Answer:
20.76%
Step-by-step explanation:
[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]
which rounds to 20.76%
Answer:
About 0.2076 or 20.76%.
Step-by-step explanation:
Recall that compound interest is given by the formula:
[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.
Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:
[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]
Simplify and divide both sides by 8000:
[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]
Raise both sides to the 1/28th power:
[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]
Solve for r. Hence:
[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]
Use a calculator. Hence:
[tex]r=0.2076...\approx 0.2076[/tex]
So, the quarterly rate of interest must be 0.2076, or about 20.76%.
Determine if each statement is always, sometimes, or never true.
Parallel lines are
coplanar.
Perpendicular lines are
coplanar.
Distance around an unmarked circle can
be measured
Answer:
1) Parallel lines are "ALWAYS"
coplanar.
2) Perpendicular lines ARE "ALWAYS"
coplanar.
3) Distance around an unmarked circle CAN "NEVER" be measured
Step-by-step explanation:
1) Coplanar means lines that lie in the same plane. Now, for a line to be parallel to another line, it must lie in the same plane as the other line otherwise it is no longer a parallel line. Thus, parallel lines are always Coplanar.
2) similar to point 1 above, perpendicular lines are Coplanar. This is because perpendicular lines intersect each other at right angles and it means they must exist in the same plane for that to happen. Thus, they are always Coplanar.
3) to have the distance, we need to have the circle marked out. Because it is from the marked out circle that we can measure radius, diameter and find other distances around the circle. Thus, distance around an unmarked circle can never be measured.
Suppose that two balanced, six sided dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. (a) What is the probability that we obtain a sum of 3 before we obtain a sum of 7
Answer:
[tex]\frac{(2/36)}{(1-(28/36))} = 1/4[/tex]
Step-by-step explanation:
please help i am stuck on this assignment
Answer:
answer
x = -13/ 15, 0
Step-by-step explanation:
15x^2 + 13 x = 0
or, x(15x + 13) = 0
either, x = 0
or, 15x + 13 = 0
x = -13/15
Answer:
The answer should be C...............
imma sorry if I'm wrong
If the bearing of A from B is 125.Find the bearing of B from A
Answer:
305°
Step-by-step explanation:
The bearing in the reverse direction is 180° plus the bearing in the forward direction, that is
bearing of B from A = 180° + 125° = 305°
Kim ran 9/10 of a mile. Adrian ran 3/5 of a mile Adrian claims that Kim ran 1 3/10 times farther than him Kim says that she actually ran 1/2 times farther than Adrian who is correct
9514 1404 393
Answer:
Kim
Step-by-step explanation:
The ratio of Kim's distance to Adrian's distance is ...
(9/10)/(3/5) = (9/10)/(6/10) = 9/6 = 3/2 = 1.5
__
You need to be very careful with the wording here. Kim ran 1 1/2 times as far as Adrian. That is, she ran Adrian's distance plus 1/2 Adrian's distance.
If we take the wording "1/2 times farther" to mean that 1/2 of Adrian's distance is added to Adrian's distance, then Kim is correct.
_____
In many Algebra problems, you will see the wording "k times farther" to mean the distance is multiplied by k. If that interpretation is used here, neither claim is correct, as Kim's distance is 1 1/2 times farther than Adrian's.
On the other hand, if the value of "k" is expressed as a percentage, the interpretation usually intended is that that percentage of the original distance is added to the original distance. Using this interpretation, Kim's distance is 50% farther than Adrian's. (Note the word "times" is missing here.)
__
Since Adrian ran 1 5/10 the distance Kim ran, Adrian's claim is incorrect regardless of the interpretation. If you require one of the two to be correct, then Kim is.
Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Ox45)
0 - 6x - 5 < 10 - x
0 -6x + 15 < 10 - 5
E
우
-
3
5
2
-1
0
1
2
3
Answer:
45.9
Step-by-step explanation:
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
3х + 2 +(-5)? I need help pls
Answer:
3x + 2 - 5
3x - 3
x = 3 ÷ 3
x = 1
I hope this helped!
Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Answer:
The interval is [98,132]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 115 and standard deviation 25.
This means that [tex]\mu = 115, \sigma = 25[/tex]
Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = -0.675*25[/tex]
[tex]X = 98[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = 0.675*25[/tex]
[tex]X = 132[/tex]
The interval is [98,132]
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, -33) (1, 2) (9, 162)
HELP PLZ
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Answer:
y = x^2 +10x -9
Step-by-step explanation:
Quadratic regression generally requires the use of "technology" to aid in finding the equation of the curve of best fit. Use the technology you've been introduced to.
__
When only a few data points are provided, I prefer to use the Desmos graphing calculator. It shows the equation to be ...
y = x^2 +10x -9
Suppose that on the average, 7 students enrolled in a small liberal arts college have their automobiles stolen during the semester. What is the probability that less than 1 student will have his automobile stolen during the current semester
Answer:
[tex]P(x>1)=0.9927[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =7[/tex]
Generally the Poisson equation for \=x is mathematically given by
[tex]P(x>1)=1-P(x \leq 1)[/tex]
Therefor
[tex]P(x>1)=1-(\frac{e^{-7}*7^0}{0!}+{\frac{e^{-7}*7^1}{1!})[/tex]
[tex]P(x>1)=1-(9.1*10^{-4}+6.3*10^{-3})[/tex]
[tex]P(x>1)=1-(7.3*10^{-3}[/tex]
[tex]P(x>1)=0.9927[/tex]
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
Please help !!!! will mark brainliest !!
Answer:
the first one
Step-by-step explanation:
Is the collection og rall " student in set ? why ? class7
Answer:
in secret
Step-by-step explanation:
correct answer is in a secret
A card is drawn from a well shuffled pack of 52 cards . find the probability of '2' of spades
Answer:
[tex] \frac{1}{52} [/tex]Step-by-step explanation:
Given,
Total no. of cards = 52
No. of 2 of spades cards = 1
Therefore,
Probability of getting 2 of spades
[tex] = \frac{no. \: of \: required \: outcomes}{total \: outcomes} [/tex]
[tex] = \frac{1}{52} (ans)[/tex]
Let f(x) = 2x + 8, g(x) = x² + 2x – 8, and h(x)
Perform the indicated operation. (Simplify as far as possible.)
(g - f)(2) =
what are the following proof triangle LMN equals triangle OPQ
Answer:
D. SSS
Step-by-step explanation:
Was given to us that the corresponding sides are congruent so is SSS.
Side Side Side Theorem tells us that if am the sides of a triangle are having the same measurement with the corresponding sides of another triangle then the two triangles are congruent.
Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?
9514 1404 393
Answer:
3/4
Step-by-step explanation:
It might be easier to start by expressing the ratios with AD as the denominator.
AD/AC = 2/1 ⇒ AC/AD = 1/2
AD/AB = 3/1 ⇒ AB/AD = 1/3
From the latter, we have ...
(AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD
Then the desired ratio is ...
AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)
AC/BD = 3/4
You work as an office assistant who does data entry for a large survey company. Data entry is performed in two-person teams: one person types and the other checks that person's work for errors. Each two-person team, on average, can enter the data of 520 surveys per day. A huge collection of 7,540 surveys will arrive tomorrow and must be entered by the end of the day. In order to enter all of the survey data, how many total employees, working in two-person teams, must work tomorrow?
Answer:
you just gave your self the answer because you just need to multiply
Step-by-step explanation:
15080 is the answer
A map was created using the scale 1 inch :25
miles. If the river is 5.5 inches long on the map, then it is actually how many miles long?
Graph g(x)=-8|x |+1.
Answer:
[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]
At a local community college, 57% of students who enter the college as freshmen go on to graduate. Five freshmen are randomly selected.
a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations Round your final answer to 4 decimal places Probability
b. What is the probability that at most four will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)
c. What is the expected number that will graduate? (Round your final answer to 2 decimal places)
Answer:
a) 0.0147 = 1.47% probability that none of them graduates from the local community college.
b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.
c) The expected number that will graduate is 2.85.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
57% of students who enter the college as freshmen go on to graduate.
This means that [tex]p = 0.57[/tex]
Five freshmen are randomly selected.
This means that [tex]n = 5[/tex]
a. What is the probability that none of them graduates from the local community college?
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]
0.0147 = 1.47% probability that none of them graduates from the local community college.
b. What is the probability that at most four will graduate from the local community college?
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]
So
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]
0.9398 = 93.98% probability that at most four will graduate from the local community college.
c. What is the expected number that will graduate?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 5*0.57 = 2.85[/tex]
The expected number that will graduate is 2.85.
The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay = c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
5x + 9y = 2, 7x + 2y = 1
The angle is _______ radians.
(Type an exact answer, using pi as needed)
Answer:
fgvilgiuhuikj
Step-by-step explanation:??????????????
if triangle TAN has vertices T(0, 2), A(-1,3), and N(-2,-4), which of the following coordinates is N' of the dilation from the origin using the scale factor 3?
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
[tex] - 2 \times 3 = - 6[/tex]
[tex] - 4 \times 3 = - 12[/tex]
So our new coordinates is
(-6,-12)
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
So our new coordinates is
(-6,-12)
Step-by-step explanation:
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) c, c, c , where c > 0
Answer:
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Step-by-step explanation:
Given the data in the question;
vector is z = < c,c,c >
the direction cosines and direction angles of the vector = ?
Cosines are the angle made with the respect to the axes.
cos(∝) = z < 1,0,0 > / |z|
so
cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]
cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3
∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]
cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3
β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]
cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3
γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°
Therefore;
cos(∝) = 1/√3
cos(β) = 1/√3
cos(γ) = 1/√3
∝ = 55°
β = 55°
γ = 55°
Suppose that 70% of all voters prefer Candidate A. If 4 people are chosen at random for a poll, what is the probability that exactly 1 of them favor Candidate A?
Answer:
0.0756
Step-by-step explanation:
p(success), p = 70% = 0.7
Nunber of trials, n = 4
q = 1 - p = 1 - 0. 7 = 0.3
x = 1
The question meets the requirements of a binomial probability distribution :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 1) = 4C1 * 0.7^1 * 0.3^(4-1)
P(x = 1) = 4C1 * 0.7 * 0.3^3
P(x = 1) = 4 * 0.7 * 0.027
P(x = 1) = 0.0756
When the Bucks play Chiefs at football, the probability that the Chiefs, on present form, will win is 0.56. In a competition, these teams are to play two more pgames. If Swallows beats Bucks in at least4one of these games, they will win the competition, otherwise Bucks will win the trophy. NB: Round off to 2 decimal places. a. The probability that Swallows will win the trophy is [a] probability that Rucks will win the trophy is
Answer:
The probability that Swallows will win the trophy is 0.8064
The probability that Rucks will win the trophy is 0.1936
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability the Swallows wins is 0.56
This means that [tex]p = 0.56[/tex]
2 games:
This means that [tex]n = 2[/tex]
The probability that Swallows will win the trophy is
Probability they win at least one game, so:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]
Then
[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]
0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.
How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually
Answer:
11 half years
Step-by-step explanation:
The formula for compound interest is
A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.
If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus
1000 = 500 (1+0.07)^(t)
divide both sides by 500
2 = (1+0.07)^(t)
2 = (1.07)^(t)
Using logarithms, we can say that
[tex]log_{1.07} 2 = t[/tex]
and using a calculator, we get
10.24 = t
Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11
Type the correct answer in each box. The volume of a cube is given by and the total surface area of a cube is given by , where s is the side length of the cube. If the side length of a cube is 5 inches , the volume of the cube is ____ cubic inches and its total surface area is ____ square inches.
Answer:
hope this will help you a lot
HELP ASAP I WILL GIVE BRAINLIST
If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅? What is ∅ in degrees and radians? Be sure to show and explain all work.
Step-by-step explanation:
sin ∅ = -(√3)/2
Note that
cos²∅ + sin²∅ = 1
cos²∅ = 1 - sin²∅
= 1 - (-√3 / 2)²
= 1 - (-√3)²/ 2²
= 1 - 3/4
= 1/4
cos²∅ = 1/4
Taking square root of both sides
cos∅ = 1/2
Note that tan∅ = sin∅/cos∅
therefore, tan∅ = -(√3)/2 ÷ 1/2
= -(√3)/2 × 2/1
= -√3
tan∅ = -√3
Since sin∅ = -√3 /2
Then ∅ = -60⁰
The value of ∅ for the given range (third quadrant) is 240⁰.
NB: sin∅ = sin(180-∅)
Also, since 180⁰ is π radians, then ∅ = 4π/3