Evaluate (if possible) the six trigonometric functions of the real number t. (if an answer is underfunded, enter UNDEFINED)
T= 4 π/3
Sin t=
Cos t=
Tan t=
Csc t=
Sec t=
Cot t=
Answers
Answer:
Step-by-step explanation:
sin= - square root 3/2
cos= -1/2
tan= square root 3
csc= -2 square root 3/2
sec= -2
cot= square root3/4
Answer:
[tex]\sin\left(\frac{4\pi}{3}\right)=-\frac{\sqrt{3}}{2}\\\cos\left(\frac{4\pi}{3}\right)=-\frac{1}{2}\\\tan\left(\frac{4\pi}{3}\right)=\sqrt{3}\\\csc\left(\frac{4\pi}{3}\right)=-\frac{2\sqrt{3}}{3}\\\sec\left(\frac{4\pi}{3}\right)=-2\\\cot\left(\frac{4\pi}{3}\right)=\frac{\sqrt{3}}{3}[/tex]
We first find the corresponding angle of 4π/3.
[tex]\frac{4\pi}{3}-\pi=\frac{\pi}{3}[/tex]. And 4π/3 is in the third quadrant. There tan and cot are positive and rest are negative.
[tex]\sin\left(\frac{4\pi}{3}\right)=-\sin\left(\frac{\pi}{3}\right)=-\frac{\sqrt{3}}{2}\\\cos\left(\frac{4\pi}{3}\right)=-\cos\left(\frac{\pi}{3}\right)=-\frac{1}{2}\\\tan\left(\frac{4\pi}{3}\right)=\tan\left(\frac{\pi}{3}\right)=\sqrt{3}\\\csc\left(\frac{4\pi}{3}\right)=-\csc\left(\frac{\pi}{3}\right)=-\frac{2}{\sqrt{3}}=-\frac{2\sqrt{3}}{3}\\\sec\left(\frac{4\pi}{3}\right)=-\sec\left(\frac{\pi}{3}\right)=-2\\\cot\left(\frac{4\pi}{3}\right)=\cot\left(\frac{\pi}{3}\right)=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
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Related Questions
Question 1 of 10
2 Points
Harry took out an 80/20 mortgage to buy a house costing $175,000. The first
(80%) mortgage has an interest rate of 4.75%, and the second (20%)
mortgage has an interest rate of 7.525%. Both the first mortgage and the
second mortgage are 30-year fixed-rate mortgages. What is his total
mortgage payment for this house?
A. $730.31
B. $975.63
C. $245.32
D. $805.87
Answers
Answer:
Its b got it correct
The total monthly mortgage payment for the house is $975.63
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
The principle amount is $175000
80% of 175000 is = = $140000
20% of 175000 is = = $35000
Emi formula is :
p*r*(1-r)^n/(1-r)^n-1
For 1st part:
p = 140000
r = 4.75/12/100=0.00395
n = 360
Putting values in formula we get
= $729.508
For 2nd part:
p = 35000
r = 7.525/12/100=0.00627
n = 360
Putting values in formula we get
= $245.301
Adding both the monthly payments:
974.809 dollars
This is closest to option A.
So, option A is the answer.
And for 30 years the mortgage payment will be = 351226.80 dollars
Hence, The total monthly mortgage payment for the house is $975.63.
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A group of friends went to play minigolf at Adventureland. Anna's score was 26 putts, Daniela's score was 313131 putts, Luiza's score was 39 putts, and Vera's score was 32 putts.
Find the mean absolute deviation (MAD) of the data set.
Answers
Answer:
3.5
Step-by-step explanation:
1 / 3
First, let's find the mean.
\dfrac{26+31+39+32}{4} = \dfrac{128}{4}= \blueD{32} \text{ putts}
4
26+31+39+32
=
4
128
=32 puttsstart fraction, 26, plus, 31, plus, 39, plus, 32, divided by, 4, end fraction, equals, start fraction, 128, divided by, 4, end fraction, equals, start color #11accd, 32, end color #11accd, start text, space, p, u, t, t, s, end text
Hint #22 / 3
Next, let's find the distance each data point is from the mean.
Data point Distance from the mean
262626 \blueD{32}-26 = 632−26=6start color #11accd, 32, end color #11accd, minus, 26, equals, 6
313131 \blueD{32}-31 = 132−31=1start color #11accd, 32, end color #11accd, minus, 31, equals, 1
393939 39-\blueD{32} = 739−32=739, minus, start color #11accd, 32, end color #11accd, equals, 7
323232 32-\blueD{32} = 032−32=032, minus, start color #11accd, 32, end color #11accd, equals, 0
Hint #33 / 3
The mean absolute deviation (MAD) is the mean of the distances from the mean.
\dfrac{6+1+7+0}{4} = \dfrac{14}{4}= 3.5\text{ putts}
4
6+1+7+0
=
4
14
=3.5 putts I hope it helps.
Find the mean,median and range of the following list of values and choose the correct result.
8, 9, 10, 10, 10, 11, 11, 11, 12, 13
Answers
Mean: 10.5
Median: 10.5
Range: 5
--------------------------------------------
To find the mean you order the numbers then add then divide.
Add
8+9+10+10+10+11+11+11+12+13=105
Divide
105÷10=10.5
Mean = 10.5
--------------------------------------------
Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers.
Find the middle number. Put your left finger on 8 and your right finger on 13. Move your left finger to the right to 10 and move your right finger to 11.
the middle number is 10.5 so therefore it is the median.
--------------------------------------------
To find the range you subtract the biggest number to the smallest number.
Subtract
13-8=5
Therefore 5 is the range
Answer:
The median is 10.5 the range is 5 and the mean is 10.5
Step-by-step explanation:
To find the median you have to cross out each number till you get 2 since there are 10 numbers together then add 10 and 11 and get 21 divide by 2 which gives you 10.5 to find the mean add all the numbers then divide 105 by 10 and get 10.5 to find the range take 13-8 and get 5
Which expression is equivalent to ? Assume that the denominator does not equal zero.
Answers
Answer:
A) 4ab^2
Step-by-step explanation:
19*4 = 76
(a^2*b^3)/(a*b) = a*b^2
Implies, option A.
What is the volume of a cylinder, in cubic inches, with a height of 2 inches and a base diameter of 4 inches? Round to the nearest tenths place
Answers
Answer:
the answer for the volume of the cylinder is V≈25.13in³
Answer:
h=2 d=4
r=4/2 , radius is half of the diameter
r=2
V=π r^2h
V= π x (2)²×2
substitute variables into formula V=25.132741228718
the nearest tenths place V=25.1 inches
How to do the problem and what the answer is this thing is due today(30 points!)
Answers
Answer:
40°
Step-by-step explanation:
complementary angels makes the sum of two angles = 90°
so
<ABC + < CBD = 90°
if <ABC = 50°
then 90° - 50° = 40°
Please do this for points and brainleyst awnser
Answers
Question 1 Volume = 1008
Question 2 Area = 27.5
Question 2 Volume = 116 7/8
Question 3 Area = .25
Question 3 Volume = .125
Question 4 Area = 9.61
Question 4 Volume = 27.791
Joseph's company offers a reimbursement package of $0.45 per mile plus
$175 a year for maintenance. If x represents the number of miles, which
equation below models C the total amount of reimbursement the company
offers?
•A. C = 0.45 + 175x
•B. C = 0.45x + 175
•C. C = 45 + 175x
•D. C = 45x + 175
Answers
Answer:
B
Step-by-step explanation:
175 is the yearly cost which is the constant
The cost is related to the miles so that’s why they’re multiplied together
The total amount of reimbursement the company offers will be C = 0.45x + 175. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Joseph's company offers a reimbursement package of $0.45 per mile plus $175 a year for maintenance.
Let 'x' be the number of miles and 'C' be the number total amount. Then the equation of the line is given as,
C = 0.45x + 175
The total amount of reimbursement the company offers will be C = 0.45x + 175. Then the correct option is B.
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Which equation is the BEST fit for the data in the table?
Answers
Answer:
C
Step-by-step explanation:
It cannot be A because it is a parabola, and what that means is the x^2. So, we can immediately eliminate that. This is because if you do a sketch of it it was the "U" shape. I am not positive, but I think that it is C because of the pattern going on in the y-coordinate. It goes +2, +4, then presumably +6. So then the (0,y) is (0,12). This would mean that the equation would end with +12. That is why C is the best choice. I hope that answered your question, and is correct!
A shop sells fence panels with a wooden frame going all the way round each panel. The price of each panel is based on the area of the panel and the length of the wooden frame around the panel.
Use the prices given given in the attachment to find out how much the shop charges per square metre of the panel and per metre for the wooden frame .
a) Each 1m² of fence panel costs:?
b) I metre of wooden frame costs:?
Plz answer this question.
Answers
Answer:
a) Each 1m² of fence panel costs: £2
b) I metre of wooden frame costs: £1
Step-by-step explanation:
Let the price of 1 sq.m. of fence panel be x
Let the price of 1 m of wooden frame be y
In Fig 1
Length = 4 m
Breadth = 3 m
Area =[tex]Length \times breadth = 4 \times 3 = 12 sq.m.[/tex]
Cost of 1 sq.m. = x
Cost of 12 sq.m. = 12x
Perimeter =2(l+b)=2(4+3)=14 m
Cost of 1 m of wooden frame = y
Cost of 14 m of wooden frame = 14y
We are given that total cost of framing and fencing is 38
So. 12x+14y=38 ----1
In Fig 2
Length = 6 m
Breadth = 2 m
Area =[tex]Length \times breadth = 6 \times 2 = 12 sq.m[/tex].
Cost of 1 sq.m. = x
Cost of 12 sq.m. = 12x
Perimeter =2(l+b)=2(6+2)=16 m
Cost of 1 m of wooden frame = y
Cost of 16 m of wooden frame = 16y
We are given that total cost of framing and fencing is 40
So. 12x+16y=40---2
Substitute the value of 12x form 1 in 2
38-14y+16y=40
2y=2
y=1
Substitute the value of y in 2
12x+16=40
12x=24
x=2
So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1
In fig 3
To verify :
Length = 3 m
Breadth = 5 m
Area = [tex]Length \times breadth = 3 \times 5 = 15 sq.m.[/tex]
Cost of 1 sq.m. = 2
Cost of 12 sq.m. =[tex]15 \times 2 = 30[/tex]
Perimeter =2(l+b)=2(3+5)=16 m
Cost of 1 m of wooden frame = 1
Cost of 16 m of wooden frame = 16
So, Total cost = 30+16=46
We are given that cost of fencing and framing is 46
Thus verified
Hence
a) Each 1m² of fence panel costs: £2
b) I metre of wooden frame costs: £1
the inverse of this equation
Answers
Answer:
[tex]{f}^{ - 1}(x) = \frac{x + 11}{ - 5} [/tex]
Step-by-step explanation:
[tex]f(x) = - 5x - 11 \\ - 5x - 11 =x \\ - 5x = x + 11 \\ {f}^{ - 1}(x) = \frac{x + 11}{ - 5} [/tex]
Sam is transferring files from his friend's laptop into his flash drive. This is the formula for the size of the files on Sam's friends drive S (measured in megabytes) as a function of time t (measured in seconds): S(t)=5t+45
Use the above information to answer the following:
When the transfer began the drive had___ megabytes of files on it
Every 10 seconds, an additional___ megabytes are transferred into the drive.
Answers
Answer:
1. 45 megabytes
2. 50 megabytes
Step-by-step explanation:
Given
S(t) = 5t + 45
Required
Find S(t) when the transfer began
And find the additional transfer size at interval of 10 seconds
When the file transfer initially began, the value of t is 0.
Given that S(t)=5t+45.
Substitute 0 for t
S(0)=5 * 0 + 45
S(0) = 0 + 45
S(0) = 45.
Hence, the hard drive had 45 megabytes on it when the transfer started.
At every interval of 10 seconds. We take t to be 10, 20, 30...seconds
When t = 10
S(t)=5t+45 becomes
S(10) = 5(10) + 45
S(10) = 50 + 45
S(10) = 95 megabytes
When t = 20
S(t)=5t+45 becomes
S(20) = 5(20) + 45
S(20) = 100 + 45
S(20) = 145 megabytes
When t = 30
S(t)=5t+45 becomes
S(30) = 5(30) + 45
S(30) = 150 + 45
S(30) = 195 megabytes
Calculating the difference
Difference = S(30) - S(20) or S(20) - S(10)
Difference = 195 - 145 or 145 - 95
Difference = 50 or 50
See that the difference is the same.
So, at every 10 seconds interval, there's an additional 50 megabytes transferred
SOMEONE HELP PLSSS
suppose your friends parents invest $10,000 in an account paying 5% compounded annually. what will the balance be after 5 years?
Answers
Answer:
12,762.82$
Step-by-step explanation:
10,000(1+0.05)^5
Shane wrapped the kite with paper. How many square inches of paper did Shane use to cover the front and back? 45 POINTS
Answers
Answer:
576
Step-by-step explanation:
First off, we can use the area of a kite formula, (D1*D2)/2 to get the area of one side of the kite, which is simplified to 18 * 32 : which gets us 288. But because we are looking for the area of the front and back side, we multiply 288 by 2- getting the final answer of 576.
Answer:
576
Step-by-step explanation:
Classify the following triangle as acute, obtuse, or right.
40°
90°
50"
O A. Acute
O B. Right
O C. Obtuse
D. None of these
Answers
Answer:
B. 90
Step-by-step explanation:
In a triangle if one of the angle is 90 deg the triangle is said to be a RIGHT ANGLED TRIANGLE.
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Given triangle is a right-angle triangle. option B is correct.
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
A triangle is said to have a right angle if one of its angles is precisely 90 degrees. There are several techniques to spot a right angle triangle, including:
Take a look at the icon: A little square positioned in the corner of an angle serves as the symbol in geometry for a right angle. If you observe this symbol in one of a triangle's angles, the triangle is a right-angle triangle since the angle is a right angle.Another technique to tell if a triangle has right angles is to measure the angles with a protractor. The triangle is a right-angle triangle if one of the angles is exactly 90 degrees.Use the Pythagorean Theorem: The Pythagorean Theorem states that in a right-angle triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.Therefor, the given triangle is a right-angle triangle.
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6 Trendy T-Shirts has decided to manufacture a new design. It will
cost $400 plus $3 per shirt to produce them, and Trendy plans to
spend $5000 on advertising. The shirts will sell for $12 each.
A. How many shirts must be sold to break even (total cost equals
income from sales)?
B. What is Trendy's income (or total cost) for that many shirts?
Answers
Answer:
A)
400+3x+5000=12x
5400 = 9x
x =600
B)
Profit: zero (break even)
Total cost or Income from 600 Sales: $7200
Suppose the length of an oarfish is normally distributed with a mean of 6.5 m and a standard deviation of 1.5 m. Which group describes 16% of the oarfish population? Select each correct answer. oarfish that are between 6.5 m and 9.5 m oarfish that are shorter than 5 m oarfish that are between 3.5 m and 9.5 m oarfish that are longer than 8 m
Answers
Answer:
Step-by-step explanation:
Let x be the random variable representing the length of an oarfish. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
The given probability value is 16% = 0.16. From the normal distribution table, the z score corresponding to the probability value is - 0.99
This indicates that the sample mean is lower than the population mean
Therefore,
- 0.99 = (x - 6.5)/1.5
- 0.99 × 1.5 = x - 6.5
- 1.5 = x - 6.5
x = - 1.5 + 6.5
x = 5m
The correct answer is
oarfish that are shorter than 5 m
Answer:
oarfish that are shorter than 5
oarfish that are longer than 8 m
I Just took the test!
Find def, help geometry
Answers
Answer:
d
Step-by-step explanation:
How many extraneous solutions does the equation below have? StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction 0 1 2 3
Answers
Answer:
a. 0
Step-by-step explanation:
hope this helps!
The solutions to the equation n³+3n²+n-33=0 are n=-11, n=-3, and n=1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, 9/(n²+1) = (n+3)/4.
Here, 9×4=(n²+1)×(n+3)
36=n²(n+3)+1(n+3)
36=n³+3n²+n+3
n³+3n²+n+3-36=0
n³+3n²+n-33=0
The equation n³+3n²+n-33=0 can be solved by factoring. The factors of -33 are -1 and 33. Since the coefficient of the n³ term is 1, this means that n-1 and n+33 are factors of the equation.
Dividing both sides of the equation by n-1, we get:
n²+3n+33/(n-1)=0
Factorizing the numerator, we get:
(n+11)(n+3)=0
Solving this equation, we get n=-11 and n=-3.
Therefore, the solutions to the equation n³+3n²+n-33=0 are n=-11, n=-3, and n=1.
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PLEASE HELP!!
The figure is made up of a rectangle and 2 right triangles.
What is the area of the figure?
O 1259 units2
O 1292 units2
O 1413 units2
O 1566 units2
Answers
The rectangle is 28×34 and the two triangles are (1/2) 11 (28) and (1/2) (9)(34)
A = 28(34) + (1/2) 11 (28) + (1/2) (9)(34)
A = 1259
Answer: 1259 sq units
Solve for Q. Reduce any fractions to lowest terms. Don’t round your answer, I don’t use mixed fractions.
50q + 43 > -11q +70
Answers
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > -11q +70
Add 11 q to each side
50q+11q + 43 > -11q+11q +70
61q +43 > 70
Subtract 43 from each side
61q+43-43 > 70-43
61q > 27
Divide each side by 61
61q/61 >27/61
q > 27/61
Answer:
q > 27/61
Step-by-step explanation:
hope this helps!!
Which number is divisible by 5
A 44
B 125
C 116
D 114
Answers
Answer:
B
Step-by-step explanation:
Please help with this
Answers
Answer:
C. [tex]c = \frac{-7+-\sqrt{129} }{8}[/tex]
Step-by-step explanation:
Before we start, you can think of the variable "c," as x.
The quadratic formula/equation is:
[tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
The setup is:
[tex]ax^2+bx+c=0[/tex]
[tex]4c^2+7c-5=0[/tex]
Plug in the numbers accordingly to the letter associated, like so:
[tex]x = \frac{-7+-\sqrt{7^2-4(4)(-5)} }{2(4)}[/tex]
[tex]x = \frac{-7+-\sqrt{49+80} }{8}[/tex]
[tex]x = \frac{-7+-\sqrt{129} }{8}[/tex]
In 1925, the population of a city was 90,000. Its
population increases by 2.1% per year. What will the population be in 2020?
Answers
Answer:
17,955,000
Step-by-step explanation:
Answer:
闭嘴黑鬼
Step-by-step explanation:
I really need to solve this quick.
Answers
Answer:
a)
Theoretical: 10/30 = 1/3
Experimental: 12/30 = 6/15
Step-by-step explanation:
the theoretical probability is if every number was rolled an equal amount of times. as there are 3 options and a number was chosen 30 times, if we divide 30 by 3 we will get the theoretical probability of choosing a 2
30 ÷ 3 = 10
the theoretical probability = 10/30 or simplified 1/3
the experimental probability is the result when one of the numbers from
1 to 3 were actually randomly selected 30 times. the chart shows that the 2 was selected 12 times out of 30 therefore the experimental probability = 12/30 or simplified 6/15
Theoretical:
fraction: 1/3
decimal: 0.33∞
percentage: 33%
Experimental:
fraction: 6/15
decimal: 0.4
percentage: 40%
I hope this was helpful :-)
helpppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz ASAP
Answers
Answer:
7x=42
Solve:
7x=42
7x=42/7
/7
x = 6
6 is the maximum cost lisa can spend for each party favor bag.
What is the solution to the equation = 3?
x = 1
x = 3
x = 9
x = 27
Answers
Multiply both sides by 9.
x/9 = 3
(x/9) * (9) = (3) * (9)
x=27
The solution of the expression x/9 = 3 is,
⇒ x = 27
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The expression is,
⇒ x/9 = 3
Now, Simplify the expression as;
⇒ x/9 = 3
Multiply by 9, we get;
⇒ 9 × x/9 = 9 × 3
⇒ x = 27
Thus, The solution is,
⇒ x = 27
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What is the product of 2x + y and 5x – y + 3?
Answers
Answer:10x^2+11xy-6y^2
Step-by-step explanation:
( 2 x + 3 y ) ( 5 x − 2 y ) = 2 x ( 5 x − 2 y ) + 3 y ( 5 x − 2 y )
= 10 x 2 − 4 x y + 15 x y − 6y 2
= 10 x 2 + 11 x y -6 y 2 .
What is the area of the kite?
Answers
Answer:168
Step-by-step explanation:
.5×16×21
8×21
Answer: 336in ^2
Step-by-step explanation:
multiply 16*21 =336in^2
−2y<8
y<−8
y<−4
y>−8
y>−4
Answers
Answer:
y > -4
Step-by-step explanation:
−2y<8
Divide each side by -2, remembering to flip the inequality since we are dividing by a negative
-2y/-2 > 8/-2
y > -4
Answer:
Last option
y > -4
Step-by-step explanation:
-2y < 8
Switch sides
-8 < 2y
-4 < y
Or
y > -4
