Use separation of variables to find the general solution to the following differential equation.
Answers
Therefore, the general solution to the differential equation is
Y = e⁽ˣ⁾2+X+C) - 1 or Y = -e⁽ˣ⁾2+X+C) - 1
What exactly is a different equation?A differential equation is an equation that connects the derivatives of one or more unknown functions. It is an equation that uses the derivatives of a function or functions, in other words. Many physical processes, including the motion of objects under the influence of forces, the movement of fluids, and the spread of disease, are modelled using differential equations in science and engineering. Ordinary differential equations (ODEs) and partial differential equations (PDEs) are the two primary categories of differential equations.
To solve this differential equation using separation of variables, we first need to separate the variables Y and X on opposite sides of the equation:
dY / (Y + 1) = (2X + 1) dX
Following that, we incorporate both sides of the problem:
∫ dY / (Y + 1) = ∫ (2X + 1) dX
The integral on the left side can be evaluated using the substitution
u = Y + 1 and du = dY:
ln|Y + 1| = ∫ dY / (Y + 1) = ln |u| + C1
where C1 is the constant of integration.
The integral on the right side can be evaluated using the power rule of integration:
∫ (2X + 1) dX = X² + X + C2
where C2 is another constant of integration.
Putting these results together gives the general solution to the differential equation:
ln|Y + 1| = X² + X + C
where C = C1 + C2 is the combined constant of integration.
To solve for Y, we exponentiate both sides of the equation:
|Y + 1| = e⁽ˣ⁾2+X+C)
Taking into account the absolute value, we have two cases:
Case 1: Y + 1 = e⁽ˣ⁾2+X+C)
Y = e⁽ˣ⁾2+X+C) - 1
Case 2: Y + 1 = -e⁽ˣ⁾2+X+C)
Y = -e⁽ˣ⁾2+X+C) - 1
Therefore, the general solution to the differential equation DY/DX=(Y+1)(2X+1) is:
Y = e⁽ˣ⁾2+X+C) - 1 or Y = -e⁽ˣ⁾2+X+C) - 1
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Related Questions
Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed
1 meter≈ 3.28 feet
1 Lite≈ 0.26 gallons
1 kilogram≈ 2.20 pounds
15.048 dL≈ qt
Answers
15.048 deciliters is equivalent to 1 quart.
What is conversion?Conversion is the process of changing a quantity from one unit of measure to another unit of measure using a conversion factor or a formula.
We have:
To convert meters to feet, multiply by 3.28.
To convert liters to gallons, multiply by 0.26.
To convert kilograms to pounds, multiply by 2.20.
To convert deciliters to quarts, divide by 15.048.
Let's use these conversions to convert the given measurement:
15.048 dL = qt
Dividing both sides by 15.048, we get:
1 dL = qt/15.048
Multiplying both sides by 0.946353, which is the number of quarts in a liter, we get:
0.946353 dL = qt/15.048 * 0.946353
Simplifying the right-hand side, we get:
0.946353 dL = qt/15.961
Multiplying both sides by 3.78541, which is the number of liters in a gallon, we get:
3.78541 * 0.946353 dL = 3.78541 * qt/15.961
Simplifying the left-hand side, we get:
3.58702 L = qt/4.22676
Multiplying both sides by 4.22676, we get:
15.1485 L = qt
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Line F has a slope of −6/3, and line G has a slope of −8/4. What can be determined about distinct lines F and G?
The lines will intersect.
Nothing can be determined about the lines from this information.
The lines are parallel.
The lines have proportional slopes.
Answers
Reasoning:
If we simply the slopes of both lines, line F has a slope of -2 since -6/3=-2, and line G also has a slope of -2 since -8/4=-2. Because the slopes are equal, the lines rise and run at the sane rate, and as long as they have different y-intercepts, they will be parallel. Essentially, both lines will have the same “steepness” but start at different points, so they never intersect.
Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and five have a master’s degree. If the department chairperson selects five applicants at random for an interview, find the probability that all three have a PhD
Answers
Answer:
0.3788
Step-by-step explanation:
12 people want to teach math at a college.
6 people have a PhD.
5 people have a master's degree.
boss wants to interview 5 people for the job.
chance that all 5 of the people interviewed have a PhD.
total number of ways to select 5 applicants out of 12 is given by the combination:
combinations formula :
nCr = n! / r! * (n – r)!
C(12, 5) = 12! / (5! * 7!) = 792
number of ways to select 3 applicants with a PhD out of the 6 available is:
C(6, 3) = 6! / (3! * 3!) = 20
remaining 2 applicants can be selected from the remaining 6 applicants with a master's degree:
C(6, 2) = 6! / (2! * 4!) = 15
total number of ways to select 5 applicants with 3 having a PhD is:
20 * 15 = 300
P(3 PhDs) = 300 / 792
P(3 PhDs) = 0.3788 (rounded to four decimal places)
So, the probability of selecting five applicants for an interview where all three applicants have a PhD is approximately 0.3788
ChatGPT
Hannah is working in England for 3 months on a project for her company. One weekend Hannah decides to go to France with her car on the ferry, then explore the French countryside. In England, speed limit signs are posted in miles per hour (mph) and Hannah's rental car only shows the speed in miles per hour. In France, speed limit signs are posted in kilometers per hour (kph). Hannah looks up the conversion and learns that 1 kph = 0.62 mph.
On the road that Hannah is currently on, the posted speed limit is 130 kilometers per hour. What is the maximum whole-number speed, in miles per hour, that Hannah can drive without exceeding the speed limit??
A. 82 mph
B. 79 mph
C. 209 mph
D. 80 mph
Answers
Answer:
To convert 130 kph to mph, we can use the conversion factor 1 kph = 0.62 mph:
130 kph × 0.62 mph/kph ≈ 80.6 mph
So the maximum whole-number speed that Hannah can drive without exceeding the speed limit is 80 mph (option D).
Step-by-step explanation:
Explanation: I was doin sth like this last year
Does anybody know what 3,600 is as 1 unit less than 4,000???
Answers
Answer:
Amount of change: 4,000 - 3,600 = 400
Percent of change: 400/4,000 = 1/10 = 10%
There was a 10% decrease in the number of visitors:
Based on this equation, estimate the rating of chips whose cost is $1.10.
Round your answer to the nearest hundredth.
Answers
The rating of chips whose cost is $1.10 is obtained replacing the value of x on whichever's equation is correct by 1.10.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
Missing InformationThe problem is incomplete, hence the procedure to estimate the rating of chips whose cost is $1.10 is presented.
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Help please with this.
Answers
A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The lengths of the corresponding segments are given as follows:
EH = 2.XW = 4.Hence the scale factor is given as follows:
k = 4/2
k = 2.
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What is the American dollar exchange rate for Mexican pesos?
(Subject: Economics)
Answers
Answer:
1 Mexican Peso = 0.0552 US Dollar Hope this helped! Have a great day! :)
Step-by-step explanation:
Answer:
1 United States Dollar is equivalent or equal to 18.24 (Mexican peso)
Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 6 (Multiplicity 2); 3i
Enter the expanded polynomial. Let a represent the leading coefficient.
f(x) = a( )
Answers
Answer:
Step-by-step explanation:
The polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be formed as follows:
Since the zero 6 has a multiplicity of 2, it appears twice in the factored form of f(x), i.e., (x-6)(x-6) = (x-6)^2.
The other zero is 3i, which means its complex conjugate, -3i, is also a zero. Therefore, the factored form of f(x) can be written as:
(x-6)^2(x-3i)(x+3i)
Expanding this expression, we get:
f(x) = (x-6)^2(x^2 + 9)
Multiplying this out, we get:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324
Therefore, the polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be written as:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324.
f(x) = a(x - 6)^2(x - 3i)(x + 3i)
To expand this polynomial, we can use the fact that (a + b)(a - b) = a^2 - b^2. Substituting a = x - 6 and b = 3i, we get:
(x - 6 + 3i)(x - 6 - 3i) = (x - 6)^2 + 9
Therefore, the expanded polynomial is:
f(x) = a(x - 6)^2(x - 3i)(x + 3i)
f(x) = a(x - 6)^2(x^2 + 9)
f(x) = a(x^4 - 12x^3 + 57x^2 - 108x + 81)
So, the expanded polynomial is f(x) = a(x^4 - 12x^3 + 57x^2 - 108x + 81).
If there are two trains traveling at 80 mph each which one will get there first?
Answers
This year's property taxes on a parcel are $1,743.25. If a sale of the property is to be closed on
August 12, what is the approximate tax proration that will be charged to the seller based on a 360-day
year?
Answers
Answer:
$1070.16
Step-by-step explanation:
You want the prorated amount of taxes if the annual amount is $1743.25 and the sale closes August 12, based on a 360 day year.
Months and daysA 360-day year assumes months are 30 days. The tax charged to the seller will be that for 7 months plus 11 days:
(7·30 +11)/360 × $1743.25 = $1070.16
The seller will pay $1070.16 of the tax bill.
__
Additional comment
We have presumed the buyer pays the taxes for August 12, the first day they own the property.
Using elimination method (linear combination), what would the resulting equation be after adding both equations together?
Answers
Answer:
The resulting linear equation is 3d = 12, so d = 4 and e = 0.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
The entries in both columns when matched are
Equation of line of best fit: y = -x + 8Slope = -1y-intercept = 8Matching the entries in column A and BFrom the question, we have the following parameters that can be used in our computation:
The graph
When the line of best fit is drawn, we have
(8, 0) and (0, 8)
The equation is calculated as
y = mx + c
So, we have
8 = 0 * m + c
0 = 8 * m + c
This gives
c = 8
0 = 8 * m + 8
So, we have
m = -1
This means that the equation is
y = -x + 8
Using the above as a guide, we have the following:
Equation of line of best fit: y = -x + 8
Slope = -1
y-intercept = 8
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Determine the intervals in which the function is decreasing
Answers
The intervals in which the function is decreasing. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]. Option 3
How do you find the interval in which the function is decreasing?We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.
To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.
We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).
We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.
From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].
The above answer is in response to the question below as seen in the picture.
Determine the interval(s) in [tex][-\pi, \pi ][/tex] on
which f(x) = 2 sin x - x
is decreasing.
1. [tex][-\frac{\pi }{3}, \frac{\pi }{3} ][/tex]
2. [tex][-\frac{\pi }{6}, \frac{\pi }{6} ][/tex]
3. [tex][-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ][/tex]
4. [tex][-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ][/tex]
5. [tex][-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ][/tex]
6. [tex][-\frac{\pi }{6}, \frac{5\pi }{6} ][/tex]
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6. Cones A and B both have volume 487 cubic units, but have different dimensions.
Cone A has radius 6 units and height 4 units. Find one possible radius and height
for Cone B. Explain how you know Cone B has the same volume as Cone A.
Answers
The dimensions of cone B is radius, 6.8 units and height 7 units.
What are the possible dimensions of cone B?
The possible dimensions of cone B is calculated as follows;
Volume of cone = ¹/₃πr²h
Volume of cone A = ¹/₃π(6²)(4) = 150.8 units³
Volume of cone B = 487 units³ - 150.8 units³ = 336.2 units³
The dimensions of cone B is calculated as;
¹/₃πr²h = 336.2 units³
r²h = 321
Let the height of cone B = 7, then the radius of the cone is calculated as;
7r² = 321
r² = 321/7
r² = 45.86
r = √45.86
r = 6.8 units
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A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval. a. between 29 and 37 b. between 33 and 45 c. at least 29 d. at most 21
Answers
Step-by-step explanation:
We can use the standard normal distribution to calculate probabilities for a normal distribution with mean 33 and standard deviation 4. We just need to standardize the intervals using the formula:
z = (x - mu) / sigma
where x is the specific value in the interval, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.
a. Between 29 and 37:
z1 = (29 - 33) / 4 = -1
z2 = (37 - 33) / 4 = 1
Using a standard normal distribution table, the cumulative probability of z being between -1 and 1 is approximately 0.6827.
So the probability that a randomly selected x-value from the distribution is between 29 and 37 is approximately 0.6827.
b. Between 33 and 45:
z1 = (33 - 33) / 4 = 0
z2 = (45 - 33) / 4 = 3
The cumulative probability of z being between 0 and 3 is approximately 0.4987.
So the probability that a randomly selected x-value from the distribution is between 33 and 45 is approximately 0.4987.
c. At least 29:
z = (29 - 33) / 4 = -1
The cumulative probability of z being less than -1 is approximately 0.1587. So the probability that a randomly selected x-value from the distribution is at least 29 is approximately 1 - 0.1587 = 0.8413.
d. At most 21:
z = (21 - 33) / 4 = -3
The cumulative probability of z being less than -3 is very close to 0. So the probability that a randomly selected x-value from the distribution is at most 21 is approximately 0.
FIND THE SPACE SAMPLE AND TOTAL POSSIBLE OUTCOMES
Sunscreen
SPF 10, 15, 30, 45, 50
Type Lotion, Spray, Gel
Answers
The space sample would include the lotion, spray and gel, with the SPF and there are 15 possible outcomes.
How to find the sample space ?The enumeration of sample space and all potential results can be achieved by duly considering various combinations of SPF and sunscreen variety. It is achievable to list the entire gamut of possibilities when each type of sunscreen is matched with every value of SPF:
The sample space would look like this:
SPF 10 LotionSPF 10 SpraySPF 10 GelSPF 15 LotionSPF 15 SpraySPF 15 GelSPF 30 LotionSPF 30 SpraySPF 30 GelSPF 45 LotionSPF 45 SpraySPF 45 GelSPF 50 LotionSPF 50 SpraySPF 50 GelThis shows that there are 15 possible outcomes in the sample space.
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A squirrel on the ground sees a hole in a tree that could be its new home. The squirrel is 8 feet away
from the base of the tree and sees the hole at an angle of elevation of 43°. How high up the tree is the
hole? Round your answer to the nearest hundredth foot.
Answers
tan(43°) = h/8
Multiplying both sides by 8, we get:
h = 8 * tan(43°)
Using a calculator, we get:
h ≈ 7.19 feet
Therefore, the hole in the tree is approximately 7.19 feet high. Rounded to the nearest hundredth foot, the answer is 7.19 feet.
Let h be the height of the hole above the ground. Then, we have:
tan(43°) = h/8
Solving for h, we get:
h = 8 tan(43°)
h ≈ 7.07 feet
Therefore, the hole is approximately 7.07 feet above the ground.
A golf ball is hit with an initial velocity of 140 feet per second at an inclination of 45 degrees to the horizontal. In physics, it is established that the height h of the golf ball is given by the function h(x)=(-32x^2/140^2)+x, where x is the horizontal distance that the golf ball has traveled. Complete parts (a) through (g). Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 80 feet. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
Answers
The distance that the ball has traveled when the height of the ball is 80 feet is either about 9.86 feet or about 3.64 feet.
We are given that;
Velocity= 140feet
Inclination= 45degrees
Function h(x)=(-32x^2/140^2)+x
Now,
To find the distance that the ball has traveled when the height of the ball is 80 feet, we need to solve the equation:
h(x) = 80
Substituting h(x) with the given function, we get:
(-32x2/1402) + x = 80
Multiplying both sides by 140^2 and simplifying, we get:
-32x^2 + 140x - 11200 = 0
Dividing both sides by -32 and simplifying, we get:
x^2 - (35/4)x + 350 = 0
Using the quadratic formula, we get:
x = [ (35/4) ± √( (35/4)^2 - 4(350) ) ] / 2 x ≈ 9.86 or x ≈ 3.64
Using a graphing utility, we can confirm that these are the approximate x-intercepts of the function h(x) - 80.
Therefore, by graphing the answer will be about 9.86 feet or about 3.64 feet.
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A particle moves along the x-axis so that at time t > 0 its position is given by x(t)= t^3 - 6t^2 - 96t. Determine all intervals when the speed of the particle is increasing.
Answers
Answer:
(-4, 2)∪(8, ∞)
Step-by-step explanation:
Given a particle's position is described by x(t) = t³ -6t² -96t, you want the intervals where speed is increasing.
SpeedThe speed of the particle is the magnitude of its rate of change of position.
The rate of change of position is ...
x'(t) = 3t² -12t -96 = 3(t² -4t) -96
x'(t) = 3(t -2)² -108
This describes a parabola that opens upward, with a vertex at (2, -108). It has zeros at x = 2 ± 6 = {-4, 8}.
The magnitude of the speed is shown by the blue curve in the attachment. Between t=-4 and t=8, it is the opposite of the parabola described by the above equation.
AccelerationThe rate of change of speed is the derivative of speed with respect to time. The green curve in the attachment shows the particle's rate of change of speed. Speed is increasing when the green curve is above the x-axis.
Between the point when speed is 0, at t=-4, and when it reaches a local maximum, at t=2, it is increasing. Speed is increasing again after it becomes 0 at t=8.
The intervals of increasing speed are (-4, 2) ∪ (8, ∞).
__
Additional comment
We have made the distinction between speed and velocity. Velocity is the signed rate of change of position. If position is plotted on a number line increasing to the right, then velocity is positive anytime the particle is moving to the right. Velocity is increasing if acceleration is to the right (positive).
Velocity of this particle is increasing on the interval (2, ∞).
The average daily balance of a credit card for the month of March was $1900 and the unpaid balance at the end of the month was $1700. If the annual percentage rate is 32.4% of the average daily balance, what is the total balance on the next billing date, April 1?
Round your answer to the nearest cent.
Answers
Using the average daily balance, the total balance on the next billing date, April 1 is $5,059.73.
What is the average daily balance?The average daily balance is a credit card method of computing finance charges.
To determine the average daily balance, the sum of the daily balances over your billing cycle is divided by the number of days in the billing cycle.
The finance charge is then the product of the average daily balance multiplied by the APR and the number of days involved, divided by 365 days.
Average daily balance = $1,900
Unpaid balance at month-end = $1,700
APR = 32.4%
The finance charge for the month = $9.73 ($1900 x 32.4% x 30/365)
The total balance on the next billing date, April 1 = $5,059.73 ($5,050 + $9.73)
Thus, on April 1, the next billing cycle, the balance on the card is $5,059.73.
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Find inverse of the following f(x)=x^3+9
Answers
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~x^3+9\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~y^3+9} \\\\\\ x-9=y^3\implies \sqrt[3]{x-9}=y=f^{-1}(x)[/tex]
Problem:
Pierre is 3 years older than his brother, Claude.
1. Write an equation that represents how old Pierre is (p) when Claude is (c) years old.
2. How old is Pierre when Claude is 17 years old?
Answers
p = c + 3
where p is Pierre's age and c is Claude's age.
2. To find out how old Pierre is when Claude is 17, we can substitute 17 for c in the equation we just wrote:
p = c + 3
p = 17 + 3
p = 20
Therefore, Pierre is 20 years old when Claude is 17 years old.
bird was sitting 33 feet from the base of an oak tree and flew 65 feet to reach the top of the tree. How tall is the tree?
Answers
Thus, the height of the oak trees of found to be 98 feet.
Explain about the addition:In maths, addition is the process of adding two or more numbers together. The numbers that added are known as addends, while the outcome of the addition process, or the final response, is known as the sum.
In general, the definition of addition is the coming together of two or so more groups of items into one group. According to mathematics, addition is an arithmetic operation that determines the total or sum of two or more numbers.The plus (+) addition symbol is placed between the two integers being added. One of the fundamental numerical operations is addition.Given data:
Height of the bird from the base of the oak tree: 33 feet.
Height flew by the bird to reach at the top of the tress: 65 feet.
So,
Height of the oak tree = 33 + 65
Height of the oak tree = 98 feet
Thus, the height of the oak trees of found to be 98 feet.
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Help Please Be Fast
Answers
The maximum value of the objective functions are 2600, 27 and 1980
Solving the objective function graphicallyGiven that
Max Z = 8x + 16y
Where the constraints are
3x + 6y ≤ 900
x + y ≤ 200
y ≤ 125
x, y ≥ 0
Plotting the constraints 3x + 6y ≤ 900, x + y ≤ 200 and y ≤ 125 on the same graph, the coordinates of the feasible region are:
(x, y) = (100, 100), (75, 125) and (50, 125)
So, we have
Z = 8(100) + 16(100) = 2400
Z = 8(75) + 16(125) = 2600
Z = 8(50) + 16(125) = 2400
Hence, the maximum value is 2600
Solving the objective function graphicallyGiven that
Max Z = 6x + 3y
Where the constraints are
2x + y ≤ 8
3x + 3y ≤ 18
y ≤ 3
x, y ≥ 0
Plotting the constraints 2x + y ≤ 8, 3x + 3y ≤ 18 and y ≤ 3 on the same graph, the coordinates of the feasible region are:
(x, y) = (3, 3), (2.5, 3) and (2, 4)
So, we have
Z = 6(3) + 3(3) = 27
Z = 6(2.5) + 3(3) = 24
Z = 6(2) + 3(4) = 24
Hence, the maximum value is 27
Solving the objective function by simplexGiven the objective function, the constraints and the final simplex tableau
We have the final values to be
Z = 1980
This means that the maximum value is 1980
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Find the value of x in the triangle shown below.
X=
4.5
56°
4
4
X°
Answers
Answer:
68.9 degrees
Step-by-step explanation:
To find this we can use the rule of sines.
It states [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We will use 56 degrees and its complementary measurement, which is discovered by observing the opposite side from the angle, which is 4. Then, we will find the side that compliments x, which is 4.5. Then we can plug those values into the rule of sines.
[tex]\frac{sin56}{4}=\frac{Sinx}{4.5}[/tex]
Then, we want to get Sin x by itself.
[tex]\frac{sin56}{4}*4.5=sinx[/tex]
Then, we can solve for sin x.
[tex]0.932667269124=sinx[/tex]
finally, we need to take the inverse of sin to find our solution.
[tex]sin^{-1} (0.932667269124)=sin^-^1(sinx)\\x=68.85\\[/tex]
Which can be rounded to 68.9.
PLEASE ANSWER FAST I NEED THE ANSWER
Answers
The direction and speed the plane traveling is at About 84.3° west of north at approximately 502.5 mph. Option C
How do we calculate the direction and speed of the traveling plane?We need to first find the distance between points A and C using the distance formula; Distance AC = √((x2 - x1)² + (y2 - y1)²)
If we input the figures as seen in the diagram, it becomes
Distance AC = √((-30 - 20)² + (520 - 20)²)
which is 502.49. if we round it off, it becomes 502.5
We have to find find the angle θ that the plane is traveling using the law of cosines
cos(θ) = (AB² + BC² - AC²) / (2 x AB x BC)
cos(θ) = (500² + 50² - 502.5²) / (2 x 500 x 50)
which is -0.000125
θ = arccos( -0.000125)
θ = 90.0071621563 (in degrees)
Give than the wind is blowing west, the angle should be measured west of north.
180° - 90.01° = 90°
It only mean that the plane is travelling at approximately 84.3° west of north
The answer is based on the question below;
A plane is set to fly due north, but it is pushes off course by crosswind blowing west. At 1 pm, the plane is located at point A and at 2pm, the plane is located at point C, as shown in the diagram. In what direction and at what speed is the plane traveling?
A. About 5.7° west of north at approximately 500.1 mph.
B. About 5.7° west of north at approximately 502.5 mph
C. About 84.3° west of north at approximately 500.1 mph.
D. About 84.3° west of north at approximately 502.5 mph
Point C coordinates (-30, 520)
Point A (20, 20)
Distance from A to B on a straight course is 500
B to C is 50
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What is the length of the unknown leg
of the right triangle?
2 ft
3 ft
(The figure is not drawn to scale.)
The length of the unknown leg of the right triangle is ft.
(Round to one decimal place as needed.)
Answers
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
Explain about the right triangle:A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
What a Right Triangle Looks Like
In a right triangle, the right angle is often the biggest angle.The longest side is the hypotenuse, which is the side that faces the right angle.A right triangle cannot include any obtuse angles.For the given right triangle:
Let the unknown length be 'x'.
Using the Pythagorean theorem:
3² = 2² + x²
x² = 3² - 2²
x² = 9 - 4
x² = 5
x = 2.2
Thus, the unknown leg x of the right angled triangle is found as 2.2 ft.
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A spinner has 10 equally sized sections, 3 of which are green and 7 of which are yellow. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads?
Answers
Okay, here are the steps to solve this problem:
* There are 10 sections on the spinner, 3 of which are green and 7 of which are yellow.
* So there is a 3/10 = 0.3 probability that the spinner will land on green.
* A fair coin has a 1/2 probability of landing on heads.
* For the spinner and coin toss to both have the desired outcome (green and heads), we multiply their individual probabilities:
* 0.3 * 1/2 = 0.15
Therefore, the probability that the spinner lands on green and the coin toss is heads is 0.15.
The expression (cscx + cotx)? is the same as____.
Answers
The expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x. (option a).
The given expression is (cscx + cotx)². To simplify this expression, we can use the formula for squaring a binomial, which is (a + b)² = a² + 2ab + b². In this case, a = cscx and b = cotx. Therefore, we can substitute these values into the formula to get:
(cscx + cotx)² = csc²x + 2(cscx)(cotx) + cot²x
So the expression (cscx + cotx)² is the same as csc²x + 2(cscx)(cotx) + cot²x.
Hence the correct option is (a).
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