The helicopter traveled approximately 175.5 miles east and 299.1 miles south.
How to find the helicopter traveled?Let's say the building is located at point A and the helicopter travels to point B. We know that the bearing of B from A is 558°e, which means the angle formed by the line AB and the east direction is 558°.
Next, we can use trigonometry to find the horizontal and vertical components of the distance traveled. Let x be the horizontal distance (in miles) traveled by the helicopter and y be the vertical distance (in miles) traveled. We can then use the following equations:
cos(558°) = x / d
sin(558°) = y / d
where d is the total distance traveled (in miles). We can also use the formula:
d = r * t
where r is the speed of the helicopter (100 mph) and t is the time taken for the flight (3.8 hours). Substituting this into the first two equations, we get:
x = d * cos(558°)
y = d * sin(558°)
d = r * t = 100 * 3.8 = 380 miles (rounded to the nearest mile)
Substituting the values of d and the angle into the equations for x and y, we get:
x = 380 * cos(558°) ≈ -175.5 miles
y = 380 * sin(558°) ≈ 299.1 miles
Note that the negative sign for x indicates that the helicopter traveled west, not east. We can take the absolute value of x to get the distance traveled east:
|x| ≈ 175.5 miles
Therefore, the helicopter traveled approximately 175.5 miles east and 299.1 miles south.
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-9 -7 -5 sequence name pls
Which measurement is closest to the circumference of circumference of the parachute in feet
The closest measurement to the circumference of the parachute in feet is 78.54 feet. The calculation was done by multiplying the radius by 2π (the constant pi, approximately equal to 3.14), which gives the circumference of a circle is 78.54 feet.
The circumference of the parachute can be calculated using the formula
C = 2πr
where r is the radius of the parachute.
Given that the radius of the parachute is 12.5 feet, we can substitute this value in the formula and calculate the circumference
C = 2πr
C = 2π(12.5)
C ≈ 78.54 feet
Therefore, the circumference of the parachute is closest to 78.54 feet.
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--The given question is incomplete, the complete question is given
" Which measurement is closest to the circumference of circumference of the parachute in feet if radius is 12.5. "--
at the end of a football game, the players were given the choice of having a bottle of water or a bottle of juice. Of all the players, 14 chose bottle of water, which was 2/3 of the total number of players.Write and solve an equation to determine p, the total number of players on the team
Answer:Therefore, the total number of players on the team is 21.
Step-by-step explanation:Let's start by using algebra to represent the information given in the problem.
Let p be the total number of players on the team.
The number of players who chose water is given as 14.
This is also equal to 2/3 of the total number of players, so we can write:
14 = (2/3) * p
To solve for p, we can isolate it on one side of the equation by multiplying both sides by the reciprocal of 2/3, which is 3/2:
14 * (3/2) = (2/3) * p * (3/2)
21 = p
Identify and describe each quadrilateral. Write square, rectangle, rhombus, trapezoid, or parallelogram on the blanks provided before each number.
_________1. Has one pair of parallel sides.
_________2. Has two pairs of parallel sides and its opposite sides are equal.
_________3. Is a parallelogram and four right angles and four equal sides.
_________4. A parallelogram and four equal sides (a slanted square)
_________5. A parallelogram that has four right angles and it's opposite sides are parallel.
â
Trapezoid 1. Has one pair of parallel sides.
Parallelogram 2. Has two pairs of parallel sides and its opposite sides are equal.
Square 3. Is a parallelogram and four right angles and four equal sides.
Rhombus 4. A parallelogram and four equal sides (a slanted square)
Rectangle 5. A parallelogram that has four right angles and it's opposite sides are parallel.
1. Trapezoid: A trapezoid has one pair of parallel sides, while the other two sides are non-parallel. The parallel sides are called bases, and the non-parallel sides are called legs.
2. Parallelogram: A parallelogram has two pairs of parallel sides and its opposite sides are equal. The opposite angles are also equal, and the consecutive angles are supplementary.
3. Square: A square is a parallelogram with four right angles and four equal sides. It is a special case of both a rectangle and a rhombus, as it has all their properties.
4. Rhombus: A rhombus is a parallelogram with four equal sides, which can be thought of as a slanted square. It has opposite equal angles, and its diagonals are perpendicular bisectors, dividing the rhombus into four congruent right-angled triangles.
5. Rectangle: A rectangle is a parallelogram that has four right angles, and its opposite sides are parallel. The opposite sides are also equal, and its diagonals are congruent, bisecting each other at right angles.
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tice Problems
Scientists have calculated that recycling 10 pounds of paper, results in 8 fewer gallons of
water being required to produce an equivalent amount of new paper. If a school begins a
recycling program and is able to increase the amount of paper they recycle by 500 pounds
per month, calculate number of gallons of water this conserves over an entire year.
By increasing their recycling by 500 pounds per month, the school conserves 4,800 gallons of water in a year.
Determine the ratio of water conserved per pound of paper recycled:
8 gallons of water are saved for every 10 pounds of paper recycled.
Calculate the water saved for each pound of paper:
8 gallons/10 pounds = 0.8 gallons/pound.
Find the increase in paper recycled per month:
500 pounds/month.
Calculate the water saved per month:
[tex]500 $ pounds/month \times 0.8 $ gallons/pound = 400 $ gallons/month.[/tex]
Calculate the water saved in a year:
[tex]400 $ gallons/month \times 12 months = 4,800 $ gallons/year.[/tex]
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A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x2 - 250x + 525 and R(x) = -3x2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit
Based on the cost and revenue function, if they want to make a profit, the range of pulp in tons per day that they should produce is between 152.6 and 152.8 tons per day.
To find the range of pulp in tons per day that will generate profit, we need to set the profit function equal to zero and solve for x. The profit function P(x) is given by:
P(x) = R(x) - C(x)
Substituting the given revenue and cost functions, we get:
P(x) = -3x^2 + 1000x - 400
Setting P(x) = 0, we can solve for x using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values from our profit function, we get:
x = [-(1000) ± sqrt((1000)^2 - 4(-3)(-400))] / 2(-3)
Simplifying, we get:
x = [1000 ± sqrt(1000000 + 4800)] / 6
x = [1000 ± sqrt(1004800)] / 6
x ≈ 152.7 or x ≈ 55.6
Since we're looking for the range of pulp in tons per day that will generate profit, we only want the positive solution, which is approximately 152.7 tons per day. Therefore, the company should produce between 152.6 and 152.8 tons per day to generate profit, rounded to the nearest tenth of a ton.
Note: The question is incomplete. The complete question probably is: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x^2 - 250x + 525 and R(x) = -3x^2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit.
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Jay has five fewer $100 bills in his wallet than $50 bills. If he has only $50 and $100 bills in his wallet, and the total amount of money in his wallet is $1300, let’s find the number of notes of each denomination.
Let’s assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as ____.
Now, the total amount contributed by $50 notes is $50x
And. The total amount contributed by $100 bills is $100×( ____ )
Jay has 7 $100 bills in his wallet.
Let's assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as x - 5.
Now, the total amount contributed by $50 notes is $50x.
And the total amount contributed by $100 bills is $100*(x-5).
Since the total amount of money in his wallet is $1300, we can write an equation:
$50x + $100*(x-5) = $1300
Simplifying this equation, we get:
$50x + $100x - $500 = $1300
$150x = $1800
x = 12
So, Jay has 12 $50 bills in his wallet.
Using the earlier equation, the number of $100 bills can be found:
x - 5 = 12 - 5 = 7
Therefore, Jay has 7 $100 bills in his wallet.
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A 2-quart carton of pineapple juice costs $8.08. What is the price per cup?
$
Answer:
$1.01
Step-by-step explanation:
We Know
A 2-quart carton of pineapple juice costs $8.08
1 quart = 4 cups
2 quarts = 8 cups
So, 8 cups of pineapple juice cost $8.08.
What is the price per cup?
We Take
8.08 / 8 = $1.01
So, the price per cup is $1.01
Solve (d-8) (6d-3) using the box method show work
6d^2 - 51d + 24
that's it
...............................
Median & IQR Question: The data shows the number of hours a part-time waiter works each week. Tell whether each statement about the data is True or False. Statements and numbers are listed in the picture.
The statements regarding the median and the quartiles are given as follows:
a. True.
b. True.
c. False.
What are the median and the quartiles of a data-set?The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The ordered data-set in this problem is given as follows:
7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.
Hence:
The first quartile is of 8. -> option b is true.The median is of 9. -> option a is true.The third quartile is of 11.More can be learned about median and quartiles at https://brainly.com/question/3514929
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Stevie has a yard cleanup business. He initially spent $175 for equipment (mower, rakes, bags, etc. ). He charges $12 hours for cleanup. How many hours of work will he need to do in order to make at least $1200? (Let hh = number of hours worked)
Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment.
How to find hours of work?to find the business hours of work, Let's start by defining the variables given in the problem:
The initial cost of equipment is $175.
Stevie charges $12 per hour for cleanup.
Stevie wants to make at least $1200.
The number of hours worked is represented by h.
Now, we can set up an equation to solve for h:
Total earnings - Total cost = Desired profit
We can express the total earnings as the product of the hourly rate and the number of hours worked:
Total earnings = $12h
The total cost includes the initial cost of equipment plus any additional costs incurred during cleanup:
Total cost = $175 + additional costs
Since we don't know the value of the additional costs, we'll leave it as a variable.
Substituting these expressions into the equation, we get:
$12h - ($175 + additional costs) = $1200
Simplifying the equation, we get:
$12h - $175 - additional costs = $1200
$12h - $1375 = additional costs + $1200
$12h - $1375 = additional costs
Now we have an equation that relates the number of hours worked to the additional costs incurred during cleanup. We want to find the minimum value of h that satisfies this equation, since Stevie wants to make at least $1200.
To do this, we need to estimate the additional costs incurred during cleanup. Let's assume that Stevie spends an average of $4 per hour on additional costs (e.g., gasoline, trash bags, etc.). Then, the equation becomes:
$12h - $1375 = $4h + $175
Simplifying further, we get:
$8h = $1200
h = 150
Therefore, Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment and the estimated additional costs incurred during cleanup.
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Lindsey wears a different outfit every day. Her outfit consists of one top, one bottom, and one scarf.
How many different outfits can Lindsey put together if she has 3 tops, 3 bottoms, and 3 scarves from which to choose? (hint: the
counting principle)
3 outfits
B9 outfits
24 outfits
D) 27 outfits
HELP WORTH 30 POINTS
What is the value of b?
100
110
55
90
Ozone (O3) is a major component of air pollution in many cities. Atmospheric ozone levels are influenced by many factors, including weather. In one study, the mean percent relative humidity (x) and the mean ozone levels (y) were measured for 120 days in a western city. Mean ozone levels were measured in ppb. The following output (from MINITAB) describes the fit of a linear model to these data. Assume that assumptions 1 through 4 for errors in linear models hold.
The regression equation is
Ozone = 88. 8 - 0. 752 Humidity
Predictor Coef SE Coef T P
Constant 88. 761 7. 288 12. 18 0
Humidity -0. 7524 0. 13024 -5. 78 0
S = 11. 43 R-Sq = 22. 0% R-Sq(adj) = 21. 4%
Predicted Values for New Observations
New Obs Fit SE Fit 95. 0% CI 95. 0% PI
1 43. 62 1. 2 (41. 23 46. 00) (20. 86, 66. 37)
Values of Predictors for New Observations
New Obs Humidity
1 60
Required:
a. What are the slope and intercept of the least-squares line?
b. Is the linear model useful for predicting ozone levels from relative humidity? Explain.
c. Predict the ozone level for a day when the relative humidity is 50%.
d. What is the correlation between relative humidity and ozone level?
e. The output provides a 95% confidence interval for the mean ozone level for days where the relative humidity is 60%. There are n = 120 observations in this data set. Using the value "SE Fit," find a 90% confidence interval.
f. Upon learning that the relative humidity on a certain day is 60%, someone predicts that the ozone level that day will be 80ppb. Is this a reasonable prediction? If so, explain why. If not, give a reasonable range of predicted values
a. The slope and intercept of the least-squares line are -0.752 and 88.761, respectively.
b. The linear model may be useful for predicting ozone levels from relative humidity, but only to a limited extent. The R-squared value of 0.22 indicates that only 22% of the variation in ozone levels can be explained by relative humidity.
Additionally, the 95% prediction interval for a new observation (20.86, 66.37) is relatively wide, which suggests that the model may not be very precise in its predictions.
c. To predict the ozone level for a day when the relative humidity is 50%, we plug in x = 50 into the regression equation: Ozone = 88.8 - 0.752(50) = 53.8 ppb.
d. The correlation between relative humidity and ozone level can be found by taking the square root of the R-squared value, which gives us a correlation coefficient of 0.47.
This indicates a moderate positive correlation between relative humidity and ozone levels.
e. To find a 90% confidence interval for the mean ozone level for days where the relative humidity is 60%, we use the formula:
Mean ozone level ± (t-value)*(SE Fit)/sqrt(n), where the t-value is obtained from a t-distribution with n-2 degrees of freedom and a 90% confidence level.
For n = 120 and a 90% confidence level, the t-value is approximately 1.66. Plugging in the values, we get: 43.62 ± 1.66*(1.2)/sqrt(120), which simplifies to (42.39, 44.85).
f. To determine if a predicted ozone level of 80 ppb is reasonable when the relative humidity is 60%, we can calculate the 95% prediction interval for a new observation with x = 60: 43.62 ± 2.064*(11.43) = (21.18, 66.06).
Since the predicted value of 80 ppb falls outside of this range, it is not a reasonable prediction.
A more reasonable range of predicted values would be the 95% prediction interval, which gives us a range of (21.18, 66.06).
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Use the box plots for 3 and 4.
chess
checkers
18
20
10 12 14 16
ages of club members
which group has a greater range?
chess
checkers
the ranges are the same.
Both the chess and checkers group have the same range.
How to find the of ages for each group?
The box plots range for the ages of club members in the chess and checkers group are given. Based on the box plots, it appears that both groups have similar ranges, and it is difficult to determine which group has a greater range.
The range is a measure of variability that indicates the difference between the smallest and largest values in a dataset. In the chess group, the smallest value is 18, and the largest value is 20, which gives a range of 2. In the checkers group, the smallest value is 10, and the largest value is 20, which also gives a range of 10.
Although the difference between the smallest and largest values in the checkers group is greater than that in the chess group, the box plots suggest that the checkers group has more outliers than the chess group. An outlier is a data point that is significantly different from other observations in a dataset. The presence of outliers can increase the range of a dataset.
Therefore, despite the larger difference between the smallest and largest values in the checkers group, the presence of outliers makes it difficult to determine which group has a greater range. Overall, the box plots show that both groups have similar ranges, but the checkers group has more variability in the form of outliers.
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When the mortgage is completely paid off for Mark and Lynne’s house, it will be 3 times as old as it is now. If they have 12 years left on the mortgage, how old is the house right now?
The house is currently 6 years old.
It is mentioned that when the mortgage is completely paid off for Mark and Lynne's house, it will be 3 times as old as it is now. They have 12 years left on the mortgage.
Let's denote the current age of the house as x. When the mortgage is paid off, the house will be x + 12 years old (since they have 12 years left on the mortgage). At that point, the house will be 3 times its current age, so we can write the equation:
x + 12 = 3x
Now we can solve for x:
12 = 2x
x = 6
So, the house is currently 6 years old.
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Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #13
The value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
∵ ΔJLM is a right triangle, as ∠MJL=90°
∴ tan(∠JML)= JL/JM [∵ tan∅=perpendicular/hypotenuse]
⇒ tan(51°)=JL/14
⇒ JL=14×tan(51°)
= 14×1.23
= 17.29
∴ JL=17.29
Again, ΔJKL is a right triangle, with ∠JKL=90°
∴ cos(∠JLK)=KL/JL [∵ cos∅=base/hypotenuse]
⇒cos(72°)= KL/17.29
⇒KL=17.29×cos(72°)
= 17.29×0.309
= 5.34
∴ KL=5.34
Hence, the value of KL is 5.34.
Also, tan(∠JLK)=KJ/KL
⇒tan(72°)=JK/5.34
⇒JK=5.34×tan(72°)
= 5.34×3.077
= 16.434
∴ JK=16.434
And, cos(∠JML)=JM/ML
⇒cos(51°)=14/ML
⇒ML=14/cos(51°)
=14/.629
=22.25
∴ ML=22.25
Hence, the value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
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Gloria buys last year's best-selling novel, in hardcover, for $18.70 . This is with a 15% discount from the original price. What was the original price of the novel?
The original price of the novel is $21.5
How to calculate the original price of the novel ?The first step is to write out the parameters given in the question
Last year, Gloria buys a novel for $18.70
This price is with a discount of 15% form the original price
The original price of the novel can be calculated as follows
15/100 × 18.70
= 0.15 × 18.70
= 2.805
The next step is to add 2.805 to the price of the novel last year($18.70)
= 18.70 + 2.805
= 21.5
Hence the original price of the novel before the addition of the discount is $21.5
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Newton’s Method!!!!!!
The approximate value of x using the newton method is 0.7
Calculating the value of x using the newton methodFrom the question, we have the following expression that can be used in our computation:
[tex]\frac{x}{x^2+1}-\sqrt{1-x}[/tex]
Also, we have the function f(x) to be
[tex]f(x) = x(x^2+1)^{-1} -\sqrt{1-x}[/tex]
And we have the differentiated function to be
[tex]f'(x) = \frac{1}{x^2+1} - \frac{2x^2}{(x^2 + 1)^2} + \frac{1}{2\sqrt{1-x}}[/tex]
The value of x using the newton method is given as
[tex]x_n = x_{n-1} - \frac{f(x_{n-1})}{f'(x_{n-1})}[/tex]
Set [tex]x_{n-1}[/tex] = 0
So, we have
x₁ = 0 - -1/1.5 = 0.67
x₂ = 0.67 - undefined = undefined
So, we have
x₁ = 0.67
When approximated, we have
x = 0.7
This means that the value of x using the newton method is 0.7
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what is the aproximate length of the base triangle ?
The approximate length of the base of the triangle is 5 units
What is area of triangle?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as;
A = 1/2 bh
The hexagon is divided into six equal triangles.
The area of the hexagon is 65 units²
Therefore, the area of the triangle = 65/6
= 10.83
Area of a triangle = 1/2 b h
height = 4.3 units
10.83 = 1/2 × 4.3 × b
4.3b = 10.83 × 2
4.3b = 21.66
divide both side by 4.3
b = 21.66/4.3
b = 5.04
therefore the approximated value of the base is 5 units.
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2n-1/3=n+2/2 please help me
[tex] \sf \longrightarrow \: \frac{2n - 1}{3} = \frac{n + 2}{2} \\ [/tex]
[tex] \sf \longrightarrow \: 2( 2n - 1) = 3(n + 2) \\ [/tex]
[tex] \sf \longrightarrow \: 4n - 2 = 3n +6 \\ [/tex]
[tex] \sf \longrightarrow \: 4n = 3n +6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: 4n - 3n= 6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: 1n= 6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: n= 8\\ [/tex]
[tex] \longrightarrow { \underline{ \overline{ \boxed{ \sf{\: \: \: n= 8 \: \: \: }}}}} \: \: \bigstar\\ [/tex]
a)cos 165 in terms of sine and cosine of acute angle
Cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).
How did we get the value?We can use the trigonometric identity cos(180 - x) = -cos(x) to find cos(165) in terms of cosine of an acute angle.
Since 165 = 180 - 15, we have:
cos(165) = cos(180 - 15) = -cos(15)
To express cos(15) in terms of sine and cosine of an acute angle, we can use the following trigonometric identities:
sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)
Let's take x = 7.5, which is half of 15 (the acute angle):
sin(15) = 2sin(7.5)cos(7.5)
cos(15) = cos^2(7.5) - sin^2(7.5)
Now, we can solve for cos(15):
cos(15) = cos^2(7.5) - sin^2(7.5)
= (1 - sin^2(7.5)) - sin^2(7.5)
= 1 - 2sin^2(7.5)
Therefore, we have:
cos(165) = -cos(15)
= -[1 - 2sin^2(7.5)]
= -1 + 2sin^2(7.5)
So, cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).
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The Bullock family is looking to rent a
large truck for their upcoming move. With Heather's Moving, they would pay
$10 for the first day plus $8 per
additional day. With Newton Rent-a-
Truck, in comparison, the family would
pay $80 for the first day plus $1 per
additional day. Before deciding on which
company to use, Mrs. Bullock wants to
find out what number of additional days
would make the two choices equivalent
with regards to cost. What would the
total cost be?
To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:
Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x
To find the point at which the costs are equal, we can set the equations equal to each other:
10 + 8x = 80 + x
Now, we can solve for x (additional days):
7x = 70
x = 10
So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:
Total cost = 10 + 8(10) = 10 + 80 = $90.
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Identify the parent function for g(x) = (x + 3)^2 and describe the transformation.
The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.
What is function?Each element of a set (referred to as the domain) is mapped by a rule known as a function to a particular element of this other set (called the range). A function is, in other words, a connection between two subsets in which every member of the domain has a unique relationship to every element of the range. One popular approach to write a function is via function notation, which entails writing the function name surrounded by the incoming signal in parentheses, as in the following example: f (x). For instance, the formula f(x) = 2x + 1 takes the input x and produces the result 2x + 1.
given,
The fundamental quadratic function f(x) = x² serves as the parent function for g(x) = (x + 3)².
Since the argument of the function (x + 3) is x shifted left by 3 units, the graph of f(x) is horizontally displaced to the left by 3 units.
Given that the coefficient of the squared term is 1, the graph of the resulting function is shifted up by a factor of 1.
As a result, the transformation can be represented as a 3 unit horizontal shift and a 1 unit vertical stretch.
The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.
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Which amount should be entered for the balance after the atm withdrawal on 6/2/18?a) $1346.42b) $1456.42c) $1536.42d) $1756.42
Unfortunately, there is no way to answer this question without more information.
We would need to know the amount of the ATM withdrawal, as well as the starting balance before the withdrawal, in order to calculate the ending balance.
For example, if the starting balance was $1500 and the withdrawal was for $50, the ending balance would be $1450.
However, if the starting balance was $1300 and the withdrawal was for $50, the ending balance would be $1250.
Without this information, we cannot determine the correct answer.
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AREA OF TRAPEZOID PLS ANSWER ASAP
If Tan=3 /5 fine the remaining trigonometric functions
The remaining trigonometric functions are:
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3
sec (θ) = (√34)/5
cot(θ) = 5/3
How to find the remaining trigonometric functions?Trigonometry is a branch of mathematics that deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Since tan θ = 3 /5
Recall: tan = opposite/adjacent. Thus, opposite = 3, adjacent = 5
hypotenuse = √(3²+5²) = √34
Therefore, the remaining trigonometric functions are
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3 (csc (θ) = 1/sin (θ))
sec (θ) = (√34)/5 (sec(θ) = 1/cos (θ))
cot(θ) = 5/3 (cot(θ) = 1/tan (θ))
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Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 3x^4 – 4x^3-12x^2 + 1, {-2, 3] absolute minimum value
absolute maximum value
The absolute maximum value of f(x) on the interval [-2,3] is 201 and occurs at x = -2, and the absolute minimum value of f(x) on the interval [-2,3] is -79 and occurs at x = 2.
To find the absolute maximum and absolute minimum values of f(x) on the interval [-2,3], we need to first find the critical points of the function and evaluate the function at these points as well as at the endpoints of the interval.
To find the critical points, we need to find where the derivative of the function equals zero or does not exist. Taking the derivative of f(x), we get:
f'(x) = 12x^3 - 12x^2 - 24x
Setting this equal to zero and factoring out 12x, we get:
12x(x^2 - x - 2) = 0
Using the quadratic formula to solve for x^2 - x - 2 = 0, we get:
x = -1, 0, 2
These are our critical points.
Now we evaluate f(x) at the critical points and the endpoints of the interval:
f(-2) = 201
f(-1) = 6
f(0) = 1
f(2) = -79
f(3) = 16
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A sculpture is made of solid tin in the shape of a cone. The sculpture is 70 inches tall, and its base has a radius of 9 inches. If tin costs $1. 75 per cubic inch,
how much did the tin for the sculpture cost?
Use 3. 14 for 1, and do not round your answer.
Answer:
Step-by-step explanation:
A flat screen television costs $1600. It may be purchased for $100 down and 24 easy monthly payments of $80 each. What simple interest rate was charged on the purchase per monthly payment?
The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.
To determine the simple interest rate charged per monthly payment on the flat screen television, please follow these steps:
1. Calculate the total amount paid in monthly payments: 24 payments * $80 = $1920.
2. Subtract the down payment: $1920 - $100 = $1820.
3. Subtract the original cost from the total amount paid: $1820 - $1600 = $220. This is the total interest paid.
4. Divide the total interest by the number of monthly payments: $220 / 24 = $9.1667 interest per month.
5. Calculate the interest rate per monthly payment: ($9.1667 / $1600) * 100 = 0.5735% per month.
The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.
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