Answers
The given trigonometric equation is csc²x-1 =cotx/tanx is proved LHS=RHS.
What is the trigonometric equation?A trigonometric equation is one that involves one or more of the sixs sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.
The given trigonometric equation is csc²x-1 =cotx/tanx.
Here, csc²x-1 =cosx/sinx ÷ sinx/cosx
csc²x-1 =cosx/sinx × cosx/sinx
csc²x-1 =cos²x/sin²x
csc²x-1 =cot²x
We know that, cot²x+1=csc²x
So, cot²x=cot²x
Hence, proved LHS=RHS.
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Related Questions
After kicking, one coach likes to play practice games with 6 players on each
team. She doesn’t like any team to have more or fewer than 6 players and
she doesn’t like anyone to be left off a team. What are the possible numbers
of players who must show up to practice so that the coach can make these
teams?
Answers
Answer:
The possible numbers of players are multiples of 6 (6, 12, 18, etc.).
Step-by-step explanation:
For the coach to be able to form teams of 6 players each, the total number of players must be divisible by 6. This means that if there are 6, 12, 18, 24, 30, etc. players, the coach can divide them evenly into teams of 6. Any other number of players would result in either having a team with more or fewer than 6 players, or leaving some players out. Hence, the possible numbers of players are multiples of 6.
Is the following true or false?
Every sample space S is a finite set.
Answers
The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.
Explanation:The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.
For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.
Therefore, it is incorrect to say that every sample space is a finite set.
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Even that the perimeter of a square varies directly with the side length what happens to the perimeter area of a square if the side length increases from s= 12 to s=36 inches?
Answers
Answer: The perimeter triples.
Step-by-step explanation:
Since there is a direct variation, if the side length triples, so does the perimeter.
Match the mathematical expression with its translation.
1. x + y = 6
y divided by x
2. x + y
x minus y
3. xy
the product of two numbers
4.
x subtracted from y
5. y ÷ x
six less than a number is y
6. y = x - 6
six times a number equals y
7. x - y
the sum of two numbers is six
8. 6 x = y
the product of two numbers is six
9. xy = 6
the sum of x and y
10. y - x
x divided by y
Answers
The following mathematical expression matched with its translation:
1. x + y = 6 (the sum of two numbers is six)
2. x + y (the sum of x and y)
3. xy (the product of two numbers)
4. x ÷ y (x divided by y)
5. y ÷ x (y divided by x)
6. y = x - 6 (six less than a number is y)
7. x - y (x minus y)
8. 6 x = y (six times a number equals y)
9. xy = 6 (the product of two numbers is six)
10. y - x (x subtracted from y)
How to write mathematical expression?Mathematical expression can be translated as thus;
the sum of two numbers is six
Let the unknown numbers be x and y respectively
So,
x + y = 6
six less than a number is y
x - 6 = y
also written as
y = x - 6
six times a number equals y
6 × x = y
6x = y
also written as
y = 6x
Therefore, mathematical expressions are algebraic representation of mathematics in words.
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Select the phrase from the drop-down menu that
best completes the sentence.
Several values of a quadratic function are given
in the table.
X -5
y
-7
-2 -1 2
8 9
6
8 9
0 -40 -72 -91
There is a maximum between the two input values
>
Finish
Answers
Answer:
"of -1 and 2."
Step-by-step explanation:
The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.
I need help with this question
Answers
The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
The given graph is an exponential function and should take the form;
[tex]f (x) = a (b)^x[/tex]
Hence, using values from the graph;
For ( -1, 0.2 ) = a • b..........(i)
For (0, 0.8); 10.5 = a • b².........(ii)
=> x=0 and y= 0.8
So.
0.8=a(1/2)^0
0.8=a
Thus, the rule for the function is; y=0.8(1/2)^x
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AB formed by (-4, 7) and (-2, 6)
CD formed by (2, -2) and (-8, 3)
Is is parallel or perpendicular?
Answers
Line AB and CD are two parallel lines
What is the slope of a line:The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by
Slope (m) = [ y₂ - y₁]/[x₂ - x₁]Note:
When two lines are parallel lines then the slope two line is equal When two lines are perpendicular lines then the product of the slope of two lines will be equal to '-1'
Here we have
AB formed by (-4, 7) and (-2, 6)
Slope of AB = (6 - 7)/(-2 + 4) = -1/2
CD formed by (2, -2) and (-8, 3)
Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2
Here Slope of AB = Slope of CD
As we know the slope of parallel lines is equal
Therefore,
Line AB and CD are two parallel lines
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Which of the following pairs of numbers results in a product that is irrational? Choose a, b, c or d.
Answers
The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
What are irrational numbers?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
1. The product of the numbers are:
a. √2 (√8) = √16 = 4
b. √49 (∛ 8) = 14
c. √3 (2/ √3) = 2
d. √2(4)
Option d is the correct answer.
Similarly, taking the product:
2. Option a is correct.
3. Option d is correct.
4. Option b is correct.
Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
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A soccer team made 2 goals out of 32 attempts in a game. What is the experimental probability that the team made a goal on any given shot? Write the probability as a decimal.
Answers
The experimental probability that the team made a goal on any given shot is 0.0625
How to determine the experimental probability that the team made a goal on any given shot?From the question, we have the following parameters that can be used in our computation:
A soccer team made 2 goals out of 32 attempts in a game
The experimental probability that the team made a goal on any given shot is calculated as:
P = 2/32
Evaluate the quotient
P = 0.0625
Hence, the probability is 0.0625
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5. Jill drew 4 rectangles 3
triangles, 2 pentagons, and
3 trapezoids. How many
angles are on the
quadrilaterals she drew?
Answers
The angles on the quadrilaterals she drew are 47 in number.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles
As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.
The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.
Number of pentagons are 2, the total number of angles is 2 × 5 = 10 angles.
The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.
Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.
Hence, the angles on the quadrilaterals she drew 47.
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Use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 52 miles per hour and 70 miles per hour. (assume the data set has a bell-shaped distribution.)
Answers
The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.
Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour.
[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].
Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.
Therefore, 75% of the vehicles would fall into this category.
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A large university accepts 60% of the students who apply. Of the students the university accepts, 45% actually enroll. If 20,000 students apply, how many actually enroll?
Please hurry will pay any amount
Answers
The number of students who got actually enrolled are, 5400
What are percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, a large university accepts 60% of the students who apply. Of the students the university accepts, 45% actually enroll, there are 20,000 students apply,
Since, the students whose application has been accepted = 20000 × 60%
= 12000
Now, the students who got admission = 12000 × 45%
= 5400
Hence, the number of students who got actually enrolled are, 5400
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if f(x)= log(x^2 + 3x) 2^3x, find f'(2)=?
Answers
Answer:
f'(2)=64
Step-by-step explanation:
After plugging in 2 for x our equation would look like
log(2^2+(3×2))×2^(3x2)
Now just follow PEMDAS, starting with the left.
1: 2^2=4, 3×2=6, 4+6= 10
2: 3×2=6, 2^6=64
3: log(10)=1
4: 1×64=64
5: f'(2)=64
Double question, double points!
Answers
The potential energy increases as the charges or the poles get further apart.
Static charges does not build up by polarization.
What is a field force?A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.
The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.
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Cincinnati’s budget is $1,130,000,000 and it’s population is 302,605. How many dollars per person are provided by the budget?
Answers
Answer:
3734.24100725
Step-by-step explanation:
This is related for all problems like this, not just this one:
When you see the key words below, this is what it means, and you can craft an equation from it:
Per = division
Of = multiplication
Using this above, we can replace the words with an equation:
The question is asking the amount of money per person.
Remember above, per means division:
Money/person
We know the amount of money and the number of people, so let's plug it in:
1,130,000,000/302,605
After division:
3734.24100725, final answer.
Hope this helps :D
A group of 8 students are painting a mural at the local library. Each student uses 1/4
of the paint in their bucket. How many total buckets of paint did the students use?
8 buckets each with 1 of 4 sections shaded.
Answers
Answer:
1/2 bucket
Step-by-step explanation:
Each of the 8 buckets is 1/4 full.
The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.
Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.
1/4 × 2 buckets = 1/2 bucket
Answer: 1/2 bucket
The distance between two villages is 30km. Kadi took 45 mins to cover the distance by motorcycle. What was his speed?
Answers
Answer:
50to70
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
You are given distance (30 km) and time ( 3/4 hr) and want km/hr
soooo 30 km / ( 3/4 hr) = 40 km/hr
PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
Answers
The set of pairs for which x and y vary inversely is given as follows:
{(-1, -2/7), (4, 1/14), (6, 1/21)}.
(third set).
What is a proportional relationship?A direct proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
For an inverse relation, the relation is modeled as follows:
y = k/x.
Meaning that when x increases, y decreases at a constant rate.
The constant is then obtained as follows:
k = yx.
Hence the third relation is then the relation for which x and y vary inversely, as:
k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.
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This rectangle represents the base of a rectangular prism. The height of the rectangular prism is 56 m.
What is the volume of the rectangular prism?
Responses
A.212 m³
B.525 m³
C.5,600 m³
D.29,400 m³
Answers
Hope this helps:D
Reflecting Graph Math Question
Answers
Answer:
Step-by-step explanation:
The reflection of point A will be at (3, -4) - that is 2 units directly below the red X.
Find the equation of the line passing through the point (8,−2) that is perpendicular to the line y=4/5x+4.
Answers
Answer: pls braiinliest :D
To find the equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4, we can use the concept of the slope of a line. The slope of a line perpendicular to another line has a negative reciprocal slope.
The slope of the line y = 4/5x + 4 is 4/5. The negative reciprocal of 4/5 is -5/4.
So, the slope of the line passing through (8, -2) and perpendicular to y = 4/5x + 4 is -5/4.
Next, we can use the point-slope form of a line to find the equation of the line:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get:
y - (-2) = -5/4 (x - 8)
Expanding and solving for y, we get:
y = -5/4x + 26/2
y = -5/4x + 13
The equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4 is y = -5/4x + 13.
Step-by-step explanation:
PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
Answers
Answer:
It's the third choice.
Step-by-step explanation:
IF y varies inversely as x then y = k/x where k is a constant,
and k = xy
For the 3rd choice
-1 * -2/7 = 2/7
4 * 1/14 = 2/7 and
6 * 1/21 = 2/7
so, this is inverse variation.
It costs 9 dollars for 4 hot dogs.
What is the price of one hot dog?
Answers
The cost of 1 hot dog is $2.25
What is proportion?Proportion is a mathematical comparison between two numbers.
Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,
Let the cost of 1 hot dog be x, therefore, setting the proportion,
4 / 9 = 1 / x
x = 9/4
x = 2.25
Hence, the cost of 1 hot dog is $2.25
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h(9)=2x-3 evaluate the solution
Answers
The solution of the expression is, 15.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ h (9) = 2x - 3
Now, Substitute x = 9, we get;
⇒ h (9) = 2 × 9 - 3
⇒ h (9) = 18 - 3
⇒ h (9) = 15
Thus, The solution of the expression is,
⇒ h (9) = 15
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How many solutions are there to the equation below?|x| = -4
A 0
B 2
C 4
D 1
Answers
Answer:
There are 0
Step-by-step explanation:
Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true
Answer:
A 0
Step-by-step explanation:
There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.
If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.
Can somebody help me with this? I need it answered fast please Also, I need to show work
Answers
The length of CE in the triangle is 20.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
From the given triangle ABC
BC=CD which are congruent sides
x-5=14
x=19
AB=DE
2x+3=6
2x=3
x=3/2
Now DE 2x+3=2(3/2)+3=6
CE=CD+DE
=14+6
=20
Hence, the length of CE in the triangle is 20.
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lydia has money in two savings accounts one rate is 8% and the other is 12% if she has $350 more in 12% account and the total interest is $336 how much is invested in each savings account
Answers
The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12% and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)
Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)
Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470
Now
y = 1470 + 350
y = $1820
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If the car climbs 60 m vertically how far must the car have travelled horizontally?
The the gradient of the slope is 2/15
Answers
The horizontal distance which the car must have travelled is equal to 450 meters.
How to calculate the horizontal distance?Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:
Pitch (slope) = V/H
Where:
V represents the rising vertical distance of an object.H represents the horizontal distance an object runs through.Based on the given image, we have the following distances and gradient (slope):
Rising vertical distance = 60
Horizontal distance (Run) = x
Gradient (slope) = 2/15
Substituting the given parameters into the formula, we have;
2/15 = 60/x
2x = 900
x = 450
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What is the value of x? - View the image attached.
Answers
Explanation:
The two horizontal sides are parallel. The side marked 34 is half as long as side x.
In other words, side x is twice as long as the side marked 34.
x = 2*34 = 68
For more information, search out "midsegment of a triangle".
The graph shows the time it takes Jacey to print T-shirts for her school’s math club.
Answers
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
What is a Proportional Quantities?If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.
Using the points on the graph in the image attached below, the table can be completed as follows:
Part A:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
Part B: Find the ratio of y to x for each of the points on the graph.
5/1 = 5
10/2 = 5
15/3 = 5
20/4 = 5
The table derived from the graph is:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
B. The quantities are proportional.
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
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"Your question is incomplete, probably the complete question/missing part is:"
The missing information are in the attachment below.