Answers
Related Questions
find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8) lies on its terminal side
Answers
Answer:
cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
cosФ = [tex]\frac{x}{r}[/tex]sinФ = [tex]\frac{y}{r}[/tex]tanФ = [tex]\frac{y}{x}[/tex]secФ = [tex]\frac{r}{x}[/tex]cscФ = [tex]\frac{r}{y}[/tex]cotФ = [tex]\frac{x}{y}[/tex]Where r = [tex]\sqrt{x^{2}+y^{2} }[/tex] (the length of the terminal side from the origin to point (x, y)You should find the quadrant of (x, y) to adjust the sign of each function∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r = [tex]\sqrt{x^{2}+y^{2} }[/tex]
∵ x = 1 and y = -8
∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ = [tex]\frac{x}{r}[/tex]
∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]
∵ sinФ = [tex]\frac{y}{r}[/tex]
∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]
∵ tanФ = [tex]\frac{y}{x}[/tex]
∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8
∵ secФ = [tex]\frac{r}{x}[/tex]
∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]
∵ cscФ = [tex]\frac{r}{y}[/tex]
∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]
∵ cotФ = [tex]\frac{x}{y}[/tex]
∴ cotФ = [tex]-\frac{1}{8}[/tex]
Find the selling price of each item original plate price of gold fish at $7.65 discount 10%
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Answer:
6.88 is what I think you're looking for
Step-by-step explanation:
Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.
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Answer:
11x-6+(19x+6)=180°
11x+19x-6+6=180°
30x=180
x=180/30
x=6
it means that
19x+6=19*6+6=114+6=120°
Jackson has 429 matchbox cars in his collection. If 4 out of 9 are blue cards, how many are not blue
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What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin?
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Answer:
-2,-3
Step-by-step explanation:
PLEASE HELP :’( last one
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Answer:
A.3
Step-by-step explanation:
1/5t+2- =17
1/5t
.1/5t
T=
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Answer:
poop i forgot my ramen noodles are in the microwave
Step-by-step explanation:
Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1 52 probability.
Required:
a. List the sample points in the event a jack is selected.
b. List the sample points in the event a club is selected.
c. List the sample points in the event a face card ( jack, queen, or king) is selected.
d. Find the probabilities associated with each of the events in parts (a), (b), and (c).
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Answer:
Kindly check explanation
Step-by-step explanation:
A deck of card:
Number of hearts = 13
Diamond = 13
Spade = 13
Club = 13
Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)
Hence, a club, diamond, spade and heart has one of each of the above numbers.
a. List the sample points in the event a jack is selected.
Jack : ( heart, club, diamond, spade)
B.) club is selected :
Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)
C)
Jack : ( heart, club, diamond, spade)
Queen : (heart, club, diamond, spade)
King : (heart, club, diamond, spade)
D) probability = required outcome / Total possible outcomes
P(jack selected) = 4 /52 = 1/13
P(club selected). = 13/52 = 1/4
P(face card selected) = 12 / 52 = 3/13
The constant of proportionality of this table is
Cups of
blue paint
cups of
yellow paint
2 10
1
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Answer:
Step-by-step explanation:
1/2
Write an inequality representing the following phrase:
One-tenth of a number h is less than or equal to ten
Answers
Answer:
[tex]\frac{1}{10} h\leq 10[/tex]
Step-by-step explanation:
Basically, we are just translating the phrase into an algebraic expression.
Name all rays with endpoint E
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Answer: Is there an image??
AE, BE, CE, and DE is the rays with endpoint E.
What is a vector?An item with both magnitude and direction is referred to be a vector.
A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.
Geometrical objects with magnitude and direction are called vectors.
A line with an arrow in its direction can also be used to represent a vector, and the length of the line relates to the vector's amplitude.
Given the figure,
The endpoint of all rays is E.
The rays associated with point E are;
AE, BE, CE, and DE
Hence "AE, BE, CE, and DE is the rays with endpoint E".
For more information about vector,
brainly.com/question/13322477
#SPJ2
if there are 7 fish and 3 drown how many are left?
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Answer:
7
Step-by-step explanation:
there are 7 left because fish can't drown
Solve:
a.) 5(x - 2) > -15
AND
b.) x/1 - 9 < -10
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Answer:
a.) x>-1
b.) x/1 - 9 < -10
Step-by-step explanation:
a.)
5(x - 2) > -15
(divide both sides)
x-2>-3
(move the constant to the right)
x>-3+2
(calculate)
x>-1
(answer)
b.)
x/1 - 9 < -10
(divide)
x-9<-10
(move the constant to the right)
x<-10+9
(calculate)
x/1 - 9 < -10
(answer)
A map has a scale of 2 in: 6 mi. If Clayton
and Centerville are 10 in apart on the map
then how far apart are the real cities?
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What is the measure of angle F?
E. 20
D. 90
F.?
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Answer:
the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now
Step-by-step explanation:
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
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Answer:
B
Step-by-step explanation:
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
Related Link: https://brainly.com/question/13581879
a diver descended 84 feet in 6 minutes. What was the divers change in depth per minute? Write and expression with a solution
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Answer:
14 depth per minute
Step-by-step explanation:
84/6 = 14
Find the product of (18k+ 2m)(m + k)
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Answer:
18k^2+2m^2+20km
Step-by-step explanation:
10a^2b^0 for a=–3, b=–8
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Answer:
90Step-by-step explanation:
Substitute a = -3 and b = -8 to the expression 10a²b⁰:
10(-3)²(-8)⁰ = 10(9)(1) = 90
a⁰ = 1 for any real number
Answer:
90
Step-by-step explanation:
10a^2b^0
Let a=–3, b=–8
10 (-3)^2 ( -8)^0
10 * 9 *1
90
Question
5°F - 32)
The function to convert Fahrenheit to Celsius is °C = (°F) =
The inverse function will
9
convert Celsius to Fahrenheit. What is the inverse function? Complete the explanation of how
determining this inverse is different than determining the previous inverses.
The inverse function is °F = -(°C)=
The F and °C (select) V need to be switched like the x and y did in the previous functions.
(select) degree measures, and because of the real-world relationship, switching them
(select) ✓ make sense.
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Answer:
[tex]F = \frac{9C + 32}{5}[/tex]
Step-by-step explanation:
Given
[tex]C = \frac{(5F - 32)}{9}[/tex]
Required
Determine the inverse function
[tex]C = \frac{(5F - 32)}{9}[/tex]
Make F the subject of formula:
Multiply through by 9
[tex]9C = 5F - 32[/tex]
Add 32 to both sides
[tex]9C + 32= 5F[/tex]
Divide through by 5
[tex]\frac{9C + 32}{5}= F[/tex]
[tex]F = \frac{9C + 32}{5}[/tex]
BRAINLIEST Multiply each side by the common denominator
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Answer:
c. x² + 2x -5 = 0
Step-by-step explanation:
Given expression;
[tex]\frac{5}{x}[/tex] = [tex]\frac{x + 2}{3}[/tex]
Unknown:
The quadratic equation equivalent to this expression:
Solution:
The common denominator here is 3x;
So, multiply both sides by 3x
[tex]\frac{5}{x}[/tex] x 3x = [tex]\frac{x + 2}{3} x[/tex] 3x
5 x 3 = (x + 2)x
15 = x² + 2x
So;
x² + 2x - 15
The quadratic expression is x² + 2x - 15
Ms Liu has $40 to buy water and popcorn at the movie theater. Popcorn costs $8 per bag and water costs 3$ per bottle. write an algebraic expression that will be used to find the amount of money left when Ms. Liu 3 bags of popcorn and 4 bottles of water.
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Answer:
S = 1 bag of popcorn
Y = 1 water
Step-by-step explanation:
S x 3 + Y x 4 = R
40 - R = (The Answer)
Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls Pls pls Pls pls Pls Pls help me pls pls pls pls pls pls ASAP pls pls pls I WILLLL GIVVVE BRAINLIEST!!!!!
Answers
Answer:
Y= -6x + 1
Step-by-step explanation:
Y=mx + b
M is your slope
B is your y intercept
What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet
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u would foils the two terms as shown below
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
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Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min
Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 + ab + b2)
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Answer:
Use the distributive property to multiply the factors on the right side of the equation.
Simplify the product by combining like terms.
Show that the right side of the equation can be written exactly the same as the left side.
Show that the right side of the equation simplifies to a cubed minus b cubed.
Step-by-step explanation:
The difference of two cubes identity a³ - b³ = (a - b)(a² + ab + b²) has been proved using; distributive property of algebra.
We want to prove that;
a³ - b³ = (a - b)(a² + ab + b²)
Now, to solve this we need to understand the distributive property of algebraic functions.This distributive property means distributing an item over others in a bracket. For example; a(b + c) = ab + acApplying this same distributive property to our question gives us;(a - b)(a² + ab + b²) = a(a² + ab + b²) - b(a² + ab + b²)
Multiplying out the brackets gives us;
a³ + a²b + ab² - a²b - ab² - b³
Like terms cancel out to give us;
a³ - b³.
This is same as the left hand side of our initial equation and thus it has been proved.
Read more at; https://brainly.com/question/2747971
The giber family purchased a house for 127,000 the first five years they paid off 12,000 each year . How much money do they still owe on the house ?
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Answer:
dndnfhhfbdhdndndnmdmdndndnen
12,000x5= 60,000
127,000-60,000= 67,000
what is Pi? explain.
Answers
Answer:
Pi is a irrational number
Step-by-step explanation:
Pi is an irrational number because it never ends it keeps going on and one.
Pi is also 3.141592654.............. never ends
A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
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Answer:
A) F(x) = 50 + ( x - 10 )*9
B) Graph
C) lim ( x ⇒ 10) F(x) = 50
Step-by-step explanation:
A) F(x) = 50 + ( x - 10 )*9 since the first 10 hours are included in initial fee
B) In Annex
C) lim (x ⇒ 10) F(x) = 50 + ( 10 -10)*9
lim ( x ⇒ 10) F(x) = 50 + 0
lim ( x ⇒ 10) F(x) = 50
what is 4/6+2/3.?(these are fractions, you're just adding fractions)
Answers
Answer:
4/3
Step-by-step explanation:
Multiply 2 by 2, and get 4, then we multiply 3 by 2 and get 6.
Since our denominators match, we can add the numerators. 4 + 4 = 8. That gives us the sum, which is 8/6. Then you divide by 2. So 8/6 / 2 gives you 4/3.
Answer:
4/3 or 1 1/3
Step-by-step explanation:
1. 4/6 + 2/3
2. 4/6 + 4/6 You have to find the LCM (least common multiple) of the two denominators. In this case it would be 6. You have to multiply 3 by 2 to get 6. What you do to the bottom you also do to the top so you have to also multiply the numerator (2) by 2.
3. 4/3 or 1 1/3 Afterward, you just have to add straight across without changing the denominator and then if you need to simplify you simplify. Without simplifying, you would get 8/6, but, most teachers will mark it as wrong if you don't simplify. You can then change the improper fraction into a mixed number depending on what your teacher wants.