Solve the equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.) tan2(x) + tan(x) − 20 = 0
Answers
The solution of equation of trigonometric functions, tan²(x) + tan(x) − 20 = 0, is equals to the x = 1.33 radians , 1.37 radians (x = arc tan(4) = 1.33 , x = arc tan(-5)= 1.37).
We know that trigonometric functions are periodic functions, solutions of trigonometric equations are then infinite and periodic. In these equations, it is essential to know the reduction formulas of each quadrant, which allows each angle in the first quadrant to be related to its corresponding angle in the other three quadrants. We have an equation which contains triagmometric function,
tan²(x) + tan(x) − 20 = 0 --(1) and we have to solve it. First we change the variable as y = tan(x). Rewrite the equation (1), y² + y - 20 = 0 --(2) which is an quadratic equation. The quadratic formula helps to solve the equation (2).
=> y = ( -1 ± √1 - 4(-20))/2
=> y = ( -1 ± √81)/2
=> y = ( -1 ± 9)/2
=> y = ( -1 + 9)/2 or (-1 -9)/2
=> y = 4, -5
Now x = tan⁻¹(y), and so, x = tan⁻¹(4) = 1.33 radians, or tan⁻¹(-5) = 1.37 radians. Hence, required value is ( 1.33, 1.37).
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Related Questions
help me please i have been stuck on this
Answers
Answer:
3 1/8
Step-by-step explanation:
You can rewrite 1 1/4 as 1 2/8, so adding them you'd get 2 9/8, or 3 1/8
If M is the set of all square numbers less than 80 and N is the set of all non-negative even numbers that are under 30, Write the lists of all elements of M and N.
Answers
Answer:
The set M of all square numbers less than 80 is:
M = {0, 1, 4, 9, 16, 25, 36, 49, 64}
The set N of all non-negative even numbers that are under 30 is:
N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
Answer:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28Step-by-step explanation:
A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.
The square numbers less than 80 are:
1, 4, 9, 16, 25, 36, 49, and 64.An even number is an integer that is divisible by 2 without leaving a remainder.
The non-negative even numbers that are under 30 are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, and 28.Therefore:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28The measure of an angle is 1°. Find the measure of the complement.
Answers
The measure of the complement of a 1-degree angle is 89 degrees.
The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.
Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:
1 degree + x degrees = 90 degrees.
To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:
x degrees = 90 degrees - 1 degree.
Simplifying the right side, we get:
x degrees = 89 degrees.
In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.
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Which of the following is the correct step for solving
-2x = 14?
A. Divide both sides by 2.
B. Multiply both sides by 1/2.
C. Add 2 to both sides.
D. Divide both sides by 2.
Answers
Answer:
Divide both sides by -2.
Compare the process of solving
|x – 1| + 1 < 15 to that of solving
|x – 1| + 1 > 15.
Answers
The solutions to the inequalities are -13 < x < 15 and x > 15 and x < -13
How to compare the process of solving |x – 1| + 1 < 15 to that of solving |x – 1| + 1 > 15?The inequality expressions are given as:
|x – 1| + 1 < 15
|x – 1| + 1 > 15
We start by solving the inequality expression |x – 1| + 1 > 15
So, we have
|x – 1| + 1 < 15
Subtract 1 from both sides
|x – 1| < 14
Remove the absolute bracket
x – 1 < 14 or x - 1 > -14
This gives
x < 15 and x > -13
Combine the inequalities
-13 < x < 15
We then continue by solving the inequality expression |x – 1| + 1 < 15
So, we have
|x – 1| + 1 > 15
Subtract 1 from both sides
|x – 1| > 14
Remove the absolute bracket
x – 1 > 14 or x - 1 < -14
This gives
x > 15 and x < -13
Hence, the solutions to the inequalities are -13 < x < 15 and x > 15 and x < -13
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What is the GCF of 12x3y5 + 18x4y2?
Answers
Answer: 6x3y2
Step-by-step explanation:
The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 20.4cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 20.4 cm, what is the single value that is the best-predicted height for that person?
Answers
The best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.
To find the best-predicted height for someone with a foot length of 20.4 cm, we need to use the linear regression equation that relates foot length and height. The linear regression equation is of the form:
y = a + bx
where y is the predicted height, x is the foot length, a is the y-intercept, and b is the slope of the regression line.
From the given information, we know that the technology found a linear correlation between height and foot length. This means that we can use the paired data to calculate the values of a and b in the regression equation.
Using the paired data and technology, we can obtain the following regression equation:
height = 34.774 + 1.4966 (foot length)
Now we can substitute the given foot length of 20.4 cm into the equation to obtain the predicted height:
height = 34.774 + 1.4966 (20.4)
height = 65.83 cm
Therefore, the best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.
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The calculation for x=0x=0 corresponds to the
point where the graph crosses the______-axis.
This is the point (______)
Answers
The calculation for x=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
In the question ,
it is given that x=0 ,
When x=0 in a point (x,y) means , that point lies on the y -axis , and it is called as the y intercept .
Y intercept is defined as the point where the graph of a line crosses the y-axis .
the point on the y-axis will be (0,y) ,
So , the graph will cross the y-axis when x=0 , and that point will be (0,y).
and the value of y will be called as the y intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
The given question is incomplete , the complete question is
The calculation for x=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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Which situation explains when a system of equations has infinitely many solutions ?
Answers
Answer:
C. when they are the same line
what is the quotient of 2.408 • 10^24 divided by 6.02 • 10^23
Answers
Answer:
2.408
Step-by-step explanation:
Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day
Answers
The unit rate of computers per day using the graph is that 12 computers are made per day.
What is a unit rate?The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.
How to find the unit rate of computers per dayTo obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
So, it is given by:
\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)
\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)
\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)
\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)
\(\bold{Slope = 12}\)
Unit rate = 12 computers per day.
The attachment of the graph is given below.
Therefore, the unit rate of computers per day is 12.
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Need help urgently. This is a simple but difficult math equation
Answers
Answer:
The last one looks like its not true
Answer:
Step-by-step explanation:
4) looks wrong , or untrue.
Fill in the values to give a legitimate probability distribution for the discrete random variable , whose possible values are , , , , and .
Answers
We must complete the table of probabilities such that the probability distribution is legitimate.
Because all the possible values of the variables are 0, 3, 4, 5 and 6, the sum of the probability of each number must sum up 1:
\(P(x=0)+P(x=3)+P(x=4)+P(x=5)+P(x=6)=1.\)Replacing the values of the table, we have:
\(\begin{gathered} 0.12+P(x=3)+P(x=4)+0.24+0.20=1, \\ P(x=3)+P(x=4)=1-0.12-0.24-0.20, \\ P(x=3)+P(x=4)=0.44. \end{gathered}\)From the last equation, we see that to have a legitimate probability, we must select values of P(x = 3) and P(x = 4) such that they sum up 1. One possible pair of values is:
• P(x = 3) = 0.2,
,• P(x = 4) = 0.24.
Answer
One possible pair of values is:
• P(x = 3) = 0.2,
,• P(x = 4) = 0.24.
What is x?
If necessary, round to the nearest tenth (one decimal place)
Please help, Thank you!
Answers
Answer:
4/x-8=8/2
4/x-8=4
4=4(x-8)
4=4x-32
4+32=4x
36=4x
dividing through by 4
x=9
converting to the nearest tenth will be 9.0
therefore x=9.0
why are inverse realashinships between operations used to solve twop step inqualites
Answers
Inverse relationships between operations are used to solve two-step inequalities because they allow us to isolate the variable on one side of the inequality.
A two-step inequality involves two operations that need to be undone in reverse order to solve for the variable. Inverse relationships between operations are used to "undo" these operations, leading to an isolated variable.
For example, consider the inequality 2x + 5 > 11. The first operation being performed on x is multiplication by 2, and the second operation is adding 5. To solve for x, we need to undo these operations in reverse order.
The inverse relationship of multiplication by 2 is division by 2, and the inverse relationship of adding 5 is subtracting 5. Therefore, we can solve the inequality as follows:
2x + 5 > 11
2x > 6 (subtract 5 from both sides)
x > 3 (divide both sides by 2)
Here, we first subtracted 5 from both sides to undo the addition of 5, and then divided both sides by 2 to undo the multiplication by 2.
Inverse relationships between operations are used in two-step inequalities because they help to simplify the equation by undoing the operations one by one, leading to an isolated variable.
By using inverse relationships between operations, we can efficiently and systematically solve two-step inequalities and isolate the variable to find the solution set.
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Find the volume of the cone. Either enter an exact answer in terms of 1 or use 3.14 for and round your final answer to the nearest FI hundredth. 10 4 units 3
Answers
167.47 units
Find the greatest common factor (GCF) of 60, 78, and
66.
10
5
13
6
Answers
Answer:
6
Step-by-step explanation:
Prime factorization of 60: 2 • 2 • 3 • 5
Prime factorization of 78: 2 • 3 • 13
Prime factorization of 66: 2• 3• 11
Common factors = 2* 3 = 6
PLEASE PLEASE PLEASE HELP
Answers
Answer:
a)
Growth rate 0.075
Growth factor 1.075
b) 59177 or approx 60000
Step-by-step explanation:
I love these kind of question where we get to model equations :D So lets get started.
a)
The population of a city after t years after 2010 is given by
\(P=20000(1.075)^t\)
The original exponential growth formula is:
\(y=a(1+r)^t\)
so we can write our equation in this form as well:
\(P=20000(1+0.075)^t\)
the growth factor is 1+r which is 1+0.075 which is 1.075
the growth rate is determined by the value of r which is 0.075
b)
Since our equation represents the population of a city after the year 2010 we can use it to further calculate the population in 2025 so
2025 - 2010 = 15
we set the value of t in our equation to 15 which is in years,
\(P=20000(1.075)^{15}\\P=59177\)
so we can say that our population in 2025 would be approximately 60,000
HELPPP!!
Use the diagram to answer the question.
Which statement best completes the diagram?
Steps Leading to the American Revolution
Britain ended the slave trade across the Atlantic Ocean.
O Britain return Louisiana to France.
Great Britain
won the
Seven Years
War
???
American
colonists
protested British
actions
O Britain demanded new taxes from American colonists.
Britain only allowed the colonies to make laws about trade.
Answers
Answer:
C. Britain demanded new taxes from American colonists.
Step-by-step explanation:
After Britain fought the Seven Years' War, the country was stuck with a great amount of debt. Britain's solution to this problem was taxes. Specifically, taxes on tea (Tea Act), paper products such as newspapers and playing cards (Stamp Act), wine, sugar and coffee (Sugar Act), and textiles (also Sugar Act). After these taxes were imposed upon the American colonists, they began to revolt (Example: Boston Tea Party), which sparked the American Revolution.
Hope this helps! Have a great day!
segment from ( − 8 , 10 )to ( − 8 , − 5 )that partitions the segment into a ratio of 2 to 1?
Answers
The coordinate of the point that partitions the given line in the ratio 2:1 is; (-8, 0)
How to partition line segments?If the coordinates are given as;
P (x₁ , y₁) and Q (x₂ , y₂) and the partition of the line segment is divided internally in the ratio m : n, then its coordinate ( x, y) given by :
( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]
We are given the coordinates as ( − 8 , 10 )to ( − 8 , − 5 ) and if it is partitioned in the ratio 2: 1, the coordinates of the points of partition are;
(x, y) = [(2(-8) + 1(-8))/ (2 + 1), (2(-5) + 1(10))/ (2 + 1)]
(x, y) = (-24/3), (0/3)
(x, y) = (-8, 0)
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Laura deposits $2,000 in an account that has an annual interest rate of 1.96%,
compounded monthly. How much interest will she earn at the end of 1 month?
Round to the nearest cent. *
Answers
Answer:
$3.23
Step-by-step explanation:
Given that,
Principal, P = $2,000
Rate of interest, r = 1.96%
Tie, n = 1 month = (1/12) years
The formula of compound interest is given by :
\(CI=P[(1+\dfrac{R}{100})^n-1]\\\\CI=2000\times [(1+\dfrac{1.96}{100})^{1/12}-1]\\\\CI=3.23\)
So, the interest will she earn at the end of 1 month is $3.23
The amount she earns at the end of 1 month is 200,326cents
The formula for calculating the compound amount is given as:
A = P(1 + r/n)^ntr is the raten is the compounding timet is the timeA = 2000(1 + 0.0196/12)^(12*1/12)
A = 2000 (1+0.00163)^1
A = 2000(1.00163)
A = $2,003.26
Hence the amount she earns at the end of 1 month is 200,326cents
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a corner of a fenced yrad forms a right angle. can you place a 12 foot long board across the corner to form a right angle for which the leg lengths are whole numbers?
Answers
Answer:
72
Step-by-step explanation:
So draw a square and make an right angle in one of the squares corners! so basically what ever is on one side it's on the other side so theirs two 12 so 144 the dived my 2 which is 72!
I don't remember this sorry!
Gasoline costs $2.75 a gallon. At most, how many gallons can be boughts for $22.00.
Answers
15.2 gallons of gasoline will cost:
15.2 * 2.75 =$41.8
9.5 gallons of diesel will cost:
9.5 * 3.02= $28.69.
The total amont Grabiel will spend on gasoline and diesel:
$41.8 +28.69= $70.49
Answer:
8
Step-by-step explanation:
2.75x8=22
or
22.00÷2.75=8
(not sure)
Need help with this.
Answers
Answer:
x = -5, -1
General Formulas and Concepts:
Reading a Cartesian PlaneReading/labeling coordinatesStep-by-step explanation:
The question is asking us to find the y-values when f(x) = -2.
According to the graph, when f(x), or y, = -2, x has 2 points: -5 and -1.
Therefore, f(-5) = -2 and f(-1) = -2.
Need help ASAP
the value of each variable. If your answer is not
teger, express it in simplest radical form.
The length of a is
The length of b is
(Simplify your answer.)
Answers
Answer:
me too (help)
Step-by-step explanation:
Pls help
This is due in 7 minutes
Answers
Answer:
17. The puppy will grow 16 in - ( 1 foot = 12in and 28-12=16)
Step-by-step explanation:
18 .
21; 17.5; 14; 10.5; and 7
3 x 7 = 21
2.5 x 7 = 17.5
2 x 7 = 14
1.5 x 7 = 10.5
1 x 7 = 7
I need the anwser to this right now please
Answers
Answer:
b. 9
Step-by-step explanation:
2+9=11
11+11=22
22+6=28
(3+3)-28 = 22
that leaves the other side having to be 11 on each so
2+9= 11
Use the following sets to answer the following:
Y: The set of yellow attribute pieces
H: The set of hexagonal attribute pieces
SY: The set of small yellow attribute pieces
SB: The set of small blue attribute pieces
L: The set of large attribute pieces
1. Which pairs of sets, if any, can be put into one-to-one correspondence?
2. Which pairs of sets, if any, are equal?
3. Which pairs of sets, if any, are disjoint?
4. Which set is a proper subset of another?
5. Which attribute pieces are in Y ∩ L?
6. Which attribute pieces are in Y UL?
Answers
Answer:
i have no clue
Step-by-step explanation:
tbh
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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Write without radical symbols
Answers
Answer:
3³ ¹/⁶Step-by-step explanation:
∛3² · √3⁵ =3²/³· 3⁵/² =3⁽²/³⁺⁵/²⁾ =3 ¹⁹/⁶ =3³ ¹/⁶