In this case, the terminal point of theta/2 can be determined using the following steps:
Since cos(theta/2) < 0 and the cosine function has a range of [-1, 1], it follows that theta/2 must be in the second or third quadrant (90 degrees to 180 degrees or 180 degrees to 270 degrees).
To find the terminal point of theta/2, we can use the formula for converting from polar to Cartesian coordinates: x = rcos(theta) and y = rsin(theta), where (x,y) is the Cartesian coordinates of the terminal point, r is the radius, and theta is the angle in radians.
In this case, the radius is 1 (since the terminal point is on the unit circle) and the angle is theta/2. Substituting these values into the formulas above, we get:
x = 1 * cos(theta/2)
y = 1 * sin(theta/2)
To find the values of cos(theta/2) and sin(theta/2), we can use the identity cos(theta/2) = sqrt((1 + cos(theta))/2) and sin(theta/2) = sqrt((1 - cos(theta))/2).
Substituting the given value of cos(theta) (-1/9) and the identities above into the formulas for x and y, we get:
x = sqrt((1 + (-1/9))/2) = -sqrt(2)/3
y = sqrt((1 - (-1/9))/2) = sqrt(8)/3
Thus, the coordinates of the terminal point of theta/2 are (-sqrt(2)/3, sqrt(8)/3).
The terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).
How to find terminal point?To find the terminal point (a₁, a₂) of theta/2, use the half-angle identity for cosine:
cos(theta/2) = ± √((1 + cos(theta)) / 2)
Given that cos(theta) = -1/9 and cos(theta/2) < 0, the negative sign should be used in the half-angle identity.
Calculate cos(theta/2):
cos(theta/2) = - √((1 + cos(theta)) / 2)
cos(theta/2) = - √((1 - 1/9) / 2)
cos(theta/2) = - √((8/9) / 2)
cos(theta/2) = - √(8/18)
cos(theta/2) = - √(4/9)
cos(theta/2) = - 2/3
Cos(theta/2) = -2/3. To find the terminal point (a₁, a₂), determine the values of a₁ and a₂.
Since cos(theta/2) is negative, a₁ is negative. To find the value of a₂, use the Pythagorean identity:
cos²(theta/2) + sin²(theta/2) = 1
Since cos(theta/2) = -2/3, calculate sin(theta/2):
sin²(theta/2) = 1 - cos²(theta/2)
sin²(theta/2) = 1 - (-2/3)²
sin²(theta/2) = 1 - 4/9
sin²(theta/2) = 5/9
sin(theta/2) = ± √(5/9)
sin(theta/2) = ± √(5) / 3
Since theta is in the second quadrant (cos(theta) = -1/9), sin(theta) is positive in the second quadrant. Therefore, sin(theta/2) = √(5) / 3.
Now, sin(theta/2) = √(5) / 3.
So, the terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).
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See the picture please
a container is in a shape of a cuboid
the container is 2/3 full of water
a cup holds 275ml of water
what is the greatest number of cups that can be completely filled with water from the container
The greatest number of cups that can be completely filled with water is 2.
What is the greatest number of cups that can be completely filled with water from the container?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
The greatest number of cups that can be completely filled with water will be:
1000ml = 1 liter
2/3l = 667ml
Therefore, the number of cups will be:
= 667 / 275
= 2
The greatest number of cups is 2.
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Please help me! Find the value of X&Y for which ABCD must be a parallelogram!
Answer:
x = 8y = 6Step-by-step explanation:
You want the values of x and y that make the quadrilateral a parallelogram, given the halves of one diagonal are marked (3x-14) and (x+2), and the halves of the other diagonal are marked (4y-7) and (y+11).
ParallelogramThe diagonals of a parallelogram bisect each other. This means the marked segments on each diagonal are congruent.
x-value(3x -14) = (x +2)
2x = 16 . . . . . . . . . add 14-x
x = 8 . . . . . . . . divide by 2
y-value(4y -7) = (y +11)
3y = 18 . . . . . . . . . add 7-y
y = 6 . . . . . . . . divide by 3
The values of x and y are 8 and 6, respectively.
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Answer:
z = 0.9
Step-by-step explanation:
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Step 1) (2z +2.4)=(4z+1) - 0.4
Step 2) (2z +2.4)=(4z+0.6)
Step 3) 1.8 = 2z
Step 4) 1.8/2 = z
Step 5) 0.9 = z
Answer:
.9
Step-by-step explanation:
it is 0.9 i did this assignment with my teacher
The circumference of a circle is 7π ft. What is the area, in square feet? Express your answer in terms of
π
Answer:
49/4 π sq feet
Step-by-step explanation:
The circumference is the distance around a circle. The formula for circumference is:
C = πd
d stands for diameter. The circumference was given, 7π.
C = πd
= 7π
The diameter is 7. This is double the radius. The radius is half the circumference, so this radius is 7/2.
The area of the circle is:
Area = πr^2
= π(7/2)^2
= π(49/4)
=49/4 π
The area is 49/4 π
square feet.
Answer:
the answer is
12.25π ft
Given that ⧍PQR≅⧍TSU, name the corresponding angles and segments.
Answer: 5,1
Step-by-step explanation:
Manuel is riding his bike. The graph represents the distance Manuel travels from his house over time.
Describe what is happening as depicted in the graph.
Observing the nature of the graph and the pattern it develops relating time and distance covered by Manuel, The graph explains the nature of distance covered in bike with respect to time.
What is a graph?A representation of the relationship between two variables, often measured along one of two right-angled axes each.
What are different types of graphs?Different types of graphs are:
Statistical Graphs.Exponential Graphs.Logarithmic Graphs.Trigonometric Graphs.Frequency Distribution Graph.Manuel drives away from house for 2 units of time and stayed at a place for another 2 units of time. He start to bike towards the house for 2 units of time and again started to travel away for a single unit of time. He stayed at a place for 2 unit of time and bike back to the house in 5 units of time.
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what is the value of x when y= -1
Answer:
x=+1
Step-by-step explanation:
the value of x will be positive 1 for we will take x=0 y=-1 where we inter change the values to be x=y-1=0
Is this graph a function or nonfunction
Answer:
Not a function
Step-by-step explanation:
If we use the vertical line test, we can get an answer quite easily. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
If we were to move a vertical line across the above graph, it would touch two places, so therefore it is not a function.
Todd is planning a vacation and is adding $5 per day towards his savings account for it. After 20 days he has a total of $150 in his savings
account.
a). Assuming this is linear relationship write an equation to model it.
b). How many days will it take Todd to build his savings up to a total of $250.
A) The equation of the model is 20x=100.
B) Todd will take 50 days to build his savings up to a total of $250.
What is meant by an equation?An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.
1 day ------ $5
20 days -------?
x=20×5
x=$100
A) Let the savings per one day =$5
For 20 days it will be $100
And it is given as 20x=100
Where x=time in days
B) Todd has $150 dollars for 20 days
Actual savings for 20 days=100
? --------250
x=(20×250)/100
x=50 days.
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Complete the sentences to compare the x- and y-intercepts for each function.
f(x) = -1/2 x + 10
g(x) = -4x - 12
The y-intercept of function fis
The x-intercept of function fis
but the y-intercept of function g is
but the x-intercept of function g is
The y-intercept of function f is 10 The x-intercept of function f is 20 but the y-intercept of function g is -12 but the x-intercept of function g is -3.
What are the x and y-intercepts?The places where a function or equation's graph crosses or "touches" the x-axis of the Cartesian Plane are known as the x-intercepts. This may be compared to a point with a y-value of zero. The locations where a function or equation's graph crosses or "touches" the y-axis of the Cartesian Plane are known as the y-intercepts. This may be compared to a point with a zero x-value.
Given two functions f(x) = -1/2 x + 10 and g(x) = -4x - 12
For function f(x)
Y-intercept of f(x) = -1/2 * 0 + 10 = 10
X-intercept of f(x) => -1/2x + 10 = 0
X-intercept of f(x) => x = 20
For function g(x)
Y-intercept of g(x) = -4*0 - 12 = -12
X-intercept of g(x) => -4x -12 = 0
X-intercept of g(x) => x = -3
Therefore, Function f's y-intercept is 10 Function f's x-intercept is 20, but the function g's y-intercept is -12 and its x-intercept is -3.
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marcus is a gardener .he pulls weeds for 18 min waters for 13min and plants for 16 min.how many total min does he spent gardening
Answer: 47 mins
Step-by-step explanation:
18 min pulls weeds + 13min water + 16 min plant = 47 mins
12 divided by 127 show your work
Answer:
10.58
Step-by-step explanation:
if m/1 +m/5=234°, find m26=
Answer:
if m/1 +m/5=234°, find m26=
m26 = 234° - (1 + 5)m = 234° - 6m
m26 = 234° - 6(26)
m26 = 234° - 156°
m26 = 78°
What is k to the 5th power then triple the result
Answer: K^15
Step-by-step explanation:
The equation is (k^5)^3
To simplify this, we take the square root of 5-time square root 3 equal square root of 15
So the answer is k^15
If you can please give me a Brainliest, thank you!
Find the nth term of this quadratic sequence 4, 7, 12, 19, 28, ...
Answer:
which grafde are you in and I think ur question is wrong
If you buy a 7.25
pound pumpkin that
costs 59 cents per
pound, how much will
you have to pay?
Answer:
you will have to pay 427.75 cents.
Step-by-step explanation:
Multiply 7.25 by 59.
Which linear inequality is represented by the graph?
y ≤ One-halfx + 2
y ≥ One-halfx + 2
y ≤ One-thirdx + 2
y ≥ One-thirdx + 2
The linear inequality that is represented by the graph is; y ≤ One-halfx + 2
How to Interpret Inequality Graphs?
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the inequality graph attached, we can see that we can calculate the slope from;
m = (y2 - y1)/(x2 - x1)
m = (3 - 2)/(2 - 0)
m = 1/2
We can also see that the y-intercept which is the point where the line crosses the y-axis is; y = 2.
The line is a solid line and not dotted and the shaded part is beneath the line and as such;
The inequality is; y ≤ One-halfx + 2
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75 divided by 18 what do it equal
Please help me. I will give a brainliest AFTER 2 people message
Reason:
The scale factor 1.75 is what we'll multiply by each dimension of the blue figure, to get the green figure.
The "3" is multiplied by 1.75 to get 3*1.75 = 5.25 which is the value of x, since both involve the top side of each respective trapezoid.
In other words,
(preimage Length)*(scale factor) = (image length)
(3)*(1.75) = x
5.25 = x
x = 5.25
Use Newton's method to find all roots of the equation correct to six decimal places. e^x = 9 - 2x
1.716762 is the correct solution up to 6 decimal places by using Newton's method.
What is Newton's method?The Newton's method is a potent tool, and in general, the convergence is quadratic: as the procedure approaches the root, the discrepancy between the root and the approximation squares, almost doubling the number of accurate digits at each step. The approach does, however, have significant drawbacks. The phrase "Newton's method" refers to Isaac Newton's explanation of a particular application of the method in his books De analysi per aequationes numero terminorum infinitas, which he wrote in 1669 and had William Jones publish in 1711, and De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson).
Given,
f(x)=eˣ+2x-9
f'(x)=eˣ+2
ˣₙ₊₁=ˣₙ-f(ˣₙ)/f'(ˣₙ)
Let, n=1
x₂=1.9074740
x₃=1.7299338
x₄=1.716825
x₅=1.7167621
x₆=1.716762
x₅≈x₆
Therefore, 1.716762 is the correct solution up to 6 decimal places.
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There is a sequence of numbers arranged in rows. Each row has six numbers. If the sequence begins as below, what is the fifth number on the 7853rd row?
0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17 ...
please help! I have a lot of points to give out lol
The fifth number in the 7853rd row as required to be determined is; 47,116.
What is the 7,853rd term of the arithmetic sequence?It follows from the task content that the fifth number on the 7853rd row of the sequence is to be determined. By observation, each column of the sequence of numbers represents an arithmetic sequence of numbers in which case;
The common difference is; 6 - 0 = 12 - 6 = 17 - 11 = 6.
Therefore, since the nth term of an arithmetic sequence is given by the formula;T (n) = a + (n - 1) d.
where a = does term
n = number of terms
d = common difference
In this scenario, the first term is the fifth number on the first row = 4.Therefore, the fifth number on the 7853rd row is; T (7853) = 4 + (7853 - 1) × 6T = 4 + (7852 × 6)T = 4 + 47,112T = 47, 116.
Therefore, the required number is; 47,116.
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A clothesline rope is 8 feet long. Which of these is another way to express 8 feetanother
Using the unit conversion concept of mathematics and converting the length provided into various units , There are multiple ways to express 8 feet such as in inches, meter or kilometer and many more.
What do you mean by unit?A unit is a reference value established by law or convention that is used as a benchmark to measure an object's physical characteristic.
What do you mean by unit conversion?By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
l= 8 feet
In inches, l= 96 inches
In meter, l =2.43 meters
In kilometer, l = 0.0024 kilometers
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Using the unit conversion concept of mathematics and converting the length provided into various units , There are multiple ways to express 8 feet such as in inches, meter or kilometer and many more.
What do you mean by unit?
A unit is a reference value established by law or convention that is used as a benchmark to measure an object's physical characteristic.
What do you mean by unit conversion?
By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
l= 8 feet
In inches, l= 96 inches
In meter, l =2.43 meters
In kilometer, l = 0.0024 kilometers
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23. दुई अङ्कको एउटा सङ्ख्या त्यसका अङ्कहरूको योगको चार गुणा छ । यदि अङ्कहरूको गुणनफल 18 भए त्यो सङ्ख्या र त्यसको विपरीत सङ्ख्या बिचको भिन्नता पत्ता लगाउनुहोस् । A number of two digits is equal to four times the sum of the digits. If the product of the digits is 18 then find the difference between the number and its reversing number.
Answer:
hence the number is 24.
Step-by-step explanation:
Two Solutions:
1.10x+y=4(x+y)
2x=y
2.10x+y+18=10y+x
x−y=−2
x−2x=−2
x=2
y=4
two digit number =24
xochitl has $2 worth of nickels and dimes. she has a total of 24 nickels and dimes altogether. graphically solve a system of equation in order to determine the number of nickels, x. and the number of dimes, y, that xochitl has
By using simultaneous linear equation, it can be calculated that
Xochitl has 8 nickels and 16 dimes
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Let the number of nickel Xochitl has be x and the number of dimes Xochitl has be y
She has a total of 24 nickels and dimes altogether
x + y = 24 .... (1)
Xochitl has $2 worth of nickels and dimes
0.05x + 0.1y = 2
5x + 10y = 200
x + 2y = 40 ..... (2)
From the graph, it is clear that the two simultaneous linear equation intersects at (8, 16)
So x = 8, y = 16
Xochitl has 8 nickels and 16 dimes
The graph has been attached
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2. What political hurdles did African American representatives have to face after they went into
office?
The political hurdles that African American representatives have to face after they went into office is Racism.
What is Racism?Racism is the belief that different groups of humans have different behavioral traits that correspond to inherited characteristics and that they can be divided based on the superiority of one race over another.
Racism stems from the belief that a person is superior to others because of the color of their skin. In the olden days, blacks were excluded from public schools, denied the right to vote, and faced racism and legal discrimination almost everywhere. This is still faces in politics as well.
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1. Which logarithm bases can you use to solve for x in the exponential equation 4^3+x= 25 ? (Select all that apply.)
log base 10
log base x
log base 4
log base 25
The logarithm bases can you use to solve for x in the exponential equation [tex]4^{3+x}[/tex]= 25 is log base 4. So, option 3 is correct.
What is meant by exponential equation?Finding the slope (m) and y-intercept (b) of a line's graph will allow us to build a linear function with the formula y=mx+ b. We may build an exponential function of the form y=a+ bx given an exponential curve graph by locating the common ratio (b) and y-intercept (a) on the graph. If your function has the formula y = a + b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.
Given equation is [tex]4^{3+x}[/tex]= 25
Applying logarithm with base 4 to both sides.
log [tex]4^{3+x}[/tex]=log 25
(3+x)log 4=log25/log 4
3+x=log 25/log 4
x=(log 25/log4)-3
So, we use log base 4.
Hence, option 3 is correct.
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The perimeter of AABC= 15 cm. Given that AB = 7 cm and /BAC = 60°, find the lengths of AC and BC and the area of the triangle.
Step-by-step explanation:
Call AB side a...which is 7
therefore b+c = 8 (editted this part due toarithmetic slip)
sketch it, use the cosine rule knowing cos 60 = 0.5and set up a simultaneous equation for the sides b+ c
7^2 = b^2+c^2 - bc
then
a + b = 15
(as this 2bcCOSA cancels down)
If the derivative of y, dy/dx i the rate of change of y (alo known a the lope or gradient)
How can we ue the 2nd derivative of y, d2y/dx2 to determine whether the vertex of a quadratic i a maximum or minimum?
Why i thi the cae?
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
As stated in the video, the rate of change of dy/dx is the second derivative ( d2y/dx2 )
Thus, at a stationary point (dy/dx = 0), when d2y/dx2 < 0 meaning the rate of change of the gradient is negative the point is a maximum point. We can see that in the image below.
And at minimum points the rate of change of gradient is positive. Thus d2y/dx2 > 0 at minimum points.
A curve has equation y=x3 -12x +6 Find the coordinates of each stationary point, and the nature of these points (minimum or maximum).
Find when dy/dx = 0
dy/dx=3x2 -12
3x2 – 12 = 0
x2 =4
x = 2 or x=-2
when x = 2 y=-10 when x= -2 y=22
Thus, coordinates of stationary points are (2,-10) and (-2,22)
Now in order to find whether they are maximum or minimum points, we have to calculate d2y/dx2
d2y/dx2 = 6x
when x=2 d2y/dx2 = 12
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
when x= -2 d2y/dx2 = -12
As d2y/dx2 is negative, the rate of change of the gradient is negative, which means that (-2,22) is a maximum point
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dellana company tested 50 products for 75 hours each. during this time, it experienced four breakdowns. compute the number of failures per hour. what is the mean time between failures?
dellana company tested 50 products for 75 hours each. during this time, it experienced four breakdowns. compute the number of failures per hour, 937.50 hours is the mean time between failures.
What is mean time?The span of time before something occurs or before a given time frame expires. We can utilise the current computers while waiting for the new ones to arrive next week.
Given that,
dellana company tested 50 products
time =75 hours
Thus, total products in hours
= 50 products × 75 hours each
= 3750 product hours
Also said that, 4 breakdowns in 3750 product hours,
so, (4/3750) = 1.067 × 10⁻³ = 0.001067 breakdowns per hour.
Also, an average of 0.001067 breakdowns per hour = λ
therefore, mean time between failures:
= 1/ λ
= 1/0.001067
= 937.50 hours
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