Which expression is equivalent to cot2B(1 – cos-B) for all values of ß for which cot2B(1 - cos2B) is defined?
Answers
From the Pythagorean identity,
[tex]\sin ^2\beta+\cos ^2\beta=1[/tex]we have
[tex]\sin ^2\beta=1-\cos ^2\beta[/tex]Then, the given expression can be rewritten as
[tex]\cot ^2\beta\sin ^2\beta\ldots(a)[/tex]On the other hand, we know that
[tex]\begin{gathered} \cot \beta=\frac{\cos\beta}{\sin\beta} \\ \text{then} \\ \cot ^2\beta=\frac{\cos^2\beta}{\sin^2\beta} \end{gathered}[/tex]Then, by substituting this result into equation (a), we get
[tex]\begin{gathered} \frac{\cos^2\beta}{\sin^2\beta}\sin ^2\beta \\ \frac{\cos ^2\beta\times\sin ^2\beta}{\sin ^2\beta} \end{gathered}[/tex]so by canceling out the squared sine, we get
[tex]\cos ^2\beta[/tex]Therefore, the answer is the last option
Related Questions
find the values of x and y that maximize the objective function c = 3x + 4y for the graph
Answers
Answer: The correct answer is x=0 and y=4 or (0,4) per the graph
Step-by-step explanation:
To find the maximum value, we must test each point using the equation:
Check for (0,4):
C=3x+4y
C=3(0)+4(4)
C=16
Check for (2,2):
C=3(2)+4(2)
C=6+8
C=14
Check for (4,0):
C=3(4)+4(0)
C=12
Answer:
Step-by-step explanation:
what is the slope intercept form of the line passing through the point (2,1) and having a slope of 4?
Answers
The equation of a line has the form:
[tex]y=mx+b[/tex]if the slope is equal to 4 then we know that: m = 4 and now we can replace the slope and the coordinate ( 2,1 ) to find b so:
[tex]\begin{gathered} 1=4(2)+b \\ 1-8=b \\ -7=b \end{gathered}[/tex]So the final equation will be:
[tex]y=4x-7[/tex]If the 10 letters are {aa,aa,aa,aa,bb,bb,cc,cc RR,RR} are available and all 10 of them are to be selected without replacement,what is the number of different permutations?
Answers
In order to calculate the number of permutations, first we start with the factorial of the number of letters.
There are 10 letters, so we start with the factorial of 10.
Then, we need to check the number of repetitions. Each repetition will be a factorial in the denominator:
[tex]x=\frac{10!}{a!\cdot b!\operatorname{\cdot}...}[/tex]We have four repetitions of aa, two repetitions of bb, two repetitions of cc and two repetitions of RR, therefore the final expression for the number of permutations is:
[tex]x=\frac{10!}{4!2!2!2!}[/tex]Calculating this expression, we have:
[tex]x=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5\operatorname{\cdot}4!}{4!\operatorname{\cdot}2\operatorname{\cdot}2\operatorname{\cdot}2}=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5}{8}=18900[/tex]Therefore there are 18900 permutations.
Suppose that the probability that you will win a contest is 0.0002, what is theprobability that you will not win the contest? Leave your answer as a decimal and donot round or estimate your answer.
Answers
Answer:
0.9998
Explanation:
The probability that you will not win the contest can be calculated as 1 less the probability that you will win a contest, so
1 - 0.0002 = 0.9998
Therefore, the answer is 0.9998
mrs Middleton makes a solution to Clean her windows she uses 2:1 ratio for every two cups of water she uses one cup of vinagar if ms middleton uses a gallon of water how mant cups of vinagara. 12 cups b. 2 quartz c. 2 pints d. 1 gallon
Answers
To answer this question we have to find (among the options) the amount that represents half the amount of water used.
Since the ratio of water to vinegar is 2:1, half of the amount of water will be used of vinegar.
In this case we have to find the answer that represents half a gallon.
That answer is 2 quarts. 2 guarts are 0.5 gallons, it means they are half the amount of water used.
It means that the answer is b. 2 quarts.
which describes the solution of the inequality y>-15? a) solid vertical line through (0,-15) with shading to the left of the line. b) dashed vertical line through (0,-15) with shading to the left of line. c) solid horizontal line through (0,-15) with shaing below line. d) dashed horizontal line through (0,-15) with shaing above line.
Answers
The solution to the inequality y > - 15 is all values of y greater than -15. This means the number -15 itself is not included; therefore, the line is a dashed line that passes through (0, -15). Furthermore, the > sign implies that the shaded region is found above the dashed line. Hence, the solution to our inequality is a dashed horizontal line through (0, -15), with shading above the line.
rewrite using a single exponent. 9 4, 9 4
Answers
We need to represent the product of two exponents as one single exponent. To do that we need to calculate their product, when the bases are equal we can conserve the base and add the exponents. We will do this below:
[tex]9^49^4=9^{4+4}=9^8[/tex]can you please solve this practice problem for me I need assistance
Answers
The missing angle in the triangle of the left is:
51 + 74 + x = 180
x = 180 - 51 - 74
x = 55°
The missing angle in the triangle of the right is:
55 + 74 + x = 180
x = 180 - 55 - 74
x = 51°
Then, both triangles are similar. This means that their corresponding sides are in proportion. These sides are:
35 in
8+7t=22 in verbal sentence
Answers
Eight plus Seven times t equals twenty-two
Explanation
Step 1
Let
a number= t
seven times a number= 7t
the sum of eigth and seven times a number=8+7t
the sum of eigth and seven times a number equals twenty-two=8+7t=22
or,in other words
Eight plus Seven times t equals twenty-two
I hope this helps you
Find the volume of the figure. Round to the nearest hundredths place if necessary.
Answers
The volume of a Pyramid
Given a pyramid of base area A and height H, the volume is calculated as:
[tex]V=\frac{A\cdot H}{3}[/tex]The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:
[tex]c^2=a^2+b^2[/tex]Solving for b:
[tex]b^{}=\sqrt[]{c^2-a^2}=\sqrt[]{19.3^2-16.8^2}=9.5\operatorname{mm}[/tex]The area of the base is the semi-product of the legs:
[tex]A=\frac{16.8\cdot9.5}{2}=79.8\operatorname{mm}^2[/tex]Now the volume of the pyramid:
[tex]V=\frac{79.8\operatorname{mm}\cdot12\operatorname{mm}}{3}=319.2\operatorname{mm}^3[/tex]The volume of the figure is 319.2 cubic millimeters
Answer the questions below about the quadratic function.g(×)=2×^2-12×+19Does the function have a minimum or maximum? minimum or maximum what is the functions minimum or maximum value?Where does the minimum or maximum value occur?x=?
Answers
Given the function:
[tex]g(x)=2x^2-12x+19[/tex]Let's determine if the function has a minimum or maximum.
The minimum and maximum of a function are the smallest and largest value of a function in a given range or domain
The given function has a minimum.
Apply the general equation of a quadratic function:
[tex]y=ax^2+bx+c[/tex]To find the minimum value, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = -12
a = 2
Thus, we have:
[tex]\begin{gathered} x=-\frac{-12}{2(2)} \\ \\ x=-\frac{-12}{4} \\ \\ x=3 \end{gathered}[/tex]To find the function's minimum value, find f(3).
Substitute 3 for x in the function and evaluate:
[tex]\begin{gathered} f(x)=2x^2-12x+19 \\ \\ f(3)=2(3)^2-12(3)+19 \\ \\ f(3)=2(9)-36+19 \\ \\ f(3)=18-36+19 \\ \\ f(3)=1 \end{gathered}[/tex]Therefore, the function's minimum value is 1
Therefore, the functions minimum value occurs at:
x = 3
ANSWER:
• The function has a minimum
• Minimum value: 1
• The minimum occurs at: x = 3
The angle of depression from the top of a sheer cliff to point A on the ground is 35º. If point A is280 feet from the base of the cliff, how tall is the cliff? Round the answer to the nearest tenth of afoot.
Answers
In this case, to calculate the tall of the cliff, consider the distance from the base of the cliff to the point A, as a hypotenuse of a right triangle.
The tall of the clift is given by:
h = 280 sin(35)
h = 280(0.573)
h = 160.60
Hence, the tal of the clift is 160.60 feet
Earth's Moon is 384,400 km from Earth. What is the correct way to write this distance in scientific notation? O A. 3.844 x 105 km OB. 38.44 x 10-4 km O C. 38.44 x 104 km O D. 3.844 x 10-5 km SUBMIT
Answers
To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive.
So, in this case, you have
Therefore, the correct way to write this distance in scientific notation is
[tex]3.844\times10^5[/tex]And the correct answer is
[tex]undefined[/tex]Plot the complex number, then write the complex number in polar form. You may express the argument in degrees.
Answers
DEFINITIONS
To represent a complex number we need to address the two components of the number.
Consider the complex number:
[tex]a+bi[/tex]Complex numbers are the points on the plane, expressed as ordered pairs (a, b), where a represents the coordinate for the horizontal axis and b represents the coordinate for the vertical axis.
Note that the imaginary part is plotted out on the vertical axis while the real part is on the horizontal axis.
QUESTION
The complex number is given to be:
[tex]4\sqrt[]{3}-4i[/tex]This means that the ordered pair representing the complex number is given to be:
[tex](a,b)=(4\sqrt[]{3},-4)[/tex]This means that the point will be positive on the real axis and negative on the imaginary axis. Therefore, the point will be in the 4th quadrant.
The correct option is OPTION B.
On the graph below, what is the length of side AB? B ...
Answers
The distance between two points in the plane is:
[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2[/tex]The points A and B have coordinates A(5,3) and B(5,6). Then the distance between them is:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(5-5)^2+(6-3)^2} \\ =\sqrt[]{(3)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]Therefore, the length of the side AB is 3 units.
is this equation no solution, one solution, or infinitely may solutions
Answers
Given:
[tex]\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-\frac{1}{4}x+2\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]To solve for x and y:
Substitute the equation (2) in (1) we get,
[tex]\begin{gathered} x+4(-\frac{1}{4}x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}[/tex]Therefore, the given system has infinitely many solutions.
The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term
Answers
SOLUTION
The following is a geometric series
We will use the formula
[tex]T_n=ar^{n-1}[/tex]Where Tn is the nth term of the series,
n is the number of terms = 8,
a is the first term = 15
And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15
Now let's solve
[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]So the 8th term = 53.748
hello I need help answering this homework question please thank you
Answers
Solution:
Case: Area
Given: A house to be painted
Method/ Final answers
a) Find the area of the garage to be painted.
(i) Front.
A = l X w - Garage door area
l= 15 ft, b= 10-4 gives 6ft
A= 15 X 6 - (10 X 7)
A= 90 - 70
A= 20 square feet
ii) Side
A= l X w
A= 6 X 5
A= 30 square feet
iii) The sum of areas
A= 20 + 30
A= 50 square feet
b) Area of the painted region around windows 5 and 6.
Since 12 in = 1 ft
Area of front door converted to feet is (20/3) ft by 3 ft
Areas of windows 5 and 6 converted to feet is 3 ft by (5/3) ft each
A= Area of space - (Area of front door + window 5 + window 6)
A= (30 X 10) - [(20/3) X 3 + 3 X (5/3) + 3 X (5/3)]
A= 300 - [20 + 5 + 5]
A= 300 - 30
A= 270 square feet.
c) Area of the painted region around windows 3
A= Total face - Area of window 3
A= (Rectangle + Parallelogram + Triangle) - Area of window 3
A= [(10 X 4) + (5 X 4) + (0.5 X 4 X 3)] - [1 X (5/3)]
A= [40+20+6] - [5/3]
A= 66 - (5/3)
A= 193/3 square feet
A= 63.33 square feet
d) Area of the region on the second floor with 2 rectangles and the region around window 4
i) region with rectangle 1 from left to right
A= 10 X (15- 6)
A= 10 X 9
A = 90
ii) region with rectangle 2 from left to right
A= 10 X (15- 6)
A= 10 X 9
A = 90
iii) Area of region around window 4
Area of space - area of window
A= 10 X (30-9-12) - [3 X (5/2)]
A= 10 X 9 - (15/2)
A= 82.5.
Total area= 90 + 90 + 82.5
= 262.5 square feet
e) Total area of the painted region (white)
262.5 + 63.33+ 270 + 50
= 645.83 square feet.
f) Additional question
The total cost if it cost $8 per sq ft
645.83 square feet X $8 per sq ft
=$5166.64
Figure A is a scale image of Figure B.27Figure AFigure B4535What is the value of x?
Answers
Answer:
x = 21
Explanation:
Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.
It follows then
[tex]\frac{27}{45}=\frac{x}{35}[/tex]which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.
Now to find the value of x, we simply need to solve for x.
We do this by multipying both sides by 35:
[tex]undefined[/tex]Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?
Answers
Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.
81 km=9 liters
9 km= 1 liter
She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
By unitary method,
22 liters = 22 × 9 km
= 198 km
Also, given that if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.
We need to find the amount of fuel she would need.
Let 139.4 km = x liters
By unitary method,
x = 139.4 / 9
x = 15.5 liters
Therefore, Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
Learn more about Unitary method here:
https://brainly.com/question/22056199
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A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure.What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.
Answers
Solution
For this case we can do the following:
We can find the value of s on this way:
[tex]s=\sqrt[]{6^2+4^2}=\sqrt[]{52}=7.21[/tex]And solving for r we got:
[tex]r=\sqrt[]{6^2+3^2}=\sqrt[]{45}=6.71[/tex]Then the answer for this case would be:
[tex]\sqrt[]{52}=7.21[/tex]the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions
Answers
You can read a pie chart as follows
Looking at the given pie chart.
The budget for Research is arounf 1/6
The budget for Engineering is around 2/6
The budget for Support is around 1/8
The budget for media and marketing are 1/16 each
The budget for sales is around 3/16
a) The department that has one eight of the budget is Support.
b) The budgets for sales and marketing together add up to
[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]Multiply it by 100 to express it as a percentage
[tex]\frac{1}{4}\cdot100=25[/tex]25% of the budget correpsonds to sales and marketing
c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3
[tex]\frac{18}{3}=6[/tex]The budget for media is 6%
The following are the annual salaries of 15 chief executive offers of major companies. The salaries are written in thousands of dollars.
Answers
The original data is:
405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633
To find the required percentiles, we need to sort the dataset from lowest to highest.
84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108
The total number of data is 15.
a) The 25th percentile is the element located at the position:
25/100 * 15 = 3.75
Rounding down, the position is 3, so the 25th perc
I need to double check 15 I got answer B
Answers
We will have that the area of one sector of the circle will be:
[tex]A=(\frac{45}{360})\pi(20in)^2\Rightarrow A=\frac{25\pi}{2}in^2[/tex]So, the solution is option B.
In the triangle below, if B = 69°, A = 32°, c = 5.7, use the Law of Sines to find a. Round your answer to the nearest hundredth.
Answers
We know that the interior angles have to add to 180°, then we have that:
[tex]\begin{gathered} C=180-69-32 \\ C=79 \end{gathered}[/tex]Hence angle C=79°.
Now that we know the angle C we can use the law of sines to find a; the law of sines states that:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]From this we have the equation:
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]Plugging the values given and solving for a we have:
[tex]\begin{gathered} \frac{\sin32}{a}=\frac{\sin 79}{5.7} \\ a=(5.7)\frac{\sin 32}{\sin 79} \\ a=3.08 \end{gathered}[/tex]Therefore a=3.08
I inserted a picture of the question Check all that apply
Answers
Recall that the line equation is of the form
[tex]y=mx+c\ldots\ldots\text{.}(1)[/tex]The points lie in the line are (2,5) and (-2,-5).
Setting x=2 and y=5 in the equa
PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..
Answers
Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]then, to solve this solve each option and compare
Step 1
[tex]6^{-5}\cdot6^2[/tex]solve
[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]so, this is not an answer
Step 2
[tex](\frac{1}{6^2})^5[/tex]solve
[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]so, this is an answer
Step 3
[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 4
[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 5
[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]so, this is not an answer
I hope this helps you
Construct a probability distribution for a discrete random variable uses the probability experiment of tossing a coin three times. Consider the random variable for the number of heads
Answers
Answer:
Explanation:
By building a tree diagram we can find the theoretical probability of each number of heads when tossing three coins.
All of the following ratios are equivalent except 8 to 12 15/102/36:9
Answers
False
1) Let's examine those ratios, and simplify them whenever possible:
[tex]\begin{gathered} \frac{15}{10}=\frac{3}{2} \\ \frac{2}{3} \\ \frac{6}{9}=\frac{2}{3} \\ \frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]2) Simplifying those ratios, all the following but 15/10 are equivalent to 8/12
3) So this is a false statement to say that all of those are equivalent except 8 to 12.
4. Driving on the highway, you can safely drive 65 miles per hour. How far can you drive in ‘h’ hours? What is the domain of the function which defines this situation?A) 65B) the number of hours you driveC) the distance you driveD)the amount of gas you use
Answers
Answer:
[tex]\text{ The number of hours you drive.}[/tex]Step-by-step explanation:
For distance, we can apply the following equation:
[tex]\begin{gathered} d=s*h \\ where, \\ s=\text{ speed} \\ h=\text{ hours} \end{gathered}[/tex]Since we know that we can safely drive 65 miles per hour, the domain will be defined by the number of hours you drive:
[tex]d=65h[/tex]