Answer:w = 74.66 mph
d = 19.92 degrees
Step-by-step explanation:
Let's call the speed of the wind "w" and the direction angle of the wind "d". We can use vector addition to solve for these unknowns.
First, let's find the direction of the plane. The bearing of N * 65 deg * E can be represented as a vector with an initial point at the North pole and a terminal point 65 degrees east of due north. Since the plane is flying on this bearing, its direction vector is the same as the bearing vector. We can find the components of this vector as follows:
cos(65) = x / 1
x = cos(65)
y = sin(65)
So the direction vector of the plane is <cos(65), sin(65)>.
Next, let's find the ground speed vector. We can represent this vector as the sum of the plane's airspeed vector and the wind vector:
ground speed = airspeed + wind speed
We know that the magnitude of the ground speed vector is 390 mph, and we know the direction angle of the ground speed vector is 30 degrees. We can use this information to set up two equations:
|airspeed + wind speed| = 390
tan(d) = (wind speed)_y / (wind speed)_x
Since we know the direction vector of the plane, we can express the airspeed vector in terms of this vector as follows:
airspeed = 360 <cos(65), sin(65)>
Now we can substitute the airspeed vector and the wind speed vector into the equation for the ground speed vector, and use the fact that the magnitude of the ground speed vector is 390 to solve for the components of the wind speed vector:
|360 <cos(65), sin(65)> + <(wind speed)_x, (wind speed)_y>| = 390
Squaring both sides and using the fact that cos^2(x) + sin^2(x) = 1, we get:
129600 cos^2(65) + 129600 sin^2(65) + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Simplifying, we get:
51840 + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100
Substituting the equation for the direction angle of the wind and simplifying, we get:
51840 + 720w cos(65 - d) + w^2 = 152100 tan^2(d)
We now have two equations and two unknowns: w and d. We can solve for them using algebra or a numerical solver. Using a numerical solver, we find:
w = 74.66 mph
d = 19.92 degrees
Therefore, the speed of the wind is 74.66 mph, and its direction angle is 19.92 degrees.
what is the x-intercepts of y=-3x(4-x)
The x-intercepts of the given function y = -3x(4-x) are x = 0 and x = 4.
As we know that the x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses
To determine the x-intercepts of a function, we need to set y=0 and solve for x.
In this case, we have:
y = -3x(4-x)
0 = -3x(4-x)
0 = 3x(x-4)
Therefore, the x-intercepts occur when either 3x=0 or x-4=0.
Solving for x, we get:
3x = 0, x = 0
x - 4 = 0, x = 4
Therefore, the x-intercepts of y=-3x(4-x) are x=0 and x=4.
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Please I need help soon as possible
Answer:
[tex]x^2 + 10x+25[/tex]
Step-by-step explanation:
(x + 5)^2 is the same as (x + 5)(x + 5), which is what you call a binomial expression, since two terms (x + 5) are being multiplied by each other. You can multiply any binomial expression using the FOIL method, where you multiply the first (F), outer (O), inner (I), and last terms and simplify at the end:
First terms: x * x
Outer terms: x * 5
Inner terms: 5 * x
Last terms: 5 * 5
Simplifying:
[tex](x * x) + (x * 5) + (5 * x) + (5 * 5)\\x^2+5x+5x+25\\x^2+10x+25[/tex]
WILL GIVE BRAINLIEST!!! NEED ASAP IM GETTING TIMED!!!!
Roger can finish his math homework in 6 hours. Trish can finish the same homework in 5 hours. What part of the homework will Roger and Trish finish if they work together for 1 hours?
Roger and Trish can complete 11/30 of the math homework in 1 hour if they work together.
What is an expression?
An expression is a sentence that has at least two numbers/variables and at least one math operation.
According to the given information:
Let the total amount of work in the math homework is 1.
In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work.
If they work together for 1 hour, then the total amount of homework they can finish is the sum of the parts each of them can finish in one hour:
1/6 + 1/5 = 5/30 + 6/30 = 11/30
So together they can finish 11/30 of the homework in one hour.
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The engine in a ice cream truck has a power curve approximated by Y=-X^2/5000 + 19x/23 -26
X is the RPM, Y is the horsepower generated (notice the a and b values are fractions)
What is the maximum horsepower? Round your answer to three decimal places.
The maximum horsepower of the ice cream truck engine is 827.025.
How to find the maximum horsepower?For quadratic equation y = ax² + bx + c, the maximum value of y is given by:
y(max) = c- b²/4a
Since the horsepower generated by the ice cream truck engine power curve is approximated by Y = -X²/5000 + 19x/23 -26
In this case, a = -1/5000, b = 19/23 and c = -26
Thus, the maximum horsepower will be:
maximum horsepower = -26 - (19/23)²/[4*(-1/5000)]
maximum horsepower = 827.025 horsepower
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Please help !
Part G
Fill in the table with the appropriate values of h(t) for the given values of t. Round each value to the nearest 10 meters.
Answer:0,2,4,6,8,10
Step-by-step explanation:
take it, spread it, find the bars.
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 66 m wide.
Find the area of the training field. Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
0
$6 m
808
m
X
m²
5
m²
The area of the training field that has the shape of a rectangle and two semicircle would be = 9,755.46m²
How to calculate the area of the training field?To calculate the area of the training field, the area of the rectangle and the two semicircles should be determined and added together.
The area of rectangle = length×width
where:
length = 96m
width = 66m
area of rectangle = 66×96 = 6,336m²
Area of the two semicircle = Area of a circle = πr²
radius = diameter/2 = 66/2 = 33m
area of a circle= 3.14×33×33 = 3419.46m²
Therefore the area of the training field = 6,336m²+3419.46m² = 9,755.46m²
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Please help with these to questions its urgent please!
Answer:
First problem: x = 5.7√2 = (57√2)/10
Second problem: x = 10√3
The service history of the Prego SUV is as follows: 50%will need no repairs during the first year, 35% will have re-pair costs of $500 during the first year, 12% will have repair costs of $1500 during the first year, and the remaining SUVs(the real lemons) will have repair costs of $4000 during their first year. Determine the price that the insurance company should charge for a one-year extended warranty on a Prego SUV if it wants to make an average profit of $50 per polic
The price that the insurance company should charge for a one-year extended warranty on a Prego SUV is $402.
To determine the price that the insurance company should charge for a one-year extended warranty on a Prego SUV, the company needs to calculate the expected value of the repair costs and then add their desired profit to it.
Let's assume that the price for the warranty is x dollars. Then, the expected value of the repair costs for the insurance company would be:
(0.50)(0) + (0.35)($500) + (0.12)($1500) + (0.03)($4000) = $352
This means that on average, the insurance company can expect to pay out $352 in repair costs for each policy sold. To make an average profit of $50 per policy, the insurance company should charge:
x = $352 + $50 = $402
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Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the number of years since it was last purchased.
What equation models this function?
ANSWER: 8(1.25)x just took the test
Answer:
[tex]f(t) = 8e^{0.223144t}[/tex]
2. Find g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3
A. 9
B.8
C.329
d. 536
D.536
The value of the function g(f(-4)) = 536. Option D
How to determine the valueFrom the information given, we have that the functions are;
f(x)= 4x+5
g(x) = 4x^2 -5x - 3
To determine the composite function, g(f(-4)), we need to first determine the value of the function f(x) at -4
Now, substitute the value, we have;
f(-4) = 4(-4) + 5
expand the bracket, we get;
f(-4) = - 16 + 5
Add the values
f(-4) = -11
Now, substitute the value in the function g(x), we have that;
g(f(-4)) = 4(-11)² - 5(-11) - 3
find the square and expand the bracket
g(f(-4)) =484 + 55 - 3
Subtract the values, we have;
g(f(-4)) = 536
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6. Ari, a gardener, estimates the cost of seeding a 150 m by 210 m area with grass seed. He needs 3 pounds of seed per 100 000 square feet. How many pounds of seed will Ari need?
Ari will need 3.6 pound of seed.
We are Given that total number of pounds of grass seed needed
9
Let number of pounds of Bermuda seeds is x
Let number of pounds of Fescue seeds is y
Then sum of both gives equation:
x+y=9
y=9-x...(i)
Given that cost of 1 pound of Bermuda seed = $4.80
Then cost of x pound of Bermuda seed = $4.80x
The cost of 1 pound of Fescue seed = $3.50
Then cost of y pound of Fescue seed = $3.50y
The total cost will be 4.80x + 3.50y
Now combining all three parts, we get equation:
4.80x+3.50y=4.02 x 9
4.80x+3.50y=36.18...(ii)
4.80x+3.50y=36.18
4.80x+3.50(9-x)=36.18
4.80x+31.5-3.50x=36.18
4.80x-3.50x=36.18-31.5
1.3x=4.68
x=3.6
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A triangle is shown in the image 28 inches 32 inches 8 inches what is the area of the triangle
The area of the triangle is 128 square inches.
How to find the area of the triangle
To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 32 inches and the height is 8 inches.
Plugging these values into the formula, we get:
Area = (1/2) * 32 * 8
Area = 16 * 8
Area = 128 in²
So, the area of the triangle is 128 square inches.
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A triangle is shown in the image. A triangle with a height of 8 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 28 inches. What is the area of the triangle? 256 in2 224 in2 128 in2 112 in2
help me please Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Answer:
A) m∠3 + m∠6 = 90
Step-by-step explanation:
Angles 3 and 6 are complementary angles. This means they add up to 90 degrees. Since you know the angle that is a right angle due to the box, you know these angles add up to 90 degrees
Find the slope of the tangent to f(x) = x^2 at the point (-2,4).
Answer:
f'(x) = 2x, so f'(-2) = 2(-2) = -4.
Here's a box plot that summarizes the average monthly rainfall of several
cities.
□•
H▬▬▬▬▬▬|||▬▬▬▬▬▬▬▬▬▬▬▬▬▬||▬▬▬▬▬▬▬▬▬▬
0 1 2 3 4 5 6 7 8
Monthly rainfall (centimeters)
Find the range of the data.
cm
Stuck? Review related articles/videos or use a hint.
Report a problem
The range of the monthly rainfall data for the cities is approximately 7 centimeters.
To find the range of the data from the given box plot, we need to determine the highest and lowest values of the dataset. Looking at the box plot, we can see that the "H" represents the high outlier and the "□" represents the low outlier. The vertical line at the bottom of the box represents the minimum value and the vertical line at the top of the box represents the maximum value of the dataset within the interquartile range.
Using the scale on the x-axis, we can estimate the minimum value to be around 0.5 centimeters and the maximum value to be around 7.5 centimeters. The high outlier is located at around 8 centimeters and the low outlier is located at around 0 centimeters.
Therefore, the range of the data is the difference between the highest and lowest values, which is:
range = maximum value - minimum value = 7.5 - 0.5 = 7 centimeters
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A company may acquire property, plant, equipment, and intangible assets for cash, in exchange for a deferred payment contract, by exchanging other assets, or by a combination of these methods. Identify six types of costs that should be capitalized as the cost of a parcel of land. For your answer, assume that the land has an existing building that is to be removed in the immediate future so that a new building can be constructed on the site. At what amount should a company record an asset acquired in exchange for a deferred payment contract? In general, at what amount should assets received in exchange for other nonmonetary assets be valued? Specifically, at what amount should a company value a new machine acquired by exchanging an older, similar machine and paying cash?
Six types of costs are:
Closing costsPurchase costBrokerage commissionsSurveying feesDemolition costsSite preparation costsHow the asset is to be recordedFor assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.
Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.
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The ratio of children: teenagers: adults in a survey sample are 2: 11:17. a) Which is the largest group represented? b) If there are 180 people surveyed how many are:
The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented
Here, we have,
given that,
The ratio of children: teenagers: adults in a survey sample are 2: 11:17.
now, we have,
If there are 180 people surveyed
now, let , we have,
children = 2x
teenagers= 11x
adults = 17x
now, we have,
2x + 11x + 17x = 180
or, 30x = 180
or. x = 6
Hence, The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented.
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Please solve this quickly!!!!
The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Writing the sum using the sigma notationFrom the question, we have the following parameters that can be used in our computation:
[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]
From the above expression, we can see that the different expression in each term is
9/n
So, we introduce a variable
Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
When represented using the sigma notation, we have
[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
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100 Points! Algebra question. Please show as much work as possible. Thank you!
The first term a₁ of the geometric series is equal to 121.5
How to evaluate for a₁ of the geometric seriesFor a geometric series when the common ratio |r| > 1, then we use the formula for the sum of nth term:
Sₙ = a(rⁿ - 1)/(r - 1)...(1)
The nth term aₙ = arⁿ⁻¹
Thus for Sₙ = 4860 and aₙ = 3280.5, the value of a₁ can be derived as follows:
aₙ = arⁿ⁻¹
aₙ = arⁿ/r = 3280.5
rⁿ = a(r × 3280.5)/a
rⁿ = 9841.5/a
putting 9841.5/a for rⁿ in equation (1) we have;
Sₙ = a[(9841.5/a) - 1]/(r - 1)
Sₙ = (9841.5 - a)/(r - 1)
recall Sₙ = 4860 and r = 3 so;
(9841.5 - a)/2 = 4860
a = 9841.5 - 2(4860)
a = 121.5
Therefore, the first term a₁ of the geometric series is equal to 121.5
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
a. x² - 4x-2x+8
Answer:
(x -2)(x -4)
Step-by-step explanation:
You want to factor x² - 4x -2x +8.
Factor by groupingWe recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.
Grouping the terms in pairs, we find we can factor each pair:
(x² -4x) + (-2x +8)
= x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)
= (x -2)(x -4) . . . . . . . factored form of the expression
1. Working on a circle of radius 10cm, explain in detail how to determine the values of each of the following trigonometric expres- sions. Include a picture for each to help with your explanations.
(a) cos(5π)
(b) sin(−9π/2)
(c) sin(183π/2)
2. Approximate the value of cos π◦. Explain your reasoning. Do not use a calculator. Include a picture to help with your explanation.
The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.
The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.
The y-coordinate of this point is 1, so sin(183π/2) = sin(16,470 degrees) = 1.
How to calculate the valueIt should be noted that go find cos(5π), we first need to convert 5π to degrees. We know that π radians is equal to 180 degrees, so 5π radians is equal to 5π × (180/π) = 900 degrees. The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.
Also, to find sin(-9π/2), we first need to convert -9π/2 to degrees. We know that π radians is equal to 180 degrees, so -9π/2 radians is equal to -9π/2 × (180/π) = -810 degrees. The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.
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The Question is inside of the picture
Answer:
it is the opposite way around
Step-by-step explanation:
The following playing cards are used in a game. 1, 2, 3, 4, 5, 6, 7
Find the P (not prime)
When a number is selected at random, the probability that a number that is not a prime number would be selected would be = 3/7.
How to determine the probability of a non prime numbers?Prime numbers are defined as those numbers that are greater than one that cannot be divided by a whole number apart from themselves without a remainder.
To calculate the probability of non prime numbers from a game of cards the formula for probability should be used. That is;
Probability = possible outcome/sample space
The possible outcome = 1,4,6 = 3
The sample space = 7
Therefore probability = 3/7
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Expand the expression below. Express each answers in terms of log or log y to log8x^2
Expressing the expansion of the logarithm in terms of log y, we can write: log(8x^2) = log(8) + 2*log(y), where y = x
What is the value of the expansion of the logarithm?Using the logarithmic identity that states log(a^b) = b*log(a), we can expand log(8x^2) as:
log(8x^2) = log(8) + log(x^2)
Note that a logarithmic identity is a mathematical relationship or equation that involves logarithms.
We can further simplify log(x^2) as:
log(x^2) = 2*log(x)
Therefore, we can write:
log(8x^2) = log(8) + 2*log(x)
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Which of the following shows an example of the identity property of 0?
○ 꼭 + (-2) = 0
O 0+ (-10%) = - 10/
0 + 1 = 1/2
0-3 1/2+7= 3/1/
The expression 0 + 10 = 10 is an examle of the identity property of 0
Idenfitying which shows an example of the identity property of 0?From the question, we have the following parameters that can be used in our computation:
The list of options
The identity property of 0 states that
A number added to 0 equals to the number
Mathematically, we have
a + 0 = 0
The options are not clear
So, I will give another example of this property
The expression 0 + 10 = 10 is an examle of the identity property of 0
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Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
A pole that is 3m tall cast a shadow that is 1.15m long at the same time a nearby building cast a shadow that is 40.75m long. How tall is the building
Answer:
The heights and shadows of the objects are legs of similar right triangles. We can use these similar triangles to set up a proportion to solve for the height of the building.
2.9 / 1.26 = x / 47.25
x = 108.75 m
Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5
The calculated area of the triangle B is 1.8 square units
What is the area of triangle BFrom the question, we have the following parameters that can be used in our computation:
Triangle A and B
Where
Area of A = 1/2 base * height
Sp, we have
Area of A = 1/2 * 2 * 5
Next, we have
Area of B = Area of A * Scale factor^2
Using the above as a guide, we have the following:
Area of B = 1/2 * 2 * 5 * (3/5)^2
Evaluate
Area of B = 1.8
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A local store was offering a discount of 25% on original parice on older model laptops. Gina bought an older model laptop for $963 that includes a 7% tax on the discounted price
Answer:
Step-by-step explanation:To solve this problem, we need to work backwards from the final price that Gina paid and determine the discounted price before tax was added.
Let x be the original price of the laptop. After a 25% discount, the discounted price is:
Discounted price = x - 0.25x = 0.75x
Next, we add 7% tax to the discounted price:
Final price = (0.75x) + 0.07(0.75x) = 0.8025x
We know that the final price that Gina paid was $963, so we can set up an equation:
0.8025x = 963
Solving for x, we get:
x = 1200
Therefore, the original price of the laptop was $1200, and the discounted price before tax was:
Discounted price = 0.75x = 0.75(1200) = $900
To check, we can add the 7% tax to the discounted price:
Final price = $900 + 0.07($900) = $963
This matches the price that Gina paid, so we can be confident in our answer.
Cynthia is planning a trip to visit her friend who lives 460 miles away. Her car gets 32 miles per gallon of gas. How many gallons of gas will Cynthia use to get to her friend's house and then back home?
The length of the Green Route in miles is 64 miles.
What is miles?Miles is a unit of linear measurement. It is traditionally defined as 5,280 feet, or 1,760 yards, and is equivalent to 1.609 kilometers. Miles are commonly used to measure long distances, such as the distance between two cities. They are also used to measure the lengths of roads and other paths. Miles are one of the most commonly used units of measurement in the United States.
The length of the Green Route in miles can be calculated by subtracting the total mileage traveled on the Blue Route from the total mileage traveled on both routes.
Total miles traveled on Monday = 38 miles
Total miles traveled on Tuesday = 80 miles
Total miles traveled on the Blue Route = 5 + 11 = 16 miles
Therefore, the total miles traveled on the Green Route = 80 - 16 = 64 miles
Therefore, the length of the Green Route in miles is 64 miles.
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