Answers
Answer:
[tex]\textsf{C.} \quad \sin x[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]
Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:
[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]
Therefore:
[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]
Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:
[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]
[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]
Cancel the common factor cos²x:
[tex]=\dfrac{\sin^2x}{\sin x}[/tex]
Simplify:
[tex]= \sin x[/tex]
Therefore:
[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]
Related Questions
Explain how to find 20% of 160
Answers
Answer: 20% of 160 is 32.
Step-by-step explanation:
The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.
To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.
Let us now find the 20% of 160.
20% = 0.2
percentage = 160 × 0.2
= 32
Rewrite in simplest terms: (5x + 5y) - (-x + 10y)
Answers
Answer:
6x - 5y
Step-by-step explanation:
( remove the unnecessary parentheses)
= 5x + 5y + x - 10y
= 6x + 5y - 10y
= 6x + 5y
help me with this please i need help because i dont get it <33
Answers
Answer:
C
Step-by-step explanation:
consider the coordinates of the same points on both figures
top left vertex of figure P (- 8, 8 )
top left vertex of figure Q (- 4, 4 )
note that both coordinates from Q are half the coordinates of P
then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is
(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )
)) Of the 90 people who attended the Baybridge Middle School Winter Formal, 18 are
not students at Baybridge.
4) Shade the grid to show the fraction of the people who attended the formal who are not
students at Baybridge.
) What percent of the people who attended the Winter Formal are not students at
Baybridge Middle School? You can use your model to help.
Answers
Answer:
Step-by-step explanation:
To find the percent of the people who attended the Baybridge Middle School Winter Formal who are not students at Baybridge, we can use the following steps:
Find the fraction of non-student attendees: 18 attendees out of 90 total attendees can be represented as 18/90.
Convert the fraction to a decimal: 18/90 = 0.20, which can be rounded to 0.2.
Convert the decimal to a percentage: 0.2 * 100 = 20%.
So, 20% of the people who attended the Baybridge Middle School Winter Formal are not students at Baybridge.
Solve the formula A=1/2h (a+b) for b 
Answers
A = 1/2 h(a+b)
multiply by 2
2A = h(a+b)
divide by h
2A/h = a + b
subtract a
(2A/h) - a = b
which can be rewritten the other way around for
b = (2A/h) - a
How can using a 'Polygon Family Tree' help you to classify 2D figures into a hierarchy of sets and subsets?
Answers
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
What are plane figures?A figure that totally resides in one plane is referred to as a plane figure or a two-dimensional figure. Two-dimensional figures are drawn when you sketch, whether by hand or with a computer programme. Two-dimensional models of actual objects can be found in blueprints.
Closed, two-dimensional shapes known as polygons are created by three or more-line segments that only meet at their ends.
How do you classify 2D figures?Circles, triangles, squares, rectangles, pentagons, quadrilaterals, hexagons, octagons, and other basic 2D shapes include these. All shapes—aside from the circle—are categorized as polygons because they have sides. Regular polygons are those with equal sides and angles on all of their faces.
To know more about polygon visit:
brainly.com/question/1592456
#SPJ1
Your friend wants to write code for Linux computer systems and says, “Why do I need to install Linux? I never open it and use it the way I do my browser.” How would you explain to your friend the difference between an operating system like Linux and an application like their web browser? In your answer, discuss how both Linux and at least one other operating system function, comparing those to an application like a browser.
Answers
Answer:
That's not math. Please classify your question correctly.
3. What is the volume of this complex figure?
3 m
4 m
6 m
4 m
7m
Answers
The volume of the rectangular prism is 140 cubic meters
What is the volume of the figureThe volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.
The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.
This problem is a two rectangular prism joined together.
The volume can be calculated as;
V = l * w * h
v = (4 * 7 * 3) + (2 * 7 * 4)
v = 140m³
Learn more on volume of a rectangular prism here;
https://brainly.com/question/23665595
#SPJ1
at a movie theater, tickets cost 15$ for adults and 8$ for children. a group of 28 movie goers cost 308$. how many adults and how many children are in the group?
Answers
The number of adult and children in the group is given as follows:
Adult: 12.Children: 16.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: number of adults.Variable y: number of children.There were a total of 28 people, hence:
x + y = 28
y = 28 - x.
They spent a total of $308, hence:
15x + 8y = 308.
Replacing the second equation into the first, the value of x is given as follows:
15x + 8(28 - x) = 308
7x = 84
x = 84/7
x = 12.
Then the value of y is given as follows:
y = 28 - x = 28 - 12 = 16.
More can be learned about a system of equations at https://brainly.com/question/30374328
#SPJ1
PLS HELP ANSWER QUICKLY PLS
Answers
Answer:
10
Step-by-step explanation:
a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
c = 10
If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
Answers
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
Learn more on lowest common denominator here;
https://brainly.com/question/10749076
#SPJ1
Wendy and Roger camped out at a state park, and then hiked back to their cars, which were
parked on opposite ends of the park. Wendy headed due north at 3 miles per hour, and Roger
hiked due south at 6 miles per hour. In how long were the two friends 2 miles apart?
If necessary, round your answer to the nearest minute.
Answers
In 30 minutes the two friends 2 miles apart.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.
We know that, Time= Distance/Speed
Now, T₁= 2/3
T₂= 2/6 =1/3
T=T₁-T₂
T=2/3+1/3
T=1/3
T=0.33 hours
= 30 minutes
Therefore, in 30 minutes the two friends 2 miles apart.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ9
This is a two-part question:
1. Jack's gasoline-powered model airplane travels in a circle while the cord is held. How far does it travel in 5 full circles if the cord is 15 ft.?
2. Last Saturday Jack flew his airplane 100 times around a circle with a cord of 50 ft. If Jack increases the length of the cord by 10 ft and fly it for 100 circles, how much further will the plane travel?
Answers
1. The plane travelled a distance of 471.239 ft
2. The plane would travel further by 6283.185 ft
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]
Part 1:
Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times
The total distance travelled by plane is [tex]15*2\pi *15[/tex]
[tex]=150\pi[/tex]
= 471.239 ft
Part 2:
Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.
The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])
If he increases the length by 10 ft, The cord will now be 60 ft.
The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])
Now,
100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])
= 100 * (2*(60-50))*[tex]\pi[/tex])
= 100 * 2 * 10 * [tex]\pi[/tex]
= 2000 * [tex]\pi[/tex]
= 6283.185 ft
To learn more about circumference, refer below:
https://brainly.com/question/20489969
#SPJ1
Expression
9x - 2 + 16x + 8 - x + 10
What are the coefficients in this expression?
Answers
The coefficients in the expression "9x - 2 + 16x + 8 - x + 10" are the numerical values that multiply the variables. In this expression, the coefficients are 9, -2, 16, 8, -1, and 10.
So, the expression can be written as:
9x + 16x - x + 10 = 24x + 10
where 9, -2, 16, 8, -1, and 10 are the coefficients of the expression.
Answer:
The coefficients in this expression would be 10, -2, 8, -1, 10, 9, 16
Step-by-step explanation:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
PLS HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the solution to the equation given the replacement set?
25 - 3r = 10; {3, 4, 5, 6,}
Responses
3
4
5
6
Answers
Answer:
r = 5
Step-by-step explanation:
25 - 3r = 10 ( subtract 25 from both sides )
- 3r = - 15 ( divide both sides by - 3 )
r = 5
the solution from the replacement set is 5
3/4 minus what equals 1/2
Answers
Answer:
W =1 1/4Step-by-step explanation: Let W = what. W - 1/2 = 3/4. Add 1/2 to each side. W -1/2 +1/2 = 3/4+1/2. W = 3/4+1/2.
Step-by-step explanation:
An urn contains 3 white balls and 7 red balls. A second urn contains 7 white balls and 3 red balls. An urn is selected, and the probability of selecting the first urn is 0.3. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
Answers
Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
Step-by-step explanation:
Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.
First, let's find P(A):
P(A) = 0.3
Next, let's find P(B|A):
P(B|A) = (3/10) * (3/10) = 9/100
Finally, let's find P(A and B):
P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027
So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
Hual takes out a $3200 student loan at 6.4% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and
borrows another $12,400 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and
payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.6%. Find the total
amount of interest that will accrue until payments begin.
(a) Find the total amount of interest that will accrue for loan 1 (community college).
The total amount of interest that will accrue for loan 1 (community college) is $_____ Round your answer to two decimal
places, if necessary.
Part 2 of 3
A ALEKS-Erika Ramirez - Test 2-Chapter 7
(b) Find the total amount of interest that will accrue for loan 2 (state university).
The total amount of interest that will accrue for loan 2 (state university) is $____
Answers
Answer:
a) $4096 b) $1884,8 ■■ im not 100% sure
Step-by-step explanation:
a) 3200×0.064×2=$4096 in intrest
b) 12,400×0.076×2=$1884,8 in intrest
A boat heading out to sea starts out at Point A, at a horizontal distance of 1246 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 14°. At some later
time, the crew measures the angle of elevation from point B to be 5°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answers
Answer:2304.9
Step-by-step explanation:
Answer:
2304.9 ft
Step-by-step explanation:
You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.
TangentThe tangent relation for sides in a right triangle is ...
Tan = Opposite/Adjacent
In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:
tan(14°) = h/1246
tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B
SolutionSolving these equations for d, we have ...
h = 1246·tan(14°) = (1246+d)·tan(5°)
d·tan(5°) = 1246·(tan(14°) -tan(5°))
d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet
The distance from point A to point B is about 2304.9 feet.
<95141404393>
20. A line passes through (4, 6) and (9, 9).
a. Write an equation for the line in slope-intercept
form.
y=3/5x+18/5?
b. Rewrite the equation in standard form using
integers.
Answers
Its 10/29 so its answers this
The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answers
Answer:
Step-by-step explanation:
B
Graphing Quadratic Functions 1. List a, b, and c. 4. What is the y-intercept? 5. Create a table and graph. X f(x) Quadratic Function f(x) = x² - 2x + 6 2. Find the axis of symmetry. F Y 10 9 8 7 6 5 4 3 2 1 -9-8-7-6-5-4-3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 3. Find the vertex. tx 1 2 3 4 5 6 7 8 9 10 X
Answers
The value of a, b, and c are 1, -2, and 6 respectively.
The y-intercept of this quadratic function is 6.
The axis of symmetry of this quadratic function is 1.
The vertex of this quadratic function is (1, 5).
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = x² - 2x + 6, we have:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(-2)/2(1)
Axis of symmetry, Xmax = 2/2 = 1.
Vertex (h, k) = (1, 5).
In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
y-intercept = 6.
Lastly, we would create a table and then graph the quadratic function as follows;
x y
0 6
2 2
5 11
Read more on quadratic function here: brainly.com/question/13159926
#SPJ1
What is the rate of change for the equation y= 4x +40?
Answers
Answer:
4 would be the rate of change
Step-by-step explanation:
y=mx+b mx = slope
The slope represents the rate of change. Then the rate of change will be 4.
Are square and rectangle similar
Answers
Answer:
no
Step-by-step explanation:
squares sides are all equal
rectangle only have 2 side alike
A tailor charges a basic fee of $20 plus $4 per letter to sew an athlete's name on the back of a jacket. Write a linear equation that will find the cost c to have a name containing x letters
Answers
The equation will be;
c = 20 + 4x
What are Linear Equations?Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.
A linear equation that will find the cost c to have a name containing x letters will be;
c = $20 + 4x
where c = cost
$20 = basic fee
x = number of letters
Learn more about linear equations here: https://brainly.com/question/2030026
#SPJ1
The following data represent the weights (in grams) of a
random sample of 50 candies
(a) Determine the sample standard deviation weight
SH gram
(Round to two decimal places as needed)
0.98
0.85
0.92
0.98
0.71
Part 1 of 6
0.88
0.86
0.75
0.85
0.85
0.86
0.78
0.75
0.75
0.74
Cm
0.82
0.85
0.91
0.78
0.72
O
081
0.81
0.81
0.81
0.84
Points: 0 of 4
087
0.85
0.89
0.77
0.85
0.97
0.74
0.89
0.82
0.86
0.82
084
0.91
0.87
0.94
0.85
0.71
0.83
0.87
0.94
0.81
0.81
0.78
0.77
0.85
Answers
The sample standard deviation weight of the 50 candies is, 0.07 grams.
What is standard deviation ?The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.
To find the sample standard deviation weight,
we can use the formula:
[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]
where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.
We can first find the sample mean weight:
[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50
[tex]\bar x[/tex] = 0.8456
Next, we can calculate the sample standard deviation:
s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))
s = sqrt(0.0045916)
s = 0.0678
Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.
To know more about standard deviation check:
#SPJ1
Geometry!!! Please help due soon!!!!y
Answers
Y=34
X=37
it all measures up to 180
Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements.
If there are no possible solutions, submit an empty answer.
Answers
Answer: 2 hours babysitting
Step-by-step explanation:
18 x 9 = 162
180-162= 18
meaning he'd have to work 2 hours babysitting to get to meet his requirement.
hours used = 11
hours left= 3
which of the following statements are equivalent to the statement "the price increased by 1/2 if what it was before"
Answers
Answer:
The question is incomplete
Answer:
It was 1/3 before
Step-by-step explanation:
Solve for x, each figure is a trapezoid
Answers
From the given trapezoid the value of the x is 1.
What is the trapezoid?
The sum of all the angles in a trapezoid is equal to 360°. The sum of the angles on the same side is equal to 180°.
We have,
Since a Trapizode has 360 Degrees total and since the sides are equal we can say that
180 = 66 + ∠R
∠R = 180 - 66
∠R = 114
so,
180 = 66 + (-2 + 116x)
180 = 66 - 2 + 116x
180 = 64 + 116x
180 - 64 = 116x
116 = 116x
x = 1
Therefore, from the given trapezoid the value of the x is 1.
To learn more about the trapezoid visit,
https://brainly.com/question/15224239
#SPJ1
