The given equation 1 value of F(x) is 0.109 and in equation 2 F(x) is -4 respectively.
What in mathematics is trigonometric?Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.
if x⁰=π in eq1
then [tex]f(x)= sin\ 2 \pi[/tex]
[tex]f(x) = 0.109[/tex]
if x⁰= -1 in eq2
then [tex]f(x)=3(-1)-(-1)^2[/tex]
[tex]f(x) = -4[/tex]
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Consider sequences of positive real numbers of the form , in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of does the term 3000 appear somewhere in the sequence ?
a. 1
b. 2
c. 3
d. 4
e. more than 4
No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.
What is meant by sequences?An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.
To estimate a few terms of the sequence in order to obtain a feel how it looks like.
In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].
This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].
We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:
[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]
[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]
[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]
[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]
[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]
At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.
Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].
As [tex]$a_2=2000$[/tex], we only have four possibilities left.
Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.
The equation [tex]$a_4=2001$[/tex]
solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]
There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.
Therefore, the correct answer is option (D) 4.
The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........ in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?
(A) 1
(B) 2
(C) 3
(D) 4
(E) more than 4
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How is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used?
We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
What is the tangent of the angle?
The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.
The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.
Here,
We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.
We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
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I need help, I don’t know what comes next I’m confused???
Answer:
x^2-9
Step-by-step explanation:
-3 + 3 = 0 so the x terms cancel out. This leaves you with only x^2-9
im not sure how to answer thank you
The value of x in the triangle WXY is 27°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠VWY + ∠XWY = 180° (sum of angle in straight line)
6x + ∠XWY = 180°
∠XWY = 180 - 6x
∠XYW + ∠ZYW = 180° (sum of angle in straight line)
∠XYW + 4x = 180°
∠XYW = 180 - 4x
∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
10x = 270
x = 27°
The value of x is 27°
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5 times a number,incrased by 8
Answer:
5 × x + 8
Would be the equation you are looking for.
How does the parabola open? Is the vertex a minimum or maximum value?
g(x) = (4-x)(2+7x)
Answer:
g (x) = −7 x 2 + 26 x + 8
Step-by-step explanation:
Round 7.3084 to 2 decimal places.
Answer:
[tex] \sf \: 7.31[/tex]
Step-by-step explanation:
Now we have to,
→ round a number to 2 decimal places.
The number is,
→ 7.3084
Let's solve the problem,
→ 7.3084
→ ≈ 7.308
→ [tex] \boxed{ \sf ≈ 7.31} [/tex]
→ ≈ 7.3
Hence, the answer is 7.31.
What is the value of W?
Answer:
Step-by-step explanation:
Let angle A = w - 15 degree , angle B = -w + 1 degree and angle X = w + 34 degrees then:
We know that the exterior angle of a triangle is equal to the sum of two interior opposite angles.
therefore, w + 34 = w - 15 + (-w +1)
w + 34 = w - 15 - w + 1
w = -15 - 34 = - 49 degrees
since angle cannot be negative
therefore w = 49 degrees
The annual cost of Randall coverage is 4900. The college pays 62% of the cost. How much is Devi red from his biweekly paycheck for medical insurance?
$1862 is Devi red from his biweekly paycheck for medical insurance
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The annual cost of Randall coverage is 4900.
The college pays 62% of the cost.
We need to find How much is Devi red from his biweekly paycheck for medical insurance
Let us convert 62% to decimal value by dividing with 100
62/100=0.62
Now multiply 0.62 with 4900
0.62×4900
3038
Now subtract 3038 from 4900
4900-3038
1862
Hence, $1862 is Devi red from his biweekly paycheck for medical insurance
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11. Manuel has two different recipes for chocolate chip
muffins. The table shows the amount of chocolate chips
needed per batch for each recipe. He has 10 cups of
chocolate chips. The equation 2b = 10 can be used to
find b, the number of batches of muffins he can make if
he uses Recipe 1. Can Manuel make 3, 4, or 5 batches if
he uses Recipe 1?
n
JID
Recipe Chocolate Chips (cups)
1
2
2
1
Answer:
Manuel can make 5 batches of muffins using Recipe 1
Step-by-step explanation:
You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.
SolutionDivide both sides of the given equation by 2 so solve for the value of b.
(2b)/2 = (10)/2
b = 5
Manuel can make 5 batches of muffins using Recipe 1.
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Write and solve an equation to find the value of x.
Answer:
x = 60
Step-by-step explanation:
Let the two opposite angles be equal and let's call them y.
Because of the theory of angles on a straight line 120 +y = 180
y = 60
Because of the theory of angles on a straight line 2x + y = 180
2x + 60 = 180
2x = 120
x = 60
Alternatively. (also a lot easier)
120 and 2x are opposite angles so they are equal and so;
2x = 120
x = 60
Please mark as brainliest if this answer is helpful.
A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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tony wants to add 97 to 298 and first add 100 to 300 what must he now subtract from this result to obtain 97+298
Step-by-step explanation:
Let A be the sum from 100 to 300
so the sum of 97 to 298 =
A - (299+300) + 97 +98
= A - 403
The top of a plateau is the highest point in an area. The difference between the top of the plateau and the lowest point in the area is 250 meters. Which word describes this 250-meter measurement
Relief refers to the highest and lowest point elevation in an area.
Relief
Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.
elevation
The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.
geology
Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.
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Answer: Relief
Step-by-step explanation:
Relief refers to the highest and lowest point elevation in an area.
Slope is the measure of steepness
Topography refers to the arrangement of the land in an area
Elevation on the other hand is the distance above sea level
Make a box plot for the given data : 17,29 ,32,30,14,9,39,10,32,23
Answer:
It can't add a plot for those numbers-
Step-by-step explanation:
-6/7 on a coordinate plane ( I need 3 ordered pair if so pls help)
-6,7 is in 2nd Quadrant of a coordinate plane because the coordinate of x is negative integer and the coordinate of y is positive integers.
What is coordinate?It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. We may have observed the use of grids in mathematics. We can plot any point using these grids and its coordinates.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
The X-axis is the horizontal axis and the Y-axis is the vertical axis of a coordinate plane, which has four quadrants.
To plot -6, 7 point on coordinate first we find the point -6 on the left side of plane on x axis. the we go upward and find point y=7 parallel to y axis.
this point is -6,7.
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Share $60S in the ratio 4:5:7:
Answer:
15:18.75:26.25
Step-by-step explanation:
4:5:7
Total=16
60/16 = 3.75
4 x 3.75 = 15
5 x 3.75 = 18.75
7 x 3.75 = 26.25
15:18.75:26.25
Answer: $15 : $18.75 : $26.25
Step-by-step explanation:
4 + 5 + 7 = 16
4/16 × $60 = $15
5/16 × $60 = $18.75
7/16 × $60 = $26.25
In the story "How Tacos Conquered America" and "The Story of Spaghetti and
Meatballs" have a lot of similarities and differences. Read more to find out what they
have in different and what they have in common. Although the stories had a lot of
similarities it also had a lot of differences for reference Where do these beloved foods
have their roots Tacos were Originated in mexico where a owner of taco bell
"There was just one problem. The cooks at the restaurant hated making them! Each cornmeal tortilla shell had to be
individually fried in scalding oil. The cooks had to turn each tortilla by hand until it was perfectly crispy. The process
was dangerous and painful. The cooks had the burns to prove it ".Juvencio Maldonado was going to
change that. He got to work and made his Mechanical fryer which made up to 7 tacos at a time
and no more burns.
Dose this sound good
Determine whether y varies with x if so find the constant of variation and write the equation A. No b. Yes k= -2 and y= -2x
The equation is y = 2x and the constant of variation k = 2
Therefore, the correct answer is option d.
Here, we can clearly see that y varies directly with x, because as x increases, y increases with the same proportion and vice versa. The constant of variation, k, is the coefficient of proportionality between x and y. To find the constant of variation, we can divide the value of y by the value of x for any one of the given points.
For example, for the point (-2, -4) we have:
k = -4 / -2 = 2
So the equation relating x and y is: y = kx = 2x
Hence, the equation is y = 2x and the constant of variation k = 2
Therefore, the correct answer is option d.
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The complete question is -
Determine whether y varies directly with x. If so, find the constant of variation and write the equation.
x | y
-2 | -4
-4 | -8
-16 | -32
a. No
b. yes; k=-2 and y=-2x
c. yes; k=1/2 and y=1/2x
d. yes; k=2 and y=2x
4x + 4y = -8
-2x - 2y = 4
Answer: To solve this system of equations, you can use the substitution method.
First, you can solve one of the equations for one of the variables in terms of the other. For example, you can solve the first equation for y:
y = (-4x - 8)/4
Then, you can substitute this expression for y into the second equation to find the value of x:
-2x - 2((-4x - 8)/4) = 4
-2x + 4x + 8 = 4
2x = -4
x = -2
You can then substitute this value of x back into the first equation to find the value of y:
y = (-4(-2) - 8)/4 = (8 - 8)/4 = 0
Thus, the solution to the system of equations is x = -2 and y = 0.
Step-by-step explanation:
What fraction is no solution?
No solution is a fraction that cannot be represented as a fraction of integers.
A fraction is a division of two numbers, and no solution occurs when the divisor is 0, because division by 0 is undefined.
For example, consider the fraction 2/0. This is a fraction with no solution because division by 0 is undefined. To explain this further, let's look at the formula for division: a/b = c. In this formula, a is the dividend, b is the divisor, and c is the quotient. In the fraction 2/0, the dividend is 2 and the divisor is 0, so when we try to calculate the quotient, we get c = 2/0. Since division by 0 is undefined, the result is no solution.
To summarize, no solution occurs when a fraction's divisor is 0 because division by 0 is undefined. This means that no fraction can be represented as a fraction of integers when the divisor is 0 because there is no solution.
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The annual gym subscription for a single member is Rs.1000, while an annual family membership is Rs.1500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost 5/7 of a family membership. Determine the amount of the proposed increase.
The amount of the proposed increase is, Rs 1071.4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The annual gym subscription for a single member is Rs.1000,
And, An annual family membership is Rs.1500.
Here, A single membership increased cost 5/7 of a family membership.
Hence, The increased cost = 5/7 of 1500
= 1071.4 Rupees
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A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag.
. Mr. Johannsen has a farm with 3 cows, 8 chickens, and some ducks. If the total number of farm animal legs is 40, how many ducks does Mr. Johannsen have on his farm
The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.
To determine this:
Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.
Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.
We know the total number of farm animal legs is 40 legs.
So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.
Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.
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b. Consider a circle with centre O and radius of 4 units. The distance of point P is 2 units from centre. Find the distance of inverse of point P' from the centre O.
Morgan collects toy horses. she has 34 in her collection. she got 23 horses for her birthday. she dropped a box and broke 5 of them. how many toy horses does she has now
Answer:
34 + 23 = 57
57 - 5 = 52
Therefore, she has 52 toy horses.
what is 5x5+9x7
Whell help please i just wanted to put 5x5+9x7 but it didnt let me so yay
Answer: 88
Step-by-step explanation:
Answer: 88
Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88
An instructor gives four -hour exams and one final exam, which counts as three -hour exams. Find a student's grade if she received , , , and on the -hour exams and on the final exam. Round your answer to one decimal place if necessary.
One final test that lasts three hours is given in addition to four-hour exams that are given by the teacher. The student's last grade is an 83.29.
What is students final average ?The final exam result was an 80, which counts as 31 hour examinations if the exam scores range from 60 to 81, which totals to 97,87. In order to accomplish this, we must multiply three eighty by 62, 81, 97, and 87, which equals a 31-hour exam.
The whole time for the final exam, which is 31 hours, will be added up and divided by 7, giving us an average final grade for the student of 81.To reduce the number's number of significant digits in order to approximate it. Rounding down from 15.4 to 15.5, from 15.51 to 15.5 or 16, from 0.499 to 0, and from 970,000 to 1 million.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
How do you find the sides of a triangle?In a right triangle, the hypotenuse is the longest side, the "opposite" side is the one that faces a particular angle, and the "adjacent" side is the one that faces that angle.
Step 1: Simplify both sides of the equation.
[tex]$$4 g-6=8$$\\Step 2: Add 6 to both sides.$$\begin{aligned}& 4 g-6+6=8+6 \\& 4 g=14\end{aligned}$\\$Step 3: Divide both sides by 4 .$$\begin{aligned}& \frac{4 g}{4}=\frac{14}{4} \\& g=\frac{7}{2}\end{aligned}$$[/tex]
[tex]$g=3 \frac{1}{2}$[/tex]
Therefore, the correct answer is option a)[tex]$g=\frac{7}{2}$[/tex].
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If 70% of the members remembered the password but 21 members forgot, then how many members were there in all?
Please show work if you can
Thxs
Answer:
70 members
Step-by-step explanation:
Let's call the number of total members x. We know that 30% or [tex]\frac{3}{10}[/tex] of the members forgot, so our equation looks like this:
[tex]\frac{3}{10}x = 21[/tex]
Then, we will multiply both sides by 10 to get rid of the fraction:
3x = 210
Finally, we will divide both sides by 3 to find out our variable, x:
x = 70
So, there are 70 members in total.
Hope this helped!