use reference angles to evaluate sec(13Pi/4) enter exact answers
Answers
Answer:
-√2
Explanation:
Given the trigonometric function:
\(\sec \mleft(\frac{13\pi}{4}\mright)\)• The function cos is periodical with a period of 2π
,• The reference angle is an angle less than 2π and that is positive.
We can write this as:
\(\sec \mleft(\frac{13\pi}{4}-2\pi\mright)=\sec \mleft(\frac{5\pi}{4}\mright)\)Since the angle π is in the third quadrant, subtract π from it.
\(\begin{gathered} \sec \mleft(\frac{5\pi}{4}\mright)=\sec \mleft(\frac{5\pi}{4}-\pi\mright) \\ =\sec \mleft(\frac{\pi}{4}\mright) \end{gathered}\)• Secant is the inverse of cosine.
,• Note that cosine is negative in Quadrant III.
Thus:
\(\begin{gathered} \sec \mleft(\frac{\pi}{4}\mright)=\frac{1}{-\cos \mleft(\frac{\pi}{4}\mright)} \\ =1\div-\frac{1}{\sqrt[]{2}} \\ =1\times-\sqrt[]{2} \\ =-\sqrt[]{2} \end{gathered}\)Therefore:
\(\sec (\frac{13\pi}{4})=-\sqrt[]{2}\)Related Questions
Enter a positive value for d that makes this statement true: 34×d is less than 34 but greater than zero HELP PLSS FASTT
Answers
Answer:
0.5 (any number between 0 and 1)
Step-by-step explanation:
34 * 0.5 = 17
34 > 17 > 0
what is the percent decrease on a Tv that has been marked down from $550 to $420? round to the nearest tenth
Answers
550 - 420 = 130
130/550 = 24%
The percent decrease on a TV after the markdown to the nearest tenth is 23.6%.
What is the percent decrease on the TV after the markdown?The percent decrease formula can be expressed as:
Percent decrease = [( original value - new value ) / original value ] × 100%
Given the data in the question:
The original value of the TV = $550
New value after markdown = $420
Percent decrease =?
Plug the given values into the above formula and solve for the percent decrease.
Percent decrease = [( original value - new value ) / original value ] × 100%
Percent decrease = [( 550 - 420 ) / 550 ] × 100%
Percent decrease = [ 130 / 550 ] × 100%
Percent decrease = 0.2363 × 100%
Percent decrease = 23.6%
Therefore, the percent decrease is 23.6%.
Learn about Percent increase here: https://brainly.com/question/19062651
#SPJ3
write an expression for the sequence of operations described below. 7 times k subtracted from 40
Answers
Answer:
7 times k = 7k
hence,
7k-40 is the answer
11. What is the unknown number in
Sequence 2 in the chart?
Sequence Number
Sequence 1
Sequence 2
A 126
B 127
c 147
D 154
2 3 5
7
14 21 35 49
?
1
7
21 42 63 105
Answers
The missing number in Sequence 2 is 780.
To find the missing number in Sequence 2, let's analyze the pattern:
In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...
In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:
2 x 126 = 252
3 x 127 = 381
4 x 128 = 512
5 x 129 = 645
...
Looking at this pattern, we can see that the missing number in Sequence 2 should be:
6 x 130 = 780
For similar question on Sequence.
https://brainly.com/question/7882626
#SPJ8
One shirt at H&M cost $7. what is the cost of 40 shirts
Answers
Answer:
$280
Step-by-step explanation:
7•40=$280
Thomas obtained a bank loan of k10 000 from BSP bank.He repays the money with 36% interest in one year.Calculate his installment payment he pays in one fortnight?
Answers
Thomas' installment payment that he pays in one fortnight is approximately k523.08.
To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).
First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:
Interest = Principal × Interest Rate
= k10,000 × 0.36
= k3,600
The total amount to be repaid is the sum of the principal and the interest:
Total Amount = Principal + Interest
= k10,000 + k3,600
= k13,600
Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:
Number of Fortnights = 52 weeks / 2
= 26 fortnights
To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:
Installment Payment = Total Amount / Number of Fortnights
= k13,600 / 26
≈ k523.08
Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.
It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.
For more such questions on installment visit:
https://brainly.com/question/28330590
#SPJ8
List all the subsets of the given set.
{e, n, t}
Answers
The subsets of the set {e, n, t} are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
\(2^n\)
The set for this problem is given as follows:
{e, n, t}
The cardinality is given as follows:
n = 3.
Hence the number of subsets is given as follows:
2³ = 8.
The subsets are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
In which {} is the empty set.
More can be learned about the subsets of a set at brainly.com/question/13458417
#SPJ1
Express each of the following numbers as a power of two
(2^3)^4
4*4*4*4*4
Answers
Answer:
2^12
2^10
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Step-by-step explanation:
to the power to the power of - we multiply the powers.
(2³)⁴ = 2¹²
as this is the same as
2³ × 2³ × 2³ × 2³
so, the power is 4×3 = 12
to the power of times to the power of times to the power of ... - we add the powers (if the base is the same).
2²×2²×2²×2²×2² = 2¹⁰
the power is 2+2+2+2+2 or 5×2 = 10
Is 237405 divisible by 11
Answers
Hello!
237405 | 11 ?
237405 : 11 = 21582,(27)
Answer: false
Good luck! :)
Hello,
Is 237405 divisible by 11?
a=sum of digits in rank odd : 5+4+3 = 12
b=sum of digits in rank even: 0+7+2=9
Calculate the difference: d=a-b=12-9 =3
d is not a multiple of 11 so, then number 237405 is not divisible by 11.
I’m really confused what does j=, L=, M=
Answers
Answer: J = 83, L = 97, M = 97
Step-by-step explanation:
Since it is a isosceles trapezoid, J = K and M = L. Also, a trapezoid is cyclic, so K and L are supplementary.
During each week of piano lessons, William learns to play 2 new pieces. Write an equation that shows the relationship between the weeks of lessons x and the total number of pieces learned y.
Answers
Answer:
William can find how many piano pieces he has learned by using the equation y = 2x.
Step-by-step explanation:
We are given that William learns two piano pieces per week.
We are tasked with finding the equation that represents this relationship (the number of weeks that William has received piano lessons and the total number of piano pieces that William has learned).
The number of weeks that William has attended piano lessons is represented by the variable x.The total number of piano pieces that William has learned is represented by the variable y.Therefore, take for example that William has been taking piano lessons for four months. This would roughly equate to sixteen weeks.
\(x=16\)After analyzing this, we know that he learns two pieces a week. So, we can multiply our number of weeks by two in order to receive the total amount of pieces learned.
\(x \times 2\)Finally, we need to set this equal to the total number of pieces learned, or our previously defined variable y.
\(y=x\times 2\)In mathematics, we want to simplify everything as much as possible. There is a statement that if a constant and a variable are to be multiplied, we can remove the multiplication symbol and place the constant and the variable together.
\(y=2x\)Therefore, our equation is \(\bold{y = 2x}\).
Hurry and answer this please I have to have this right or I'll have to be held back.From a group of 5 boys and 3 girls, a boy AND a girl will be selected to attend a conference. In how many ways can the selection be made?
Answers
Answer:
15 ways
Step-by-step explanation:
girl 1 and boy 1
girl 2 and boy 1
girl 3 and boy1
girl 1 and boy 2
girl2 and boy 2
girl 3 and boy 2
girl 1 and boy 3
girl 2 and boy 3
girl 3 and boy 3
girl 1 and boy 4
girl 2 and boy 4
girl 3 and boy 4
girl 1 and boy 5
girl 2 and boy 5
girl 3 and boy 5
NEED TO SHOW ALL WORK) For each of the equations given below, use the triangle method to solve for the
desired variable.
Answers
Answer:
1) \(a=\dfrac{F}{m}\)
2) \(m=\dfrac{p}{v}\)
Step-by-step explanation:
1) The given equation is
\(F=ma\)
We need to solve this for a.
In the given triangle place single variable i.e., F, on the top and variables in the product in the bottom (order of m and a does not matter) as shown in the below figure.
Using the triangle and the operations (× and ÷), we get
\(F=ma\)
\(a=\dfrac{F}{m}\)
\(m=\dfrac{F}{a}\)
Therefore, the required answer is \(a=\dfrac{F}{m}\).
2) The given equation is
\(p=mv\)
We need to solve this for m.
In the given triangle place single variable i.e., p, on the top and variables in the product in the bottom (order of m and v does not matter) as shown in the below figure.
Using the triangle and the operations (× and ÷), we get
\(p=mv\)
\(m=\dfrac{p}{v}\)
\(v=\dfrac{p}{m}\)
Therefore, the required answer is \(m=\dfrac{p}{v}\).
What is the square root of ab2?
Answers
Answer:
Step-by-step explanation:
A delivery company has a fleet of vans. The annual operating cost in dollars) per van is C = 0.37m + 2600, where m is the number of miles traveled by a van in a year. What number
of miles will yield an annual operating cost of $13,700?
mi
Answers
Answer:
Step-by-step explanation:
put C=13,700 and find m
The number of miles that will yield an annual operating cost of $13,700 is approximately 30,000 miles.
How to determine What number of miles will yield an annual operating cost of $13,700To find the number of miles that will yield an annual operating cost of $13,700, we need to solve the given equation for \(m\):
\[C = 0.37m + 2600\]
Given \(C = 13700\), we can substitute this value into the equation and solve for \(m\):
\[13700 = 0.37m + 2600\]
Subtract 2600 from both sides:
\[11100 = 0.37m\]
Now, divide both sides by 0.37:
\[m = \frac{11100}{0.37}\]
Calculate the value of \(m\):
\[m \approx 30000\]
So, the number of miles that will yield an annual operating cost of $13,700 is approximately 30,000 miles.
Learn more about operating cost at https://brainly.com/question/30566291
#SPJ3
What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
For more such questions on square
https://brainly.com/question/27307830
#SPJ8
Angle measure labeled a
The arc mesure labeled c
Answers
Step-by-step explanation:
angle measure a =48/2=24°
the arc measure =360°-48°=312°
stay safe healthy and happy.Write and solve an inequality to find the possible values of x.
Answers
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
Read more about inequality at
https://brainly.com/question/32124899
#SPJ1
In a box-and-whisker plot, the "box" portion contains 50% of the data.
A. True
B. False
Answers
Answer: True
Step by step explanation
You have decided to build your shelter close enough to the coastline to be able to fish but far enough away to not bear the brunt of the bitter cold winds. After watching previous seasons of the show, you decide that 50 meters is a good distance away from the coastline. To estimate, you will convert meters to feet (you do not have a tape measure). How many feet is this?
Answers
50 meters in feet is 164.042 feet
How to convert from meters to feetIn order to convert meters to feet we would have to cross multiply
That is. one meter is given as 3.28084 feet
We are to convert 50 meters to feet, hence we would have:
If 1 meter = 3.28084
50 meters = ?
When we cross multiply, we would have
? = 3.28084 * 50 meters
? = 164.042
Hence the amount of 50 meters in feet is given as 164.042 feet
Read more on unit conversion here:https://brainly.com/question/13016491
#SPJ1
Find mZCEF if mZCEF= 2x + 30,mZDEC = x + 102, and mZDEF = 132°DEFA) 30°C) 410B) 29°D) 320
Answers
1) Gathering the data
m∠CEF=2x +30
m∠DEC=x+102
m∠DEF=132
2) From the picture we infer that
m∠DEF = m∠CEF+m∠DEC
132 = m∠CEF +x +102
132-x-102=m∠CEF
m∠CEF=30
y=4x+2=y=2x+-8 what is the value of x
Answers
Answer:
x=-5
Step-by-step explanation:
since the y's cancel out, set the first equation equal to the second and solve like you'd normally do.
please help?
A car is traveling at 60 mi/hour. What is the car's speed in feet per second?
Answers
Answer:
88 feet per second
Step-by-step explanation:
quick maths
trouve trois nombres entiers consécutifs dont la somme vaut 513
Answers
Answer:
170, 171, 172
Step-by-step explanation:
x + x + 1 + x + 2 = 513
3x + 3 = 513
3x = 510
x = 170
x + 1 = 171
x + 2 = 172
Approximate 5.7255 to the nearest thousand
Answers
round 5.7255 to thousands place
place after thousands place (5) rounds up the 5 before it
therefore 5.726 ur ans
MARK above ANS as branliest
Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
Answers
The area of the rectangle is given by the equation A = ( 9x² - 64 ) yards²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the width of the rectangle be W = ( 3x - 8 ) yards
Let the length of the rectangle be L = ( 3x + 8 ) yards
Now , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = ( 3x - 8 ) ( 3x + 8 )
On simplifying the equation , we get
Area of Rectangle = ( 3x )² - ( 8 )²
Area of rectangle A = ( 9x² - 64 ) yards²
Hence , the area of the rectangle is ( 9x² - 64 ) yards²
To learn more about area of rectangle click :
https://brainly.com/question/15225905
#SPJ1
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
The money will double in value in approximately 11.6 years.
How to determine the time when the money will double?From the question, we have the following parameters that can be used in our computation:
Principal amount, P = $900Rate of interest, R = 6%Number of years = tNumber of times compounded, n = 12 i.e. monthlyWhen the money doubles, the amount is
A = 900 * 2
A = 1800
The compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
1800 = 900 * (1 + (6%)/12)^(t*12)
Divide both sides by 900
2 = (1 + (6%)/12)^(t*12)
Also, we have
2 = (1.005)^(t*12)
Take the logarithm of both sides
12t = log(2)/log(1.005)
Evaluate the quotients
12t = 139
Divide both sides by 12
t = 11.6
Hence, the number of years is 11.6 years
Read more about compound interest at:
brainly.com/question/2455673
#SPJ1
Please solve this question
3x-9<12
Answers
Answer:
Step-by-step explanation:
3x-9<12
You carry the 9 to the other side and do the inverse(opposite of take away
3x<12+9
3x<21
3x/3x
To cancel out the the x you must devide them together and then devide 21÷3
21/3=7
X<7
Answer: x<7 or (-infinity,7)
Step-by-step explanation:
3x-9<12
3x<21
x<7
Aspen has 10 pairs of white socks and 1 pair of red socks. What is the chance that Aspen wears a pair of black socks?
Answers
Answer:
no chance
Step-by-step explanation:
he doesn't have any black socks
Answer:
Step-by-step explanation:
Of the ten socks,
10/11 chance of wearing white socks
1/11 chance of wearing red socks
0/11 chance of wearing any OTHER color
Black socks fall into the final row, which is the OTHER color, meaning there is no chance he can wear black socks.
I dont really know how to do this, but its not too hard. PLS helpppp
Answers
Answer:
8
Step-by-step explanation:
I think it's 8 because the g function and f function are intersecting at the point 8 of the y axis. But I am not really sure