1 + cos20/sin 20= cot 0
Answers
To prove the identity we need to remember the following identities:
\(\cos ^2\theta+\sin ^2\theta=1\)\(\tan \theta=\frac{\sin \theta}{\cos \theta}\)With this in mind we have:
\(\begin{gathered} \frac{\cos^2\theta+\sin^2\theta}{1+\tan^2\theta}=\frac{1}{1+\frac{\sin ^2\theta}{\cos ^2\theta}} \\ =\frac{1}{\frac{\cos ^2\theta+\sin ^2\theta}{\cos ^2\theta}} \\ =\frac{1}{\frac{1}{\cos ^2\theta}} \\ =\cos ^2\theta \end{gathered}\)This proves the identity.
Related Questions
Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates. A sandwich costs $2, and hot lunch costs $3. This system of inequalities models the scenario:
2x + 3y ≤ 15
x + y ≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set.
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically.
Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context.
Answers
The inequality is given by x + y ≥ 3 and 2x + 3y ≤ 15
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Let y represent the number of sandwich and x represent the number of hot lunch.
Michael has $15 and wants to buy a combination of school lunches to feed at least three classmates, hence:
x + y ≥ 3
Also:
2x + 3y ≤ 15
The inequality is given by x + y ≥ 3 and 2x + 3y ≤ 15
The part of the graph that is darkest is the solution. The point (5, 1) lies on the dark region, hence it is a solution.
Michael can buy 5 sandwich and 1 hot lunch for his classmates.
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Answer:
Step-by-step explanation:
A-the first equation which is 2x + 3y ≤ 15 is shaded downwards while the other equation x + y ≥ 3 is shaded upwards
B-(5,1) is included in the solution area for the 2x+3y<15 equation because when x and y are substituted ,it is still less than 15
so 5+1 is greater than 3
C-(2,3) MICHEAL can buy 2 sandwiches and 3 hot lunches which is Whitin his 15 dollar budget and can feed at least 3 of his classmates ]
i hope this is correct I'm not sure 100% especially part c if it incorrect put comment with correction
.
Five more than the product of a number and 8 equals 9.
Use the variable b for the unknown number.
Answers
The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."
To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:
8b + 5 = 9
To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:
Subtract 5 from both sides to get rid of the constant term:
8b + 5 - 5 = 9 - 5
8b = 4
Divide both sides of the equation by 8 to solve for b:
8b/8 = 4/8
b = 1/2
Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:
8(1/2) + 5 = 9
4 + 5 = 9
Both sides of the equation are equal, confirming that b = 1/2 is the solution.
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Elsevier logo el Home
Find the area of the combined rectangles.
9 ml
1 2 3 4
The area is
11 ml
19 ml
square miles.
2 ml
8 ml
5
7 ml
Answers
To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?
Follow the steps to find the value of x
1.Addition property of equality.
1/5(x)-2/3=4/3
1/5(x)-2/3+2/3=4/3+2/3
2.Multiplicative property if equality.
1/5(x)5/1=6/3(5/1)
The solution is x=
Answers
X= 10
Answer:
its 10
Step-by-step explanation:
I got it right
The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
Answers
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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Use the method on the left to solve the problem on the right. 3/4x =9
Answers
CV={(Standard Deviation)/(Mean)}*100%
You are thinking about investing money in the stock market and have narrowed your choices to one of two
stocks: TD Bank or Cenovas Energy. For TD Bank you have the following statistics:
• Mean monthly closing price: $70.00
Sample standard deviation: $6.30
The monthly closing stock prices of Cenovas Energy for the last eight months is shown below:
Closing Stock Price: ($) 18.00 19.00 12.00 16.00 17.50 12.00 7.50 10.00
(a) Calculate the mean stock price of Cenovas Energy.
Answer=$
(b) Calculate the standard deviation for the sample prices of Cenovas Energy.
Answer=$
(c) What is the median stock price for Cenovas Energy?
Answer=$
(d) What is the range in Cenovas Energy's stock price?
Answer=$
(e) Calculate the coefficient of variation for each stock.
TD Bank Answer= %
Cenovas Energy Answer= %
(f) Which stock is riskier and why?
Answers
a. The mean stock price of Cenovus Energy is 15.437.
b. The standard deviation for the sample prices of Cenovus Energy is
3.93.
c. The median stock price for Cenovus Energy is 14
d. The range in Cenovus Energy's stock price is 11.5.
e. The coefficient of variation for each stock are 28.071% Cenovus Energy for % and 9% for TD Bank.
f. As the coefficient of variation is more for TD Bank it is riskier to buy.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.
a. The mean stock price of Cenovus Energy is,
= (18 + 19 + 12 + 16 + 17.50 + 12 + 7.50 + 10)/8.
= 112/8.
= 14.
b. The variance for the sample prices of Cenovus Energy is,
= \(\frac{1}{n}\[ \sum_{i=1}^{n}[x_i - \overline{x}]^2\).
= (1/8)×[(18 - 14)² + (19 - 14)² + (14 - 12)² + (16 - 14)² +(17.50 - 14)² +(14 - 12)² +(14 - 7.50)² + (14 - 7.50)² +(14 - 10)²].
= (1/8)×[16 + 25 + 4 + 4 + 12.25 + 4 + 42.25 + 16].
= (1/8)×(123.5).
= 15.437.
Standard deviation = √(15.437).
= 3.93.
c. To find the median stock price for Cenovus Energy first we have the data set in ascending order.
7.50, 10.00, 12.00, 12.00, 16.00, 17.50, 18.00, 19.00.
So, The median of the stock price for Cenovus Energy is,
= (12 + 16)/2.
= 28/2.
= 14.
d. The range in Cenovus Energy's stock price is (19.00 - 7.50).
= 11.5.
e. The coefficient of variation for each stock is,
CV = {(Standard Deviation)/(Mean)}×100%.
CV = (3.93/14)×100%.
CV = 28.071 for Cenovus Energy.
CV = (6.30/70)×100%.
CV = 9% for TD Bank.
f. TD Bank's higher coefficient of variance makes investing riskier.
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What is 4/8 in simplest form?
1/2
2/4
1/4
Answers
Answer:
1/2
Step-by-step explanation:
Divide both the numerator and denominator by 4.
4/8 = 1/2
Answer:
1/2
Step-by-step explanation:
you can divide the numbers by 4/4 and you'll get
1/2
9^-5*9^-3 Rewrite using a single positive exponent plssss
Answers
Answer:
\(\frac{1}{9^{8}}\)
Step-by-step explanation:
When multiplying two numbers with exponents with the same base, you simply add the two exponents together, even if they're negative:
\(9^{-5}*9^{-3} =9^{-8}\)
When a number has a negative exponent (\(x^{-2}\)) it means that the number is equal to 1/that number (\(\frac{1}{x^{2}}\))
\(9^{-8}=\frac{1}{9^{8}}\)
PLEASE I NEED HELP the question is,
In the diagram of triangle LAC and triangle DNC below, LA = DN, CA = CN, and DAC is perpendicular to LCN.
a) Prove that triangle LAC = triangle DNC.
b) Describe a sequence of rigid motions that will map triangle LAC onto triangle DNC.
Answers
Answer:
1244 DCD
Step-by-step explanation:
Camp Sunshine is on the lake. Use the Pythagorean Theorem to find the distance between Francesca's house and Camp Sunshine to the nearest tenth of a meter.
Answers
The distance between Francesca's house and Camp Sunshine is 214.7 units.
Given
The coordinates of the house is (10.20)
The coordinates of the camp is (200, 120)
The coordinates of the right angle point is (200, 20)
To find a distance between two points or the length of the segment, we use the following formula:
\(\sqrt{(x2 - x1)^{2} + (y2 -y1)^{2} }\)
The distance of the house to the right angle point is
= \(\sqrt{(200 - 100)^{2} + (20-20)^{2} }\)
= \(\sqrt{190^2}\) units
= 190 units.
And
The distance from the right angle point to the Camp is:
= \(\sqrt{(200 - 200)^{2} + (20-120)^{2} }\)
= \(\sqrt{-100^2}\)
= 100 units
Use the Pythagorean Theorem to find the distance between Francesca's house and Camp
= \(\sqrt{100^2 +190^2}\) units
= \(\sqrt{46100}\) units
= 214.7 units.
So the distance between Francesca's house and Camp Sunshine is 214.7 units.
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Find the absolute extrema of the function on the closed interval.
y = 3 cos x, [0, 2π]
![Find the absolute extrema of the function on the closed interval.y = 3 cos x, [0, 2]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/n5r6hXBBsKUV7CzJ6FKe5sGu9d4w6e6B.png)
Answers
The absolute extrema for the given function occurred at the critical points for Interval [0, 2π] is 3.
Explain about the absolute extrema of function?The point wherein the minimum or maximum value of the function is reached is known as the absolute extremum (also global extremum) of the function in the given interval.
The absolute extremum, or point equivalent to the highest or least value in the entire function, is frequently the interval specified, which is the domain of the function.
The given function :
y = 3 cos x,
Differentiate the function with respect to 'x'.
y' = -3 sin x
Find the critical point , by y = 0
-3 sin x = 0
x = sin ⁻¹ (0)
Interval [0, 2π]
So, critical points are: x = 0,π, 2π
Now, evaluate function by putting the critical points;
y(0) = 3 cos 0 = 3
y(π) = 3 cos π = 0
y(2π) = 3 cos 2π = 3
Thus, absolute extrema for the given function occurred at the critical points 0 and 2π that is 3.
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Rewrite all three fractions with the lowest common denominator.
Answers
Answer:
\( - \frac{2}{4 } = - \frac{16}{32} \)
\( - \frac{6}{8} = - \frac{24}{32} \)
\( - \frac{13}{32} = \)
remains the same
Use the following sample data to answer the questions below
Favorite cola Number of responses
29
Coke
Pepsi
Diet Coke
Diet Pepsi
Coke Zero
Other
21
37.
28
19.
16
150
150
2
17)
a. Find the Probability of selecting a Coke person from this group.
Answers
Answer:
To find the probability of selecting a Coke person from this group, we need to divide the number of people who prefer Coke by the total number of people in the group.
The number of people who prefer Coke is 29. The total number of people in the group is 29 + 21 + 37 + 28 + 19 + 16 + 150 + 150 + 2 = 452.
Therefore, the probability of selecting a Coke person from this group is:
P(Coke) = Number of people who prefer Coke / Total number of people in the group = 29 / 452 ≈ 0.064
So the probability of selecting a Coke person from this group is approximately 0.064.
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
If -3 is a lower bound for the real zeros of f(x), then -2 is also a lower bound.
True or False?
Answers
The statement is false, because -2 is larger than -3.
Is the statement true?We know that -3 is a lower bound for the real zeros of f(x).
So, if we define k as the smallest real zero of f(x), we have:
-3 < k.
Then we can take, for example, k = -2.5
That is an allowed value for the real zero.
In that case, -2 is not a lower bound, because is false that:
-2 < k = -2.5
Then if -3 is a lower bound for the real zeros of f(x), we can't assume that -2 is also a lower bound (because -2 is larger than -3).
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Simplifly the expression: x-3x-(-5x)
Answers
Answer:
The answer is 3x.
Step-by-step explanation:
I used a calculator
A Triangle has a height that is half of 28 yards and an area of 56 yards^2. What is the length of the base of the trangle?
Answers
The length of the base of the triangle is 8 yards whose height is half of 28 yards.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
According to question:The following formula provides the area of a triangle:
Area = (1/2) x base x height
We are given that the height of the triangle is half of 28 yards, which is:
height = 1/2 x 28 = 14 yards
We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:
56 = (1/2) x base x 14
Simplifying this equation, we get:
56 = 7 x base
Dividing both sides by 7, we get:
base = 8
Therefore, the length of the base of the triangle is 8 yards.
The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
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x-intercept of 3 and y-intercept of 8
How do you write a lunar equation given this information and how do you write the equation in slope form
Answers
Answer:
y = -8/3x + 8
Step-by-step explanation:
Step 1: Identify which values we have and need to find in the slope-intercept form:
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
(x, y) is any point,m is the slope,and b is the y-intercept.Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.
Step 2: Find m, the slope of the line:
Since the x-intercept is 3, the entire coordinates of the x-intercept are (3, 0)Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:
0 = m(3) + 8
0 = 3m + 8
-8 = 3m
-8/3 = m
Thus, the slope is -8/3.
Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.
Optional Step 3: Check the validity of the answer:
We know that the entire coordinates of the x-intercept are (3, 0) and the entire coordinates of the y-intercept are (0, 8).Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:
Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:
0 = -8/3(3) + 8
0 = -24/3 + 8
0 = -8 = 8
0 = 0
Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;
8 = -8/3(0) + 8
8 = 0 + 8
8 = 8
Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.
Recent legal changes to marijuana laws have altered the atmosphere in which people utilize the drug. Several states have legalized marijuana as a recreational drug. Below is ‘Hypothetical’ data on the percentage of users in both states that have (hypothetically) legalized marijuana and states that have not legalized marijuana. The government desires to know if the law is a deterrent to using the drug and hires you to figure it out. Examine the data and figure out the following questions below.
Percentage of Marijuana Workers in Legal & Non-Legal Use States
% Legal Use Marijuana % Non-Legal Use Marijuana
Iowa 20.5 New York 35.6
Alabama 18.2 Michigan 33.7
Alaska 18.2 Dist. of Colum. 33.4
Tennessee 17.3 Washington 32.9
Utah 16.8 Hawaii 31.5
Nevada 16.3 West Virginia 28.9
Nebraska 16.3 Illinois 27.5
Wyoming 15.6 Oregon 27.5
North Dakota 14.2 Ohio 27.4
Louisiana 13.8 Pennsylvania 27
Arkansas 13.2 Missouri 26.6
Georgia 12.8 California 25.4
Texas 12.7 Indiana 25.1
Kansas 12.5 Wisconsin 24.5
Virginia 12 Minnesota 24.5
South Dakota 10.9 Montana 21.7
Florida 9.6 Kentucky 20.4
Mississippi 9.3 Delaware 20.3
North Carolina 8.9 New Jersey 19.9
South Carolina 5.8 Massachusetts 19.7
Rhode Island 19.4
Connecticut 18.9
Maryland 18.6
Maine 18.5
Colorado 18
Idaho 16.1
Oklahoma 12.9
New Mexico 12.8
New Hamp. 12.3
Vermont 11.9
18. What is the pooled variance?
19. Compute the appropriate statistic?
20. Discuss the findings at p<.05 (same as the 95% level)?
Answers
19. It is not clear what specific statistic is being asked to be computed. Depending on the research question, different statistics could be calculated, such as mean, median, standard deviation, or correlation coefficient.
20. It is not possible to discuss findings at p<.05 (same as the 95% level) without additional information on the research question and the specific statistic being analyzed. In general, a p-value of less than .05 indicates that there is a statistically significant difference between groups or variables, indicating that the observed difference is unlikely to be due to chance. However, without more information on the research question and the specific statistic being analyzed, it is not possible to draw conclusions or discuss findings at this level of significance.
Picture included!
Find the unknowns in the graph below:
Answers
All the values of x, y and z are,
z = 12.99
y = 7.01
x = 28.3 degree
We have to given that;
In a triangle,
Two angles are, 61.7 degree and 90 degree
And, One side is, 14.76.
Now, We can formulate;
sin 61.7° = Perpendicular / Hypotenuse
sin 61.7° = z / 14.76
0.88 = z / 14.76
z = 0.88 x 14.76
z = 12.99
And, By Pythagoras theorem we get;
14.76² = z² + y²
14.76² = 12.99² + y²
217.85 = 168.74 + y²
y² = 217.85 - 168.74
y² = 49.1
y = 7.01
And, By sum of all the angles in triangle, we get;
x + 61.7 + 90 = 180
x + 151.7 = 180
x = 180 - 151.7
x = 28.3 degree
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Maria solved an equation as shown below. 3 (x + 6) = 5 (x minus 4). 3 x + 18 = 5 x minus 20. 38 = 2 x. 19 = x.
Answers
Answer:
19
Step-by-step explanation:
The value of the x will be 19. Then Maria solved an equation correctly.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
3(x + 6) = 5(x – 4)
Maria solved an equation as shown below.
3 (x + 6) = 5 (x – 4)
3x + 18 = 5x – 20
38 = 2x
19 = x
x = 19
Then Maria solved an equation correctly.
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No
0.7
What’s the percentage
Answers
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
Victor drives a distance of 21.45 miles everyday from home to his office. He moves into a new apartment that is just 3.65 miles away from his office. Determine the distance by which Victor has lessened his drive to the office.
Answers
Answer:
17.8 miles
Step-by-step explanation:
His old house was 21.45 miles from the office. He moves to a new apartment which is just 3.65 miles from the office.
Since it asks for the distance he reduced to the office, we would do
21.45 - 3.65 = 17.8 miles
Find the interest.
. 750$, 6.5%, 2years
Answers
Answer:
simple interest=$97.50.
compound interest= $100.668
Step-by-step explanation:
Given:
Principal (P) = $750
Rate (R) = 6.5% (in decimal form, 0.065)
Time (T) = 2 years
Simple Interest = Principal*Rate*Time
Using the formula, the simple interest is calculated as follows:
Simple Interest = $750*0.065*2 = $97.50
Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.
Again:
Compound Interest = Principal*(1 + Rate)^(Time)-Principal
Using the same values as above, the compound interest can be calculated as follows:
Compound Interest = $750*(1+0.065)^(2)-$750
= $750*1.065^2 -$750
= $750 × 1.134225 - $750
= $850.66875-$750
= $100.668
Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668
find the perimeter of the triangle
Answers
Answer:
x²+14x+11
Step-by-step explanation:
Find the perimeter of the triangle.
The perimeter is:
add them
-x²+9x
2x²+6
5x+5
x²+14x+11
quizlet
Help plz:)))I’ll mark u Brainliest
Answers
Answer:
The measurement of the angle is 74.65
Step-by-step explanation:
We have the adjacent and hypoteneuse; the trig function will be cosine
\(cos^{-1}(\frac{9}{34})\\\\=74.650\)
Answer:
75°
Step-by-step explanation:
cos x = \(\frac{9}{34}\)
cos x = 0.2647
cos\(^{-1}\) ≈ 74.65
which of the following is most likely the next step in the series
Answers
Answer:
A.
Step-by-step explanation:
Let's think of this as a clock. We can see that the 2 lines start in the same place, around 3 o'clock. Next, one of the line segments shifts down to around 6 o'clock. Next, it shifts to about 9 o'clock. Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.
We can also just use a regular circle, with one of the line segments moving 90 degrees each time.
Hope this helps! :)
During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?
Answers
During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:
P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes
The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.
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The slope of a line is 3 and it passes through point (-1,4). What is the equation of the
lines
Answers
Answer:
the required equation is 3x-y+7=0
Answer: y = 3x + 7
Since 3 is the slope it should come as 3x in the equation and then you should substitute the point in the equation y = 3x + c
A middle school counselor, attempting to correlate school performance with leisure interests, found that of a group of students, 33 had seen Movie A, 29 had seen Movie B, 23 had seen Movie C, 15 had seen Movies A and B, 10 had seen Movies A and C, 9 had seen Movies B and C, 3 had seen all three films, and 5 had seen none of the three films
Answers
Answer:
A=61 ; B=56 ; C=45
Step-by-step explanation:
I don't understand the question, but this is my answer.