On a unit circle, the terminal point of 8 is ( 3 , 3 1). What is e?O A.radiansB.Eloradiansc. radiansOD. radians
Answers
We have a unit circle (radius = 1).
Then we can relate the x and y coordinates to the angle θ as:
\(\begin{gathered} x=\cos (\theta) \\ y=\sin (\theta) \end{gathered}\)As the terminal point is (x,y)=((3^0.5)/2, 1/2), we can use any of these coordinates to find θ.
We will use y=1/2:
\(\begin{gathered} y=\sin (\theta)=\frac{1}{2} \\ \theta=\arcsin (\frac{1}{2}) \\ \theta=\frac{\pi}{6} \end{gathered}\)Answer: the angle θ is θ = π/6
NOTE: we could have obtained the same result with x:
\(\theta=\arccos (\sqrt[]{\frac{3}{2})}=\frac{\pi}{6}\)Related Questions
What’s the answer to the 4th question?
Answers
Answer:
1440 Buckets of Water
Step-by-step explanation:
1 Bucket = 2.5 Gallons of Water
1 Cubic Foot = 7.5 Gallons of Water
1 Cubic Foot = 3 Buckets
480 x 3 = 1440
11 less than the quotient of
4
44 and
�
xx.
Answers
The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".
A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.
An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.
The quotient of a number"x" and 4 can be written as x/4.
So, one more than the quotient of a number x and 4 can be represented by the expression:
⇒ x/4 + 1,
Therefore, required mathematical expression is "x/4 + 1".
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The given question is incomplete, the complete question is
Write an expression to represent : One more than the quotient of a number x and 4.
expand and simplify (x+5)(x-1)
Answers
The expanded and simplified form of the expression (x + 5)(x - 1) is x² - x + 5x - 5.
What is the expanded form of the expression?Given the expression in the question;
(x + 5)(x - 1)
To expand and simplify the expression (x+5)(x-1),
we use the distributive property:
(x + 5)(x - 1)
x(x - 1) + 5(x - 1)
Now we can simplify each term by using the distributive property again:
x(x - 1) = x² - x
5(x - 1) = 5x - 5
Putting these terms back together, we have:
(x+5)(x-1) = x² - x + 5x - 5
Combining like terms, we get:
(x+5)(x-1) = x² + 4x - 5
Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.
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Caroline is planting flowers in her garden. She plans her first seven flowers in four minutes. After 12 minutes, she has planted 21 different flowers. Which equation represents this direct variation?
Answers
Answer:
21f=12m
Step-by-step explanation:
A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
Answers
Answer:
20 I guess
Step-by-step explanation:
because maybe 1 is 9
If f(x) = -x³ + x² + x, find f(-3).
Answers
Answer:
33
Step-by-step explanation:
Substitute f(-3) in the problem and you'll get f(-3) = -x³ + x² + x.
Substitute the given value into the function and evaluate.
Answer:
33.
Step-by-step explanation:
f(x) = -x³ + x² + x.
f(-3) = -(-3)³ + (-3)² + (-3)
= -(-27) + (9) - 3
= 27 + 9 - 3
= 36 - 3
= 33.
Hope this helps!
a) (10 pts) Re-express the given differential equation as a first order differential equation by utilizing matrix
and vector notation and in accordance with ()
= () form.
b) (10 pts) Is the system obtained in (a) stable, neutrally stable of unstable? Determine this using matrix.
c) (10 pts) Compute the eigenvalues and eigenvectors of matrix.
d) (10 pts) Using the results computed in (c) find and matrices and show that =
−
relationship
(i.e., the diagonalization relationship) is a valid relationship.
e) (10 pts) Compute () by utilizing your knowledge gained in previous items and obtain the mathematical
expression of () from this vector.
Answers
a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation,
let's define the vector \(x(t) = [x1(t), x2(t)]\)and rewrite the equation in the form
\(\frac{dx(t)}{dt } = Ax(t)\),
where A is a 2x2 matrix.
Let's express the given equation in matrix-vector form:
\(\frac{d}{dt} t(x1(t)) [2 ,1] [x1(t)]\)
\(\frac{d}{dt} (x2(t)) = [4 3] \times [x2(t)]\)
b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.
If all eigenvalues have negative real parts, the system is stable.
If any eigenvalue has a positive real part, the system is unstable.
If there is at least one eigenvalue with zero real part, the system is neutrally stable.
c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation
\(\Delta (A - \lambda I) = 0\),
where λ is the eigenvalue and I is the identity matrix.
The eigenvalues obtained will give us insight into the stability of the system.
d) Once we have computed the eigenvalues and eigenvectors, we can express matrix A in terms of its eigenvectors and eigenvalues.
Let's assume
\(A = PDP^{(-1)\),
where P is the matrix whose columns are the eigenvectors of A, and D is a diagonal matrix with the eigenvalues of A on the diagonal.
e) Finally, we can compute the solution x(t) by utilizing the knowledge gained in previous steps.
We can express x(t) as
\(x(t) = P \times exp(Dt) \times P^{(-1) }\times x(0)\),
where exp(Dt) is the matrix exponential of D.
By evaluating this expression, we obtain the mathematical expression of x(t) in terms of the initial condition x(0).
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is this a function. yes or no?
Answers
Answer:
No
Step-by-step explanation:
you cannot have two outputs for the same input
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Answers
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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For each of the following, find a polynomial function of the lowest degree with rational coefficients that have the given numbers as some of its zeros. a) zeros -5 and 2b) zeros 4, and -3i
Answers
The standard equation of a polynomial as a function of "x" is expressed as:
\(f(x)=(x-a)(x-b)...(x-n)\)where a, b and n are the zero's of the polynomial.
Given the following zeros -5 and 2, the required polynomial will be expressed as:
\(\begin{gathered} f(x)=(x-(-5))(x-2) \\ f(x)=(x+5)(x-2) \end{gathered}\)Expand
\(\begin{gathered} f(x)=x(x)-2x+5x-5(2) \\ f(x)=x^2+3x-10 \end{gathered}\)What are the factors of 42 to find it’s prime numbers and how do I put it in a factor tree
Answers
To create a factor tree for 42, we start by finding a pair of factors of 42, such as 2 and 21 and factor each branch until we have prime numbers.
Answer:
See below
Step-by-step explanation:
Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.
Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.
If you have a salary of $30,000, an IRA deduction of $2,000, a standard deduction of $12,000, and a FICA rate of 7.65 percent, how much did you pay in FICA taxes this year? O $1,805 O $1,958 0 $2,142 O $2,295
Answers
The required amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.
To calculate the FICA taxes paid for the given scenario, we need to multiply the salary by the FICA rate.
Given:
Salary: $30,000
FICA rate: 7.65%
FICA taxes are split between employers and employees, with both parties paying 7.65% of their income to FICA, totaling 15.3% combined.
To calculate the FICA taxes paid by the employee, we multiply the salary by the FICA rate:
$30,000 * 7.65% = $2,295
Therefore, the amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.
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A tank in the shape of a hemisphere has a radius of 8 feet. If the liquid that fills the tank has a density of 98.9 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Answer:
848,775 pounds
Step-by-step explanation:
The volume of a hemisphere with radius 8 feet is:
V = (2/3)πr^3 = (2/3)π(8^3) = 268.08 cubic feet
The weight of the liquid is given by:
W = V * ρ * g
where ρ is the density of the liquid and g is the acceleration due to gravity. Plugging in the values, we get:
W = 268.08 * 98.9 * 32.2 = 848,774.7 pounds
Rounding to the nearest full pound, the total weight of the liquid in the tank is 848,775 pounds.
Write an equation in slope-intercept form (-5,-7);y=-2x+4
Answers
Answer:
Step-by-step explanation:
First, let us substitute x and y values: -7 = -2(-5) + 4
Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).
Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:
14 + b = -7
by simplifying, we can conclude that b = -21
Finally, we can plug in the b-value into our original equation:
y = -2x + 4 - 21
After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).
How many roots do the functions have in common f(x)=x^2+x-6
Answers
To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
distinguishing between linear growth and exponential growth identify the type of function graphed to the right. linear exponential other graph
Answers
To distinguish between linear growth and exponential growth, you need to look at the equation of the function and the shape of the graph.
Linear functions have a constant rate of change, meaning that the slope of the line is always the same. The equation for a linear function is y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
Exponential functions, on the other hand, have a variable rate of change, meaning that the slope of the line changes as the x-value increases. The equation for an exponential function is y = ab^x, where a and b are constants. The graph of an exponential function is a curve that increases or decreases rapidly.
If the graph is a straight line it is linear, if it is curved and increases or decreases rapidly then it is exponential, otherwise, it would be considered as other.
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PLEASE HELP ON QUESTION 100 POINTS WILL MARK BRAINLIEST!
Answers
Answer:
188
Step-by-step explanation:
Ive attached my work
Hope it helps, Let me know if you have any questions !
whats the equation of a line that passes through point (-1,3) with slope of 1
Answers
The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:
y - 3 = 1(x - (-1))
Simplifying:
y - 3 = x + 1
Now, we can rewrite the equation in the standard form:
y = x + 4
Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
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A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229, where x represents the number of cellphones, and a marginal revenue function given by R(x)=429−2x. Find the area between the graphs of these curves and x =0. What does this area represent?
Answers
The area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
What is function?A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -
y = f(x)
Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.
We can write the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -
Area = ∫C(x) dx + ∫{C(x) - R(x)} dx
We can write the area with limits as -
Area =
∫(0.01x² - 3x + 229) dx {limits from 229 to 429}
+
∫(0.01x² - 3x + 229 - 429 + 2x) dx {limits from 429 to 629}
Area = 71548.7 + 420548.7
Area = 492097.4 square units
Therefore, the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
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Please help easy math equation. Make sure it give the answer first then explain why. Don't lie
Answers
Also, for right angles, two interior angles add up to 90 which concludes us with:
5x + 30 + 5x=90
Therefore, the answer is the 3rd choice.
A bedroom door is 9 feet tall and 4 feet wide. What is its area?
Answers
Answer:
36 square feet.
Step-by-step explanation:
9 feet times 4 feet equals 36 feet. Since it is are it has to be square feet. Therefore, the answer is 36 square feet.
Help
Find a if A = 8a
Answers
Answer:
a(A) = 0
Step-by-step explanation:
b. Passes through the point (2, -4) and is parallel to 3x + y = 5
c. Passes through the point (2, -4) and is perpendicular to 3x + y = 5
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)
now, keeping in mind that perpendicular lines have negative reciprocal slopes
\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)
so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)
\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)
area of a floor 19m by 12 m is
Answers
Answer:228m
Step-by-step explanation: 19m x 12m = 228m
Answer: 228m
Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.
A rocket is fired into the air modeling the equation h = -16t2 + 512t + 50, where "t" is the time in seconds and "h" is the
3
height in feet
Answers
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answers
because they are the same AA
Which is the best estimate for the sum of 2/9 + 10/11?
A 0 + 0 = 0 B 1/2+1/2=1 C 1 + 1 = 2 D 0 + 1 = 1
PLS HELP IM HERE WITH MY FRIENDS !!!
50 POINTS!!!!!!!!
Answers
The most accurate calculation for the product of 2, 9, and 11, is 1, or 0 + 1.
Which estimate is the best?Best estimate refers to the figure arrived at by an assessor using deterministic techniques that most accurately captures the anticipated result without optimism or conservatism.
To estimate a number is to round it up to the nearest full number.
We now have February 9 and November 11.
Hence, as 2/9 is closer to 0 than 0.5, we will estimate it to be 0.
Similarly, we will estimate 10/11 as 1 since it is closer to 1 than 0.5.
Hence, 0 + 1 = 1 is the result of adding up their estimates.
In conclusion, 0 + 1 = 1 is the best estimate for the product of the numbers 2/9 and 10/11.
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what is the interval of b, b/8=4?
Answers
hum.......... não sei não menmmmmmmm
6. Simplify the expression. 8.5(4+3h)-h
Answers
Answer:
34+24.5h
Step-by-step explanation:
sin(x)-cos(x)/sin²(x)-cos²(x) = 1
Answers
The prove of the given trigonometric function is given below.
The given trigonometric function is,
(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))
Now proceed left hand side of the given expression:
We can write the expression as,
⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))
Since we know that ,
Algebraic identity:
a² - b² = (a-b)(a+b)
Therefore the above expression be
⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))
⇒(sin²(x) + cos²(x))
Since we know that,
Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).
Then,
sin²(x) + cos²(x)² = 1 is an trigonometric identity
Hence,
(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1
Hence proved.
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