If θ is a Quadrant II angle and cosθ = -2/3 , then sinθ = _____.
Answers
[tex]\cos(\theta) = \frac{x}{r} [/tex]
In this case, x = -2 and r = 3. Use the Pythagorean Theorem to find the value of y.
[tex]x^2 + y^2 =r^2 \\ 4+y^2=9 \\ y^2 = 5 \\ y=\sqrt{5} [/tex]
Note that you pick the positive square root for y because the point is in Quadrant II.
Now, [tex]\sin(\theta) = \frac{y}{r} = \frac{\sqrt{5}}{3} [/tex]
To solve for sinθ when θ is in Quadrant II and cosθ = -2/3, use the Pythagorean identity sin2θ + cos2θ = 1. Since sinθ will be positive in Quadrant II, after calculations, sinθ equals √5/3.
Explanation:To find the sine value for an angle θ in Quadrant II, where the cosine of θ is given to be cosθ = -2/3, we can use the Pythagorean identity: sin2θ + cos2θ = 1. We already know that cosθ = -2/3, so we can solve for sinθ:
sin2θ = 1 - (cosθ)2sin2θ = 1 - (-2/3)2sin2θ = 1 - 4/9sin2θ = 5/9Since we are in Quadrant II, where sine values are positive, we take the positive square root:
sinθ = √(5/9)sinθ = √5/3So the value of sinθ when cosθ = -2/3 in Quadrant II is √5/3.
Related Questions
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights. Use x
as the variable.
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights. Use x
as the variable.
Answers
Actual weight = |Recommended weight +/- 20|
x = |430 +/- 20|
Answer:
The required absolute equation is: |x-430|=20
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Step-by-step explanation:
Consider the provided information.
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
Let x is the actual weight of the soccer ball.
The difference of actual weight and recommended weight can vary by 20 grams.
Thus, the required absolute equation is:
|x-430|=20
x-430=20 or x-430=-20
x=450 or x=410
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Explain how u would use repeated subtraction to find 8÷2
Answers
8-2=6-2=4-2=2-2=0
How many ways are there to pick a starting five from a basketball team of twelve members
Answers
Answer:
95040
Step-by-step explanation:
Given : There are 12 members in basketball team.
To Find: How many ways are there to pick a starting five from a basketball team of twelve members
Solution:
Since we are asked to find no. of ways are there to pick a starting five from a basketball team of twelve members
So, we will use permutation over here.
Formula: [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
n = 12
r = 5
Substitute the value sin the formula .
[tex]^{12}P_5=\frac{12!}{(12-5)!}[/tex]
[tex]^{12}P_5=\frac{12!}{(7)!}[/tex]
[tex]^{12}P_5=\frac{12 \times 11\times 10 \times 9\times 8 \times 7!}{7!}[/tex]
[tex]^{12}P_5=12 \times 11\times 10 \times 9\times 8[/tex]
[tex]^{12}P_5=95040[/tex]
Hence there are 95040 ways to pick a starting five from a basketball team of twelve members.
There are 95040 different ways to pick a starting five from a basketball team of twelve.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, The no. of ways to pick a starting five from a basketball team of twelve members.
As stated pick a starting five we'll use permutation.
∴ The no. of ways to pick a starting five from a basketball team of twelve members is [tex]^{12}P_5[/tex].
= 12!/(12 - 5)!.
= 12!/7!.
= 12×11×10×9×8.
= 95040 different ways.
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What two-dimensional cross-sections could we create by slicing the particular triangular prism
Answers
Which graph represents the function f(x)=8 1/3x
Answers
f(x=0) = 8^0 = 1
f(x=2) = 8^(1/3)*2 = 4
f(x=4) = 8^(1/3)*4 = 16
Answer:
The correct option is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=8^{\frac{1}{3}x}[/tex]
At x=0,
[tex]f(0)=8^{\frac{1}{3}(0)}=8^0=1[/tex]
At x=1,
[tex]f(1)=8^{\frac{1}{3}(1)}=8^{\frac{1}{3}}=2[/tex]
At x=2,
[tex]f(2)=8^{\frac{1}{3}(2)}=8^{\frac{2}{3}}=4[/tex]
At x=3,
[tex]f(3)=8^{\frac{1}{3}(3)}=8^{1}=8[/tex]
The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).
According to these coordinates we can say that the graph of f(x) is represented by option 2.
Therefore correct option is 2.
3. You are looking into two long distance telephone plans offered by GT&T. The “One Rate 5 cents” plan has a monthly fee of $7.95 and all calls are 5 cents per minute. The “One Rate 7 cents” plan has a monthly fee of $4.95 and all calls are 7 cents per minute. Under what circumstances is one plan less expensive than the other?
a. The "One Rate 5 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 1.5 minutes.
b. The "One Rate 7 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 1.5 minutes.
c. The "One Rate 5 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 150 minutes.
d. The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.
Answers
Hope this helps!
Answer:
D.The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.
Step-by-step explanation:
let the total number of minutes of calls be x minutes.
Now let us find the total cost incurred in both plan for x mins.
Plan 5 cent : 7.95+0.05x
Plan 7 cent : 4.95+0.07x
Let us find the time at which both the plans will give you same Bill.
Hence
7.95+0.05x=4.95+0.07x
7.95-4.95=0.07x-0.05x
3=0.02x
x=150
Hence at 150th min, both the plan will charge you same cost. Hence the plan giving you less Bill for 100 mins will give you high Bill in 200 mins. Let us calculate the bill incurred by both plan at 100th min.
Plan 5 cent : 7.95+0.05×100=12.95
Plan 7 cent: 4.95+0.07×100=11.95
Hence plan 7 cent is lesser than 5 cent for calls more than 150 mins
Let find which plan cost you cheaper
If two circles have the same circumference what do you know about their area
Answers
What number is greater 87 or 13.688?
Answers
how to solve -x+4=-2x-6
Answers
Add 2x to both sides
Simplify 4 - x + 2x to 4 + x
subtract 4 from both sides
subtract -6 - 4.
Answer: x = -10
-x+4 = -2x-6
add 6 to each side:
-x+10 = -2x
add 1x to each side
10 = -x
divide each side by -1
x = -10
There are two pizzas. Conor ate 1⁄4 of a pizza, Brandon 2⁄8, Tyler 3⁄4, and Audrey4⁄8. Who ate the most of the two pizzas?
A. Audrey B. Tyler C. Brandon D. Conor
Answers
Conor- 1/4
Brandon- 2/8 = 1/4
Tyler- 3/4
Audrey- 4/8 = 2/4
Out of all these, the person who ate the most was Tyler, at 3/4 of the pizzas.
B. Tyler
Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars, she added the product 8×10 to the product 8×8, for a total of 144. Which property did Sylvia use?
Answers
8 x 10 + 8 x 8 = 80 + 64 = 144
She used the Distributive property:
a x ( b + c ) = a x b + a x c
8 x 18 = 8 x ( 10 + 8 ) = 8 x 10 + 8 x 8 = 80 + 64 = 144
Answer:
Distributive property.
Answer:
distributive property
Step-by-step explanation:
im tired i just solved the problem good bye
The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0). What are the minimum and maximum values of the objective function F = 8x + 5y?
Answers
The minimum and maximum values of the objective function f = 8x + 5y are 400 and 960
How to determine the minimum and the maximum values?The vertices of the feasible region are given as:
(0, 100), (0, 80), (80, 60), (80, 0), and (120, 0)
The objective function is given as:
z = 8x + 5y
Calculate the value of the objective function using the vertices
F = 8 * 0 + 5 * 100 = 500
F = 8 * 0 + 5 * 80 = 400
F = 8 * 80 + 5 * 60 = 940
F = 8 * 80 + 5 * 0 = 640
F = 8 * 120 + 5 * 0 = 960
The minimum value above is 400 and the maximum value is 960
Hence, the minimum and maximum values of the objective function F = 8x + 5y are 400 and 960
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A school party visit the gift shop. They all want to buy a badge. Your friend needs to get 37 badges from the stock room. The badges come in packs of 10. How many packs does she need?
Answers
Answer:
She will need 4 packs.
Step-by-step explanation:
The badges come in packs of 10 but this person only needs 37 badges.
If she buys two packs, she will get 20 badges.
If she buys three packs, she will get 30 badges.
Is she buys four packs, she will get 40 badges.
She will need four packs so she can have 37 badges and there will be 3 remaining badges.
What is the area of a square deck, if one side is 10 feet long?
Answers
Answer:100 square feet
Step-by-step explanation: since we know that a square has all equal sides, and we know one length of one side is 10, we know all sides are ten then. We then multiply 10 x 10 which will equal, 100
Jackson has 50 megabytes (MB) of space left on his smartphone. He can download songs that each use 3.5 MB or videos that each use 7 MB. He wants to download at least 10 new media files. Which pair of inequalities specifies the number of song files, x, and the number of video files, y, that Jackson can download
Answers
The number of video files Jackson can download: y
x song files occupy a space of 3.5MB per file, times x files = 3.5x MB
y media files occupy a space of 7MB per file, times y files = 7yMB
(3.5x + 7y) MB must be at most 50 MB, since there is 50 MB left,
this can be represented by the inequality: [tex]i) \ \ 3.5x+7y \leq 50[/tex]
Jackson wants to download at least 10 media files, so y must be at least 10
this means that [tex]ii) \ \ \ y \geq 10[/tex]
Answer: [tex]i) \ \ 3.5x+7y \leq 50\\\\ii) \ \ \ y \geq 10[/tex]
Answer:
[tex]3.5x+7y\leq 50[/tex]
[tex]x+y\geq 10[/tex]
Step-by-step explanation:
Given : Jackson has 50 megabytes (MB) of space left on his smartphone. He can download songs that each use 3.5 MB or videos that each use 7 MB. He wants to download at least 10 new media files.
To find : The pair of inequalities specifies the number of song files, x, and the number of video files, y, that Jackson can download.
Solution :
The number of song files Jackson can download is x
The number of video files Jackson can download is y
→ x song files occupy a space of 3.5 MB per file,
So, number of space occupy by songs files = 3.5x MB
→ y media files occupy a space of 7 MB per file,
So, number of space occupy by video files = 7y MB
→ The total amount of MB used is [tex]3.5x+7y[/tex]
Jackson has 50 megabytes (MB) of space left on his smartphone.
The total amount must be less than or equal to 50 MB,
which can be represented as [tex]3.5x+7y\leq 50[/tex]
Jackson wants to download at least 10 media files,
which means [tex]x+y\geq 10[/tex]
Therefore, The two inequality form is
[tex]3.5x+7y\leq 50[/tex]
[tex]x+y\geq 10[/tex]
Find the value of $ 15,000 at the end of one year if it is invested in an account that has an interest rate of 4.95 % and is compounded in accordance with the rules below. a. compounded monthly b. compounded daily (assuming a 365-day year) c. compounded quarterly
Answers
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{twelve months, thus} \end{array}\to &12\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{12}\right)^{12\cdot 1}[/tex]
b)
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{365 days, thus} \end{array}\to &365\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{365}\right)^{365\cdot 1}[/tex]
c)
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{four quarters, thus} \end{array}\to &4\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{4}\right)^{4\cdot 1}[/tex]
A) compounded monthly; A = $15,759.579
B) compounded quarterly; A = $15,756.396
What is Compound interest?Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.
We have,
P = $15,000
R= 4.95%
a) Using A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /12[tex])^{12[/tex]
A= 15,000 x 1.0506386172
A = $15,759.579
b) Again, A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /365[tex])^{365[/tex]
c) Again, A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /4.1[tex])^{4.1[/tex]
A = 15, 000 x 1.05042644766
A = $15,756.396
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Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates of A′ of the rotated quadrilateral A′B′C′D′?
Answers
Answer:
The coordinate of A' after rotated through 180° is (3,-2)
Step-by-step explanation:
Given vertex A in a quadrilateral ABCD lies at (-3,2). Now we have to rotate the quadrilateral ABCD 180° clockwise about the origin.
The point (x,y) is when rotated about the origin through 90° in clockwise direction then the new position will be (y,-x).
Now,the point A which is given is (-3,2)
First after rotation through 90° the new point will be (2-(-3)) = (2,3)
Again this point further rotated through 90° or we can say that rotation after 180° then the new point become A' = (3,-2).
Hence, The coordinate of A' after rotated through 180° is (3,-2)
the coordinates of A′ after a 180° clockwise rotation about the origin will be (3, -2).
To solve this problem, we need to apply a 180° clockwise rotation to the point (-3, 2). A 180° clockwise rotation about the origin will map any point (x, y) to the point (-x, -y).
The coordinates of the original point are:
A (-3, 2)
Apply the rotation rule, the new coordinates will be:
[tex](-(-3), -(2)) = (+3, -2)[/tex]
Therefore, the coordinates of A′ after a 180° clockwise rotation about the origin will be (3, -2).
Which transformation would change the point (5,3) into (-5,3)?
Answers
Hope this helps! :D
MODEL WITH MATHEMATICS
Write a problem about a real-world situation in which you would either write a percent as a decimal or write a decimal as a percent.
Answers
A man in a rowboat that is a = 2 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is b = 8 miles farther down the shoreline (see the figure). He plans to row to a point P that is between A and B and is x miles from the house, and then he will walk the remainder of the distance. Suppose he can row at a rate of 2 mi/hr and can walk at a rate of 4 mi/hr. If T is the total time required to reach the house, express T as a function of x.
Answers
b-x=A by subtracting x from both sides. Therefore, a^2+(b-x)^2=P^2 and by plugging a=2 and b=8 in, we get 2^2+(8-x)^2=P^2. To find out P, we square root both sides, getting P= sqrt(4+(8-x)^2). Since the man rows 2 miles per hour, we can divide P by 2 to get how much time it takes for him to travel to point P, resulting in sqrt(4+(8-x)^2)/2. In addition, we can divide x by 4 as the man walks 4 miles per hour, getting x/4. Adding them up, we get
sqrt(4+(8-x)^2)/2+x/4 as the amount of time it will take to get to point B
Trevor earns $7.80 an hour take home pay and works 20 hours each week. Trevor wants to buy a new laptop computer to take to college that costs $780. How many weeks will it take for Trevor to achieve his goal?
Answers
7.89*20= $156 per week
156*5 weeks= $780
Answer: 5 weeks
Step-by-step explanation:
Factor the expression completely:
x³ - 3x² - 4x + 12
Answers
Jimmy’s new cell phone cost him $49.99 when he signed a 2 year plan, which was 75% off the original place. What was the original price?
Answers
The original price of the cell phone was $199.96.
Build the fraction to an equivalent fraction with the specified denominator. State the numerator. 5/12 = ?/60
Answers
The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the population in 50 years? (round your answer to the nearest person.)
Answers
or = 500 (1.15)^50
Evaluate this on your calculator.
40 miles x 25 min.=?mph
Answers
A car drove 148 miles using 4 gallons of gasoline. How many gallons will it take to drive 9 1/4 miles?
Answers
Write the following ratio using two other notations. 5/9 Use only the numbers above (not any others).
Answers
I hope this helps:)
The ratio 5/9 can be expressed as a decimal (0.555) or as a percentage (55.6%).
Explanation:The given ratio is 5/9.
Decimal: A decimal is a way of expressing a number with a fractional part. It is based on powers of 10. For example, the decimal number 0.5556 means 5/10 + 5/100 + 5/1000 + 6/10,000.
Percentage: A percentage is a way to express a number as a fraction of 100. For example, the percentage 55.56% is equivalent to the fraction 55.56/100, which means 55.56 out of every 100.
We can express this ratio using two other notations:
As a decimal: 5/9 ≡ 0.555As a percentage: 5/9 ≡ 55.6%Learn more about Ratio here:https://brainly.com/question/32531170
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It is estimated that each guest at a party will eat
9/10 pounds of chocolates. How many guests can be served with 45 pounds of chocolate?
Answers
and pretty sure you know how much that is.
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A. How fast did Car B travel? (The formula R·T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
Answers
is 60mph