The volume of the sphere that lies between the two cones is approximately 43.53 cubic units.
How to calculate the volume of the sphereTo find the volume of the sphere that lies between the given cones, we first need to determine the limits of integration.
Since the sphere has a radius of 6 (since x² + y² + z² = 36), we can use spherical coordinates to express the volume as an integral. Let's first consider the cone z = √3x² + 3y².
In spherical coordinates, this is equivalent to z = ρcos(φ)√3, where ρ is the radial distance and φ is the angle between the positive z-axis and the line connecting the origin to the point.
Similarly, the cone z = √(x²+y²)/3 can be expressed in spherical coordinates as z = ρcos(φ)/√3.
Since we're only interested in the volume of the sphere between these cones, we can integrate over the limits of ρ and φ that satisfy both inequalities.
The limits of ρ will be 0 (the origin) to 6 (the radius of the sphere).
To find the limits of φ, we need to solve for the intersection points of the two cones.
Setting the two equations equal to each other, we get:
ρcos(φ)√3 = ρcos(φ)/√3
Solving for φ, we get:
tan(φ) = 1/√3 Using the inverse tangent function, we find that: φ = π/6, 7π/6
So the limits of integration for φ will be π/6 to 7π/6.
Finally, we need to integrate over the full range of θ (the angle between the positive x-axis and the line connecting the origin to the point).
This will be 0 to 2π.
Putting it all together, the volume of the sphere between the two cones is:
∫∫∫ ρ^2sin(φ) dρ dφ dθ
With limits of integration:
0 ≤ ρ ≤ 6 π/6 ≤ φ ≤ 7π/6 0 ≤ θ ≤ 2π
Evaluating this integral gives:
V = 288π/5 - 216√3π/5
So the volume of the sphere that lies between the two cones is approximately 43.53 cubic units.
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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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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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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:
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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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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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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What is the difference between factored form and non-factored form?
Factored form is a way of expressing a polynomial as a produce of factors, place each factor is a polynomial accompanying a degree of 1 or greater.
Factored form, on the other hand, is the polynomial terms written in polynomial expanded form, outside any universal factors.
What is the difference?Factored and non-factored forms are ways to express polynomial expressions, which involve variables raised to non-negative integer powers with constant coefficients. X² + 3x + 2 is a polynomial expression.
Factored form is expressing it as a product of factors with a degree of 1 or greater. The polynomial x² + 3x + 2 can be factored as (x + 1)(x + 2). Non-factored form is the expanded expression without common factors. The polynomial (x + 1)(x + 2) can be expressed as x² + 3x + 2 in non-factored form. Factored form is a product of factors, while non-factored form is the expanded form without common factors.
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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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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
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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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
A function f(x) = 3x^4 dominates g(x) = x^4. True False
The given statement "A function f(x) = 3x^4 dominates g(x) = x^4" is True, which means that as x gets larger, the value of f(x) will increase much more rapidly than the value of g(x).
As x increases or decreases, the 3x^4 term in f(x) will grow faster or be larger in magnitude than the x^4 term in g(x). Since f(x) grows faster or has a larger magnitude than g(x), we can conclude that f(x) dominates g(x).
Therefore, the function f(x) = 3x^4 has a higher degree than g(x) = x^4
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Malia had 15 lb of birdseed. She fed her birds 5 lb of birdseed every day until all the birdseed was gone. For how many days did Malia feed the birdseed to her birds? A.20 days B. 3 days C.90 days D.75 days
Answer:
B
Step-by-step explanation:
15 pounds and 5 pounds per day so to figure out how many days you do division. The equation is 15÷5=3 so the answer is 3 days.
-9 -7 -5 sequence name pls
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
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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Solve (d-8) (6d-3) using the box method show work
6d^2 - 51d + 24
that's it
...............................
Calculate the lenght of the shadow cast on level groundby a radio mast 90m high when the elevationof the sun is 40degree
The length of the shadow cast on level ground by a radio mast 90m high when the elevation of the sun is 40 degrees is approximately 85.3 meters.
To calculate the length of the shadow, we need to use trigonometry. We can imagine a right-angled triangle, where the height of the mast is the opposite side, the length of the shadow is the adjacent side, and the angle of elevation is 40 degrees.
Using the trigonometric function tangent (tan), we can find the length of the shadow, which is equal to the opposite side (90m) divided by the tangent of the angle of elevation (40 degrees). Therefore, the length of the shadow is approximately 85.3 meters.
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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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How to simplify radical expressions with variables?.
To simplify radical expressions with variables, identify perfect square factors, simplify the radical by taking out the largest possible integer factor that is a perfect square, and then multiply by the remaining factor outside the radical. Repeat the process until no more simplification is possible.
To simplify radical expressions with variables, follow these steps
Factor the expression under the radical sign into its prime factors.
Identify any perfect squares within the factors.
Rewrite the expression with the perfect squares outside the radical sign and the remaining factors inside.
Simplify any remaining radicals if possible.
Combine any like terms if necessary.
For example, to simplify the expression √(12x²y), you would first factor 12x²y into 2 * 2 * 3 * x * x * y. Then, you would identify the perfect square of x² and rewrite the expression as 2x√(3y). Finally, you could simplify further if possible, but in this case, the expression is already in its simplest form.
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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]
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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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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Question 3 Next ſsin"" e cos"" Evaluate the indefinite integral xdu
But there seems to be some missing information in your question. Please provide more context or details so that I can assist you accurately.
Hi! I'd be happy to help you evaluate the indefinite integral. Based on the provided terms and information, it seems like you want to evaluate the following integral:
∫x * sin(e * cos(x)) dx
To solve this integral, we can use integration by parts, which is defined as:
∫u dv = u * v - ∫v du
Let's choose u = x and dv = sin(e * cos(x)) dx. Then, we need to find du and v:
du = dx
v = ∫sin(e * cos(x)) dx
Unfortunately, the integral for v does not have a simple closed-form expression. However, you can use numerical methods or software (like Wolfram Alpha) to approximate it. Once you have an approximation for v, you can plug it back into the integration by parts formula to obtain an approximation of the original integral:
∫x * sin(e * cos(x)) dx ≈ x * v - ∫v dx
Keep in mind that this is an indefinite integral, so don't forget to add the constant of integration, C, to your final answer.
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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. "--
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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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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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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HELP WORTH 30 POINTS
What is the value of b?
100
110
55
90
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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