The point on the curve with a slope of −93–√2 is (2, 0.43)
Given x(t) = 2 sin(8t) and y(t) = −9 cos(8t)
We are asked to determine the points on the curve with a slope of −93–√2.
Now, x/2 = sin(8t) --(1)
-y/9 = cos(8t) --(2)
Squaring and adding equations (1) and (2)
(x/2)² + (-y/9)² = sin²(8t) + cos²(8t)
x²/4 + y²/81 = 1
Differentiating both sides
x/2 + (2y/81) (dy/dx) = 0
Given slope = dy/dx = −93–√2
(2sin(8t))/2 + (2(−9 cos(8t))/81)(-93 - √2) = 0
sin(8t) + (2/9)cos(8t)(93 + √2) = 0
Solving for t and taking care of 0 ≤ t <π/8
we get t = 11.59°, 34.09°, 79.09°......
But only t within the given range is t = 11.59°.
Now, x = 2sin(8 x 11.59°) = 2
and y = -9 cos(8 x 11.59°) = 0.43
Hence, the point on the curve with a slope of −93–√2 is (2, 0.43)
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
I am pretty sure the answer would be (2,3)
elena is a college freshman taking an introductory statistics course. her professor has assigned the class the task of organizing data on the relationship between level of income and happiness. what will elena use to summarize her data in a single score?
Elena will likely use a measure of central tendency, such as the mean or median, to summarize her data in a single score.A measure of central tendency is a statistical value that summarizes a set of data.
It is accomplished by assigning a representative score, usually the most common value in a dataset. Elena's statistics course assignment requires her to utilise either the mean or the median to summarise the link between money and happiness.
The mean is computed by summing all of the values in a dataset and dividing by the total number of values. When a set of data is ordered numerically, the median is the midway value. Both of these metrics generate a single score that reflects the full dataset, making it easier to comprehend and make inferences from it.
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What conjectures can you make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle ?
The conjectures which you can make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle include the following below:
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.What is a Bisector?Th line that divides something into two equal parts and it is usually applied to the line segments and angles.
The following relationships between them is that if there is a point which lies on the perpendicular bisector of a segment, then it is most likely to be equidistant from the endpoints of the segment when scrutinized thereby making it the correct choice.
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For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987)=2.37. If this is an overestimate, what conclusion can be made about ??a. f opens down on the interval 0.987
The correct conclusion is:
a. f opens down on the interval 0.987 < x < 1
To determine the conclusion about the behavior of the function f, we can use the tangent line approximation and whether it overestimates or underestimates the actual value of f(0.987).
Given that the tangent line approximation at x = 1 is 2.37, and if this approximation is an overestimate of the actual value of f(0.987), it means that the function lies below the tangent line in the interval 0.987 < x < 1.
Since the tangent line has a positive slope (given that f'(1) = 4), if the function f lies below the tangent line, it must be decreasing in the interval 0.987 < x < 1.
Therefore, the correct conclusion is:
a. f opens down on the interval 0.987 < x < 1
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Complete question =
For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987) = 2.37.
If this is an overestimate, what conclusion can be made about f ??
a. f opens down on the interval 0.987 x < x < 1
b. f opens up on the interval 0.987 x < x < 1
c. f opens down at x = 0.987
d. f opens up at x = 1
Sebastian bought 3 envelopes with 6 figures each. How many figures did he buy in all?
Answer: Sebastián bought 18 figurines.
Step by step explanation:Data :
Sebastian bought = 3 envelopesEach envelope has = 6 figurinesTotal figures = ?We must bear in mind that Javier bought 3 envelopes of 6 figurines each. Calculate the total number of figurines by adding 6 + 6 + 6 therefore:
[tex]\bf \: 6 + 6 + 6 = \boxed{ \bf18}[/tex]
Rpt: Sebastián bought 18 figurines.
Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y=4–5x
The graph of the equation is attached, and the coordinates are (0, 2), (2, -3), (1, -0.5), and (-2, 7).
What is the cartesian plane?When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.
Given equation, 2y = 4 - 5x
let's find the coordinates for the graph,
when x = 0
2y = 4
y = 2
(0, 2)
when x = 2
2y = 4 - 5*2
2y = -6
y = -6/3
y = -3
(2, -3)
when x = 1
2y = 4 - 5
2y = -1
y = -0.5
(1, -0.5)
when x = -2
2y = 4 - 5(-2)
2y = 14
y = 7
(-2, 7)
coordinates for the graph are (0, 2), (2, -3), (1, -0.5), (-2, 7).
Hence graph lies in coordinates (0, 2), (2, -3), (1, -0.5), (-2, 7).
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three strangers meet at a taxi stand and decide to share a cab to cut down the cost. each has a different destination but all are heading in more-or-less the same direction. bob is traveling 10 miles, sally is traveling 20 miles, and mike is traveling 30 miles. if the taxi costs $2 per mile, how much should each contribute to the total fare? what do you think is the most common answer to this question?
The most common answer to this question is that people would suggest splitting the fare equally i.e. each person contributes $40.
Each stranger should contribute to the total fare based on the distance traveled, so the fare would be divided as follows -
Bob: 10 miles * $2/mile = $20
Sally: 20 miles * $2/mile = $40
Mike: 30 miles * $2/mile = $60
Total fare: $20 + $40 + $60 = $120
Therefore, each stranger should contribute $120/3 = $40 to the total fare.
The most common answer to this question is that people would suggest splitting the fare equally, i.e. each person contributes $40, regardless of the distance traveled. This is because it is a simpler and fairer solution, as each person benefits from the shared ride and the cost savings, regardless of the distance traveled.
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Please help me solve for the rest of them
The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,
∠7=35°,∠8=145°,∠9=115°.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
Given ∠4=115°,∠1=35°
∠2+∠4=180 ( supplementary angles)
∠2=180-115=65°
∠1+∠2+∠3=180 (sum of angles of a triangle=180°)
∠3=180-65-35=80°
∠3+∠5=180
∠5=180-80=100°
∠5=∠6=100° (opposite angles)
∠1=∠7=35° (opposite angles)
∠7+∠8=180 (supplementary angles)
∠8=180-35=145°
∠4=∠9=115° (opposite angles)
Hence,
The angles in the given triangle are ∠2=65°,∠5=100°,∠6=100°,
∠7=35°,∠8=145°,∠9=115°.
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In Exercises 27-34, determine the values ofr and s for wlhich the given system of linear equations has (a) no solutions, (b) exactly one solution, and (c) infinitely many solutions.
27.
x₁ + rx₂ = 5
3x₁ + 6x₂ = s
28.
-x₁ + 4x₂ = s
2x₁ + rx₂ = 6
(a) No solutions when r ≠ 6 and s ≠ 5. (b) Exactly one solution when r = 6 and s = 5. (c) Infinitely many solutions when r = 6 and s is arbitrary.
For the system of equations to have (a) no solutions, both r and s must have values that do not satisfy the equations. For example, if r ≠ 6 and s ≠ 5, then the equations cannot both be true. For the system to have (b) exactly one solution, both r and s must have values that satisfy the equations. For example, if r = 6 and s = 5, then the equations are both true and have one unique solution. For the system to have (c) infinitely many solutions, one of the variables must have a value that satisfies the equations, while the other variable may take on any value. For example, if r = 6 and s is arbitrary, then the equations are both true and have infinitely many solutions.
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a regular hexagon with 6 sides is inscribed in a circle with a radius of 11 millimeters. what is the area of the figure?
The area of the figure ( a regular hexagon ) is 314.37 square millimeters .
A regular hexagon which is inscribed in a circle consist of 6 equilateral triangle. All angle is equal.
So side length of the regular hexagon will be same with the radius of circle.
From the question we have following information :
1. Regular hexagon inscribed in a circle
2. Radius of circle is 11 millimeters.
To find the area of the hexagon we can use following formula
A = (3√3) / 2 * [tex]r^{2}[/tex]
Substituting r = 11mm into the equation for the area of the hexagon,
A = (3√3) / 2 * [tex]11^{2}[/tex] = (3√3) / 2 * 121 = 314.367 square millimeters
So the area of the figure is approximately 314.37 square millimeters (rounded to two decimal places).
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solve the separable differential equation. 9yy′=x use the following initial condition: y(9)=5 .
The general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.
The given differential equation is 9yy′ = x. This is a separable equation, meaning it can be solved by separating the variables and integrating both sides. To solve the equation, we start by dividing both sides by 9y to get y′ = x/9y. Now, we can solve for y by integrating both sides with respect to x. This gives us y = (1/9)∫xdy + c, where c is a constant of integration.
To determine c, we can use the initial condition given, y(9) = 5. We substitute 9 for x, and 5 for y to get 5 = (1/9)∫9dy + c. We can solve for c by subtracting (1/9)∫9dy from both sides, giving us c = 5 - (1/9)∫9dy.
Finally, we can substitute c into our equation to get the solution, y = (1/9)∫xdy + (5 - (1/9)∫9dy). This is the general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.
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State the center point and radius of the circle. Write the equation of the circle in standard form.
Answer:
Below
Step-by-step explanation:
Standard form of a circle = (x-h)^2 + (y-k)^2 = r^2
where h,k is the center
for this circle h,k = 2,-1 and radius, r= 4
so the equation would be
(x-2)^2 + (y+1)^2 = 4^2
This graph shows a proportional relationship.
What is the Constant of Proportionality?
Why is the graph proportional? How do you know? What do you see? Explain.
The graph is proportional as it represents a linear function and is depicted using a straight line.
What is direct variation?The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace.
What is constant of proportionality?When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
The graph is proportional as it represents a linear function and is depicted using a straight line. The function can also be said as a direct variation function.
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Helppp due tomorrow!!
Answer:
Length = 7.83, Width = 3.83
Step-by-step explanation:
Assign variables. Let x represent the width
Area (L x W) = 30 m²
(4 + x)(x) = 30
4x + x² = 30
x² + 4x - 30 = 0
Apply Quadratic Formula
[tex]\frac{-4 + \sqrt{4^2 - 4(1)(-30)}}{(2)(1)}[/tex]
Solve
x = -2 ± √34
x = 3. 83... or x = -7.83 (reject this one)
Width = 3.83
Length = x + 4 = 7.83
a b, 4a 5b, |a|, and |a − b|. (simplify your answer completely.)
These are the simplified expressions with A = -3 , |-3 - B|.
What is algebraic expression ?
An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.
Given that A = -3, we can substitute this value into the expressions:
A + B = -3 + B
4a + 5b = 4(-3) + 5b = -12 + 5b
|A| = |-3| = 3
|A - B| = |-3 - B| = |-3 - B|
These are the simplified expressions with A = -3 , |-3 - B|.
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Please someone help me i’m gonna cry! Determine the vertical change of a line with an x-intercept at (-2, 0) and a y-Intercept at (0, 2). Type a numerical
answer in the space provided. If necessary, use the / key as a fraction bar. Do not type spaces in your answer.
Answer:
The vertical change of the line is 2-----------------------------------
The vertical change is the difference of the y-coordinates.
The y- coordinates are 0 and 2, their difference is:
2 - 0 = 2solve each equation for x e^2− 4x = 8
subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.
e^2 - 4x = 8
4x = e^2 - 8
x = (e^2 - 8)/4
To solve for x in this equation, the first step is to subtract 8 from both sides of the equation. The next step is to divide both sides of the equation by 3.This results in the equation: x = 4.Once 8 is subtracted from both sides, the equation becomes e^2 - 4x = 0. Then, divide both sides of the equation by 4, which gives 4x = e^2/4. Finally, subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.
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5
Jed used a protractor to draw an angle measuring 58°. He asked Mark to draw an angle that would be complementary to his angle.
What should the measure of Mark's angle be?
OA. 116°
OB. 122°
OC. 32°
OD. 148°
Answer:
answer choice C.
Step-by-step explanation:
complementary angles are 2 angles that add up to 90 degrees
90=58+x
90-58=x
x=32
Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.
Check picture for full question.
Answer:
The picture won't show. are there answer options?
Step-by-step explanation:
Small room (S) - hold 3 people
Large room (L)- hold 4 people
Hudson reserved twice as many large rooms = 2x Large room #
2L + S = 66
So,
Let S = Small room
Let L = Large room
I hope this can make things slightly easier for you. I tried to make it more visible for you. Please comment if you need more help.
y=9x+9
what would be the slope of a parallel line?
Parallel lines have the same slope.
The slope of y = 9x + 9 is 9, because of the 9 in 9x.
The slope of a parallel line would also be 9.
Use the Root Test to determine whether the series convergent or divergent. [infinity] n2 + 2 7n2 + 5 n n = 1 Identify an. Evaluate the following limit. lim n → [infinity] n |an| Since lim n → [infinity] n |an| ? 1, ---Select--- .
By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .
The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and
If the limit is greater than or equal to 1, the test is inconclusive.
In the series ∑n , the nth term of the series is "n" ,
So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).
we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So, the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.
Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.
The given question is incomplete , the complete question is
Use the Root Test to determine whether the series convergent or divergent. ∑n , where n is from 1 to infinity .
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what is the bank routing number on the check? a sample check. responses 204.67 204.67 856425785 856425785 403 403 2146578212
The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.
In order to determine the routing number on a check:
Look at the bottom left corner of the check, where the routing number is printed in magnetic ink. The first nine digits of the MICR (Magnetic Ink Character Recognition) line, located at the bottom of the check, represent the routing number.The routing number may also be printed on the check in a different location, such as the top or bottom right. One could also find their bank routing number by searching online or contacting their bank directly.Learn more about bank number here: brainly.com/question/25642105
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which combination of factors will increase the chances of rejecting the null hypothesis? group of answer choices a small standard error and a large alpha level a large standard error and a large alpha level a large standard error and a small alpha level a small standard error and a small alpha level
The combination of factors will increase the chances of rejecting the null hypothesis is:
A small standard error and a large alpha level will increase the chances of rejecting the null hypothesis.
Null Hypothesis Rejection FactorsThe standard error represents the variability of the sample mean from the true population mean. A small standard error indicates that the sample mean is a good estimate of the true population mean, making it easier to detect differences and thus increasing the chances of rejecting the null hypothesis.
Alpha (α) is the level of significance, or the threshold for rejecting the null hypothesis. A large alpha level means that a smaller difference between the sample mean and the null hypothesis is required to reject the null hypothesis. This makes it more likely that the null hypothesis will be rejected if the sample mean is significantly different from the true population mean.
So, when both the standard error is small and the alpha level is large, it increases the chances of rejecting the null hypothesis.
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y = 4x + 15
-4x + 4 = 12
can someone help me with this pleasee !
(giving brainly)
Answer: y = x + 19
Step-by-step explanation:
y=4x+15-4x+4=12
y=4x-4x=15+12+4
y=x+19
Can anyone help me with this please, I need written out work not just an answer please
Answer:
hhyýuhhhí7 and Pakistan were colonized together so the britains could no win the fight with india therefore
Step-by-step explanation:
because at that time india and Pakistan were colonized together so the britains could no win the fight with india therefore Britain's plan to intimidate
Answer:
See below
Step-by-step explanation:
I am assuming you need help only for the bottom questions as the top is VERY simple (the top of the cross is literally multiplication of the numbers and the bottom of the cross is addition). This questions needed to be worth more points, with that being said
1. [tex]4y^3 - 2y + 3y^2 - 5y - y^2[/tex]
Combine like terms
[tex]4y^3 - 2y^2 - 7y[/tex]
2. [tex](2x^2 - x + 1) - (x+1)[/tex]
Remove numbers from brackets by distribution property (just imagine a one on the outside of the bracket)
[tex]2x^2 - x + 1 -x - 1\\2x^2 - 2x\\2x(x - 1)[/tex]
3. [tex]-2p^3(-2p^4 + 5p^2 - p)[/tex]
This is just distribution property, multiple the outside by inside (you add the exponents when you multiply)
[tex]4p^7 - 10p^5 + 2p^4[/tex]
4. [tex](3y-6)(2y+3)[/tex]
You multiply each term on the inside of one bracket with the ones on the inside of the other bracket
[tex]6y^2 + 6y -12y -18\\6y^2 - 6y - 18\\6(y^2 - y -3)[/tex]
5. [tex](x+6)(x-6)[/tex]
Same as above but honestly its much quicker if you know the b term in ax^2 + bx + c = 0 always equals 0 in this case
[tex]x^2 -6x + 6x -36\\x^2 - 36[/tex]
Simplify the following using trigonometric identities:
( 1 + sin (x) ) ( sec (x) - tan (x) )
Answer:
[tex](1+\sin(x))(\sec(x)-\tan(x))=\cos(x)[/tex]
Step-by-step explanation:
We are going to use the Pythagorean trigonometric identity:
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
and the following relationships between trigonometric functions:
[tex]\sec(x)=\frac{1}{\cos(x)}\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]
We can transform the expression as follows:
[tex](1+\sin(x))(\sec(x)-\tan(x))=(1+\sin(x))(\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)})=(1+\sin(x))\frac{1-\sin(x)}{\cos(x)}=\frac{(1+\sin(x))(1-\sin(x))}{\cos(x)}[/tex]
Using the formula for the difference of two squares, we can write
[tex](1+\sin(x))(1-\sin(x))[/tex]
as
[tex]1-\sin^2(x)[/tex]
which, according to the Pythagorean trigonometric identity, is equal to
[tex]\cos^2(x)[/tex]
Now we can simplify the original expression to
[tex]\frac{\cos^2(x)}{\cos(x)}=\cos(x)[/tex]
PLS ANSWER!!! Question down below! Limited time!
Answer:
Step-by-step explanation:
I NEED HELP ASAP!!
How many boxes would Alan have to sell to earn exactly $700?
Answer: Alan would have to sell exactly 180 boxes.
Step-by-step explanation:
Kiara measured a swimming pool and made a scale drawing. The scale she used was 13 centimeters : 6 meters. In the drawing, the pool is 26 centimeters wide. What is the width of the actual pool?
Someone please answer theses i give extra points!!
