. 4 minutes later, the tank contains 12 gallons of water.
A. At what rate is the amount of water in the tank changing? answers: 3/4, -3, -3/4, 3
B. How many more minutes will it take for the tank to drain completely?
C. How many minutes before Bob arrived was the tank completely full?
Answers
Answer:
A) -3/4
B) 15 more minutes
C) 80 minutes
Step-by-step explanation:
A. rate of change = -3/4
B. 16 minutes
C. 1 hour 20 minutes
What is slope?The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Given:
A) At first the tank contain 15 gallons of water.
After 4 minutes the tank contain 12 gallons of water.
So, rate of change
=12-15/4-0
=-3/4
=-3/4
B) now, Let x be the number of minutes will it take for the tank to drain completely.
So,
(3/4 gallons per minute) *x = 12 gallons
x = 12*4/3
x = 16 minutes
C) As, the tank has capacity of 75 gallons.
So, the tank of water is full when there is 10 gallons of water which is 60 gallons more.
Let 'y' be the number of minutes before Bob arrived when the water tank was completely full.
(3/4) (y) = 60
y = 60*4/3
y= 80 minutes
y= 1 hour 20 minutes
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Consider a projectile launched at a height h feet above the ground and at an angle with the horizontal. If the initial velocity is vo feet per second, the path of the projectile is modeled by the parametric equations x = tivo cos(O)) and y = h + (vo sin Ot - 16t2. A rectangular equation for the path of this projectile is y = 6 + x -0.008x2 (a) Eliminating the parameter t from the position function for the motion of a projectile to shows that the rectangular equation is as follows. v -16 (sec(0) x2 + tan(O)x+h (b) Find h, vo, and 0. (Round your answers to two decimal places.) - VOEL (c) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations. 40 60 80 100 100 150 (d) Use a graphing utility to approximate the maximum height of the projectile. (Round your answers to two decimal places.) What is the approximate range of the projectile?
Answers
The rectangular equation for the path of the projectile launched at height h and angle θ with initial velocity vo is y = 6 + x - 0.008x². To find h, vo, and θ, we can eliminate the parameter t from the parametric equations and solve for the coefficients of the resulting rectangular equation. By comparing the coefficients, we can determine h = 6, vo = √2000, and θ = arctan(√2000).
To eliminate the parameter t from the parametric equations x = tvo cos(θ) and y = h + (vo sin(θ)t - 16t²), we can solve the first equation for t and substitute it into the second equation. This gives us y = h + (x / (vo cos(θ)))tan(θ) - (16 / (vo² cos²(θ)))x². Comparing this equation with the given rectangular equation y = 6 + x - 0.008x², we can determine the values of h, vo, and θ. In this case, h = 6, vo = √2000, and θ = arctan(√2000).
Using a graphing utility, we can plot the rectangular equation y = 6 + x - 0.008x² to visualize the path of the projectile. Additionally, we can sketch the curve represented by the parametric equations x = tvo cos(θ) and y = h + (vo sin(θ)t - 16t²) to confirm that they represent the same path.
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What do these (>, ≥, <, ≤) mean
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Answer: <less than >greater than ≥ greater than or equal to ≤ less than or equal to
Step-by-step explanation: