Someone help me with proving identities? and please show the work if you can!
Answers
Answer:
See Below.
Step-by-step explanation:
11)
We have:
[tex]\displaystyle \cos\theta\cdot \cot\theta+\sin^2\theta\cdot \csc\theta=\csc\theta[/tex]
Rewrite:
[tex]\displaystyle \cos\theta\left(\frac{\cos\theta}{\sin\theta}\right)+\sin^2\theta\left(\frac{1}{\sin\theta}}\right)=\csc\theta[/tex]
Multiply:
[tex]\displaystyle \frac{\cos^2\theta}{\sin\theta}+\frac{\sin^2\theta}{\sin\theta}=\csc\theta[/tex]
Combine:
[tex]\displaystyle \frac{\cos^2\theta+\sin^2\theta}{\sin\theta}=\csc\theta[/tex]
According to the Pythagorean Identity, sin²θ + cos²θ = 1. Hence:
[tex]\displaystyle \frac{1}{\sin\theta}=\csc\theta[/tex]
Simplify:
[tex]\csc\theta=\csc\theta[/tex]
12)
We have:
[tex]\displaystyle \frac{\cos^2\theta +\sin^2\theta}{1+\tan^2\theta}=\cos^2\theta[/tex]
Pythagorean Identity:
[tex]\displaystyle \frac{1}{1+\tan^2\theta}=\cos^2\theta[/tex]
From the Pythagorean Identity, if we divide both sides by cos²θ, we acquire that tan²θ + 1 = sec²θ. Hence:
[tex]\displaystyle \frac{1}{\sec^2\theta}=\cos^2\theta[/tex]
Simplify:
[tex]\cos^2\theta =\cos^2\theta[/tex]
13)
We have:
[tex]\displaystyle \frac{\csc\theta\cdot \cos\theta}{\tan\theta +\cot\theta}=\cos^2\theta[/tex]
Rewrite:
[tex]\displaystyle \frac{1/\sin\theta\cdot \cos\theta}{\sin\theta/\cos\theta+\cos\theta/\sin\theta}=\cos^2\theta[/tex]
Multiply both top and bottom by cosθsinθ. Hence:
[tex]\displaystyle \frac{\cos^2\theta}{\sin^2\theta +\cos^2\theta}=\cos^2\theta[/tex]
By the Pythagorean Identity:
[tex]\displaystyle \frac{\cos^2\theta}{1}=\cos^2\theta[/tex]
Simplify:
[tex]\cos^2\theta=\cos^2\theta[/tex]
Related Questions
Angela recorded the price of different weights of several bulk grains. She made a scatter plot of her data. Draw a trend line for the scatter plot
Answers
9c + 1 = 10
whats the answer..?
Answers
Answer:
c = 1
Step-by-step explanation:
9 x 1 + 1 = 10
Hope this helps!
Answer:
c=1
Step-by-step explanation:
9c+1=10
9c=10-1
9c=9
9c/9c= 9/9
c=1
Two cards are drawn from a deck of 52 cards. What is the probability that the first card
drawn is a king and the second card drawn is a heart, given that the first card is
replaced? (Hint: A deck has 4 kings and 13 hearts)
Answers
Answer:
1) P(First card was a king) = 1/13 2.) 1/4
Step-by-step explanation:
1) P(First card was a king) = n(King)/n(Total) = 4/52 = 1/13
2. P(Heart)13/52 = 1/4
Answer:
1/52
Step by step explanation:
First, find the probability that the first card will be a King. Since there are 4 possible kings, and 52 cards, the probability is 4/52.
Then, find the probability that the second card will be a heart. "given that the first card is replaced" means that there are 13 possible hearts regardless of the suit of the first card. So 13/52 is the probability.
To find the probability of both occurrences, multiply them.
4/52 * 13/52 = 52/2704
52/2704 can be simplified to 1/52. So that is the probability that the first card will be a king and the second card will be a heart.
Select the correct location on the graph.
Identify the cluster in the data.
Answers
The cluster in the data is the most circles together in the middle ( data points in the range 6 ≤ y ≤ 8))
What is scatter plot?"It is a graph that presents the relationship between two variables in a data-set."
What is cluster?"The data points in a scatter plot form distinct groups known as clusters."
For given question,
We have been given the scatter plot.
We know, a cluster is a group of points that follow the same general pattern.
If we observe the graph,
The data points in the range (6 ≤ y ≤ 8) or (7 < x < 9) form a cluster.
This means, the cluster in the data is the most circles together in the middle (data points in the range 6 ≤ y ≤ 8)
Learn more about the cluster here:
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A 12 mile walking trail has a distance marker ever 1/6 of a mile. How many markers are along the trail?
Answers
Answer:
72 markers along entire trail
Step-by-step explanation:
Divide 12 miles by 1/6 mile:
12 miles
------------------------- = 72 markers
1 marker/6 miles
Identify the solution to the system of equations,answers if u know
Answers
Answer:
I will use formular for gradient
= y²-y¹
x²-x¹
2-1.5
4-1.5
1.5
3.5
Find the area of the shaded region in the picture below
Hint** - The area of a triangle is the base of the triangle times the height divided by 2
Help
Answers
Answer:
b
Step-by-step explanation:
i got it correct
Answer:
30 cm²
Step-by-step explanation:
solve for area of rectangle: 12 x 4 = 48 cm²
solve for area of triangle: 9 x 4= 36 / 2 = 18 cm²
subtract: 48- 18 = 30cm²
And right angle RST, with MS equals 90° what is sin T?
Please I’m begging you
Answers
Answer:
B
Step-by-step explanation:
Since sin is opposite over hypotenuse, the side opposite of angle T is RS and the hypotenuse is RT.
43
8/3 x ( -2 1/2)
What is the product
Answers
Answer:
−28x
Step-by-step explanation:
Otis is cutting a long piece of wood trim into smaller pieces for an art project. The line plot shows the length of the smaller pieces of wood. How many pieces of wood will be at least 1 2 foot in length?
Answers
Answer:
6
Step-by-step explanation:
From the line plot, the length of wood measuring atleast 1/2 in length include :
Piece with length 1/2 and pieces with length 2/3
Number of pieces with length 1/2 feets = 4
Number of pieces with length 2/3 feets = 2
Pieces with atleast 1/2 feet length = 4 + 2 = 6
Match the inequality to its graph.
------------------------------------------------
Here are the line graphs below.
-------------------------------------------------
A. A number line is labeled from negative 5 to 1. There is an open circle on negative 1 and the line is shaded to the left.
B. A number line is labeled from negative 3 to 4. There is a closed circle on 3 and the line is shaded to the left.
C. A number line is labeled from negative 4 to 3. There is a closed circle on 1 and the line is shaded to the left.
D. A number line is labeled from negative 6 to 1. There is an open circle on negative 3 and the line is shaded to the left.
(Here is the inequality) 4y + 3 less than or equal to y + 6
For anyone who can help explain this to me with the result and a step by step process, I WILL MARK BRAINIEST! Thanks! Need this ASAP!
Answers
Which of the following is likely to have the greatest variability? *
F. The cost of a piece of candy from a vending machine
G. The height of all the students at West Middle School
H. The age of all the students in the sixth grade
J. The number of days in a month
Answers
Answer:
G
Step-by-step explanation:
The most likely to have the greatest variability is,
⇒ The height of all students at West Middle school.
What is an expression?A Mathematical expression is defined as collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division
Now, We know that;
Greatest variability is large spectrum of possibilities.
Hence, We get;
The costs of candy from vending machine are going to be about the same price because they are all candy, so that does not vary much more.
And, The age of all the students in the sixth grade is going to be about the same because they are in the same grade.
Since, The number of days in a month is usually 31 or 30, so that also does not vary much.
This means, it has to be the height of all the students at West Middle school because it is a middle school so there are 3 different grades each having many students. This means that it will have the greatest variability.
Thus, The most likely to have the greatest variability is,
⇒ The height of all the students at West Middle school
Learn more about the mathematical expression visit:
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Jared invests 10000 in a savings account that pays 3% simple interest how many years will it take for the account to grow to 12700 if he makes no withdrawals and deposits
Answers
Answer:
9 years
Step-by-step explanation:
Given data
Principal= $10000
Rate= 3%
Final amount= $12700
The simple interest expression is given as
A=P(1+rt)
substitute
12700=10000(1+0.03*t)
12700=10000+300t
collect like terms
12700-10000= 300t
2700=300t
divide both sides by 300
t= 2700/300
t= 9 years
Pls answer this with a picture showing the correct box plot
Answers
Answer/Step-by-step explanation:
To find out the mistake of the student, let's find the min, max, median, Q1 and Q3, which make up the 5 important values that are represented in a box plot.
Given, {2, 3, 5, 6, 10, 14, 15},
Minimum value = 2
Median = middle data point = 6
Q1 = 3 (the middle value of the lower part of the data set before the median)
Q3 = 14 (middle value of the upper part of the data set after the median)
Maximum value = 15
If we examine the diagram the student created, you will observe that he plotted the median wrongly. The median, which is represented by the vertical line that divides the box, ought to be at 6 NOT 10.
See the attachment below for the correct box plot.
There are 16 ties on each rack.
Write an equation to find the total number of ties.
(Let t = ties and r = racks.)
Answers
Answer:
T(r) = (16 ties/racks)r
Step-by-step explanation:
Total number of ties = (16 ties/rack)(number of racks), or
T(r) = (16 ties/racks)r
Find the median of the data Weight (in ounces) of puppies in litter 17, 15, 19,18,17,16,22 Median: [?] oz
Answers
Step-by-step explanation:
put it in least to greatest and then put your fingers on the opposite side of the numbers and count down at the same time
pls answer i’m begging
Answers
Answer:
75
Step-by-step explanation:
Angles in a triangle add up to equal 180
That being said we can find the missing angle by subtracting the measures of the given angles from 180
Thus missing angle = 180 - 34 - 71
180 - 34 - 71 = 75
Which means that the missing angle = 75
Answer:
? = 180 - (angle 1 + angle 2)
? = 180 - (71 + 34)
? = 180 - 105
? = 75°
=> To check is the answer is right, add all 3 angles together and their sum should be 180°
Hope this helps!
if the marginal revenue is higher than marginal cost the monopoly can increase profit by
Answers
Answer:
If the marginal revenue exceeds the marginal cost, then the firm can increase profit by producing one more unit of output. For example, at an output of 4 in Figure 3, marginal revenue is 600 and marginal cost is 250, so producing this unit will clearly add to overall profits.
How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed?
a.
119
c.
2520
b.
16,807
d.
120
Answers
answer
c) 2520
Step-by-step explanation:
1st digit 1 of 7
2nd digit 1 of 6
3rd digit 1 of 5
4th digit 1 of 4
5th digit 1 of 3
7*6*5*4*3=2520 combination
whats the value for x 2.4×x=36
Answers
Answer:
16
Step-by-step explanation:
divide 36 by 2.4. equals 15
100 POINTS PLEASE HELP ASAP!!!!!!
Use the tables to answer the question.
Mineral Mohs Hardness
calcite 3
feldspar 6
halite 2.5
talc 1
Item Mohs Hardness
fingernail 2.5
penny 3
glass slide 5.5
streak plate 6.5
Luiz has an unknown mineral. He suspects he has feldspar. If he is correct, which of the items listed will be able to scratch the mineral’s surface?
A.
a penny
B.
a glass slide
C.
a streak plate
D.
his fingernail
Answers
Answer:
it's streak plate
True or False
In order for any sample to be representative, it has to be a sample size of at least 30
Answers
For example, a classroom of 30 students with 15 males and 15 females could generate a representative sample that might include six students: three males and three females
so true i think
If P(A) = 0.43 and P(
BA) = 0.89, find P(A and B).
Answers
Step-by-step explanation:
Me I don't know the answer teacher am waiting for the correction
The required probability of both A and B occurring is 0.3827.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The conditional probability of A provided B has happened, so it can be written as follows:
P(B|A) = P(A and B)/P(A)
Given that P(A) = 0.43 and P(B|A) = 0.89
We can use the formula of conditional probability:
P(A and B) = P(B|A) × P(A)
Substitute the given values in the above formula,
P(A and B) = 0.89 × 0.43
P(A and B) = 0.3827
Therefore, the probability of both A and B occurring is 0.3827.
Learn more about probability here:
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pls help with math thank you
Answers
Answer:
Dvds cost 12 games cost 19.
Step-by-step explanation:
Put the amount of dvds and video games into an equation and assign variables.
3x+2y=74
5x+2y=98
You can solve multiple ways, although I'll do graphing for this equation.
After graphing, you get 2 lines that intersect. The point of intersection is 12,19 meaning that a dvd is 12 (x) and a video game is 19 (y)
DVD = x
video games = y
3 DVD + 2 video games = $74
3x + 2y = 74
5 DVD + 2 video games = $98
5x + 2y = 98
We can easily use eliminations by changing one of the equations, with all variables becoming negative signs, in order to eliminate the variable y.
-(3x + 2y = 74)
-3x -2y = -74
Now add both equations toegther (in order to eliminate the avriable y and solve for x).
5x + 2y = 98
-3x -2y = -74
____________
2x + 0y = 24
2x = 24
x = 12 [A DVD costs $12]
Plug that value for x into one of the equations:
5x + 2y = $98
5(12) + 2y = 98
60 + 2y = 98
2y = 38
y = 19 [A video game costs $19]
ANSWER: a DVD costs $12 and a video game costs $19choose the third option.
Find the volume of the cylinder. Round your answer to the nearest tenth.
8 m
10 m
Answers
Answer:
V = 2010.6193m^3
Step-by-step explanation:
This is right assuming 8m is the radius and 10m is the height
i need help with these asap!! i’ll give brainliest :)
Answers
Answer:
1) 12 (option b)
2) 41, 9, 40 (option a)
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
1) Let the unknown leg be x cm long. Thus,
5² + x² = 13²
Simplify and solve.
25 + x² = 169
x² = 144
x = 12
2) Apply the Pythagorean Theorem.
9² + 40² = 41² = 81 + 1600 = 1681
1681 = 1681
a is true.
Just in case, let's check the other options.
5² + 8² = 9² = 25 + 64 = 81
89 = 81, false
b is false
10² + 11² = 12² = 100 + 121 = 144
221 = 144, false
c is false
3² + 4² = 6² = 9 + 16 = 36
25 = 36, false
d is false
Thus, a is the answer.
Which of the following are in the correct order from least to greatest?
77
80°, 4, 38°
2x 6
л 7л
38°, 80°, 4. 6. 2x
O
7x
O
38°, 5,80°, 621
л 7л
28, 38°, 80°, 4, 6
O
Answers
Answer:
3rd option
38, 45, 80, 210, 360
Step-by-step explanation:
The correct order from least to greatest for your options is л 7л < 38° < 4 < 80° < 6 < 2x, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The options A,B,C and D
Now,
To order numbers and angles from least to greatest, you need to compare their values and arrange them in ascending order. For numbers, you can use a calculator1 or a number sorter2 to help you. For angles, you need to measure their size in degrees using a protractor3 and then classify them as acute (< 90°), right (= 90°), obtuse (> 90°) or reflex (> 180°) angles4. The smallest angle is an acute angle and the largest angle is a reflex angle.
Therefore, by algebra the answer will be л 7л < 38° < 4 < 80° < 6 < 2x
More about the Algebra link is given below.
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Use formulas to find the lateral area and surface area of the prism.
A triangular prism has three rectangular sides of height 30 inches connecting two right triangular bases, one of which has a leg of length 24 inches and a hypotenuse of length 25 inches.
(Round to the nearest whole number as needed.)
Answers
Answer:
Step-by-step explanation:
De mais
Drag and drop the numbers 1 - 9 into the empty
boxes to the right to create a right triangle with the largest area
possible (round to the nearest TENTH, if necessary).
Each number can only be used one time, and only one number
can be placed per empty box (there will be some unused
numbers).
Answers
Answer:
9 for the hypotenuse, [tex]\sqrt{64}[/tex] and [tex]\sqrt{25}[/tex] for the two legs
Step-by-step explanation:
For these types of problems, we need to make sure that the values of legs are as big as possible while keeping the hypotenuse larger than legs because otherwise, it won’t be a right triangle.
So for the hypotenuse, we have to put the largest number in this number bank because the hypotenuse has to be larger than both legs. So the hypotenuse will equal 9. The rest is simple. Get the numbers as large as possible. Since the hypotenuse must be larger than both legs, we cannot use sqrt(81) and sqrt(64) (that would’ve been sweet). So we have to use sqrt(64) and sqrt(25) because sqrt(49) and sqrt(36) are already taken since we can only use a number once.
I'm not an expert at this and I cannot guarentee that this is correct. But I hope that this helps.
Answer please
...
..
..
Answers
Answer:
-1/16
Step-by-step explanation: