Answers
Answer:
a) multiply by cos²/cos², move sin/cos inside parentheses, simplify
d) multiply by (cot+cos); use cot=cos·csc, csc²-1=cot² in the denominator
Step-by-step explanation:
You want to prove the identities ...
sin²(x)(cot(x) +1)² = cos²(x)(tan(x) +1)²cos(x)cot(x)/(cot(x)-cos(x) = (cot(x)+cos(x)/(cos(x)cot(x))IdentitiesUsually, we want to prove a trig identity by providing the steps that transforms one side of the identity to the expression on the other side. Here, each of these identity expressions can be simplified, so it is actually much easier to simplify both expressions to one that is common.
a) sin²(x)(cot(x) +1)² = cos²(x)(tan(x) +1)²We are going to use s=sin(x), c=cos(x), (s/c) = tan(x), and (c/s) = cot(x) to reduce the amount of writing we have to do.
\(s^2\left(\dfrac{c}{s}+1\right)^2=c^2\left(\dfrac{s}{c}+1\right)^2\qquad\text{given}\\\\\\\dfrac{s^2(c+s)^2}{s^2}=\dfrac{c^2(s+c)^2}{c^2}\qquad\text{use common denominator}\\\\\\(c+s)^2=(c+s)^2\qquad\text{cancel common factors; Q.E.D.}\)
d) cos(x)cot(x)/(cot(x)-cos(x) = (cot(x)+cos(x)/(cos(x)cot(x))Using the same substitutions as above, we have ...
\(\dfrac{c(c/s)}{(c/s)-c}=\dfrac{(c/s)+c}{c(c/s)}\qquad\text{given}\\\\\\\dfrac{c^2}{c(1-s)}=\dfrac{c(1+s)}{c^2}\qquad\text{multiply num, den by s}\\\\\\\dfrac{c(1+s)}{(1-s)(1+s)}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{1-s^2}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{c^2}=\dfrac{c(1+s)}{c^2}\qquad\text{Q.E.D.}\)
__
Additional comment
The key transformation in (d) is multiplying numerator and denominator by (1+sin(x)). You can probably prove the identity just by doing that on the left side, then rearranging the result to make it look like the right side.
For (a), the key transformation seems to be multiplying by cos²(x)/cos²(x) and rearranging.
Sometimes it seems to take several tries before the simplest method of getting from here to there becomes apparent. The transformations described in the top "Answer" section may be simpler than those shown in the "Step-by-step" section.
Related Questions
full solution or dislike
Find the width of elementary gravity dam whose height is 100m. Specific gravity of dam material 22. and seepage coefficient at the base C = 0.8.
Answers
The width of the elementary gravity dam is 2750 meters determined by the specific gravity of the dam material and the seepage coefficient at the base.
The width of an elementary gravity dam can be calculated using the following formula:
Width = (Height * Specific Gravity) / Seepage Coefficient
Given:
Height = 100m
Specific Gravity = 22
Seepage Coefficient = 0.8
Plugging in the values into the formula, we get:
Width = (100 * 22) / 0.8
Simplifying the equation, we have:
Width = 2200 / 0.8
Width = 2750 meters
Therefore, the width of the elementary gravity dam is 2750 meters.
Gravity dams are solid structures built to withstand the force of water and retain it behind the dam. They rely on their weight to resist the horizontal force exerted by the water. The width of a gravity dam is a crucial design parameter that ensures its stability and ability to hold back water effectively.
The specific gravity of the dam material is an important factor in determining the dam's width. Specific gravity is the ratio of the density of a substance to the density of water. A higher specific gravity indicates a denser material, which means the dam requires a wider base to counterbalance the force of the water.
The seepage coefficient at the base of the dam is another critical parameter. It represents the rate at which water can pass through the dam's foundation. A lower seepage coefficient implies less water seepage, reducing the risk of erosion and potential failure. A higher seepage coefficient would necessitate a wider dam to accommodate the increased seepage and maintain stability.
In the given problem, with a height of 100m, a specific gravity of 22, and a seepage coefficient of 0.8, the calculated width of 2750 meters ensures the dam's stability and adequate resistance against the force of water.
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yall a Chef Boyardee Beefaroni = $0.88 if I buy 4 of them how much money i need???
Answers
Answer:
$3.52
Step-by-step explanation:
$0.88 x 4 = $3.52
(I love Chef Boyardee stuff)
Hope this helped :)
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Susan charges $8 per hour walking her neighbor’s dog. She charges $12 per hour babysitting. Part A: Define the variables. Part B: Write an expression to represent the amount Susan earns dog walking and babysitting
Answers
Answer:
Part A: The variables are the amount charged per hour dog walking and the amount charged per hour babysitting.
Part B: y=8d+12b
Step-by-step explanation:
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
Answers
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
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ILL MARK BRAINILEST !! 80 POINTS
Question 1: 11 pts
Find the vertex of the parabola y = x2 - 10x + 16.
A. (-5,91)
B. (-9,5)
C. (5,-9)
D. (8,0) and (2,0)
Answers
\(\\ \rm\rightarrowtail y=x^2-10x+16\)
\(\\ \rm\rightarrowtail y=x^2-10x+16+9-9\)
\(\\ \rm\rightarrowtail y=x^2-10x+25-9\)
\(\\ \rm\rightarrowtail y=(x-5)^2-9\)
Vertex form
y=a(x-h)^2+kSo
vertex:-
(h,k)=(5,-9)Lin's smart phone was fully charged when she started school at 8:00 a. M. At 9:20 a. M. , it was 90%
charged, and at noon, it was 72% charged.
1. When do you think her battery will die?
2. Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.
Answers
1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.
2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.
Linear functions are related to linear equations.
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HELP PLS WILL GIVE BRAINLIEST
Answers
Answer:
The answer is B and D :)
Step-by-step explanation:
It is b because the x value is getting bigger while the y value is getting smaller. :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
Options B and D
Step-by-step explanation:
Step 1: Determine what negative association is
Negative association basically means that the best-fit line for the scatter plot would be in a downwards slope which means that it has a negative association.
In the given examples, Option A wouldn't work because we can see that the best-fit line would be going up which is a positive association. Option B would work because we see the downward slope. Option C wond't work for the same reason as Option A. And finally Option D would work since we have a downward slope.
Answer: Options B and D
Jana paid $48 for 4 tickets to a movie. How much would it cost for 8 tickets? I'm aware you could probably do this problem without much effort. But the point of today's assignment is to work on writing proportions correctly. Write the proportion in the box on the left. Write the answer in the box below.
Answers
Answer:
96. (Proportions are down below)
Step-by-step explanation:
Since the tickets are being doubled, just double the amount paid or divide 48 by 4 and multiply it by 8.
48 ÷ 4 = 12
12 × 8 = 96
If you'd like to write it as a proportion, here:
4/48 = 8/96
Answer:
The cost would be $ 96
Explanation:
It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d .Based on the info. given, 1 ticket would be 12 dollars. If so it would original be, 1:12. ( if I'm wrong, I'll try better next time.
Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
Answers
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
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a man finds 1 hundred dollars and he keeps one half of it, gives 1 fourth if it to someone and and gives another 1 fifth of it to some else and he puts the rest in savings. how much did he give everyone
Answers
Which percent accurately reflect the white section in the circle?
A. 38%
B. 48%
C. 62%
D. 68%
Answers
The percent that accurately reflects the white section in the circle is 38%. So, the correct option is A).
To find the percentage of the circle that is white, we need to divide the area of the white region by the area of the entire circle and multiply by 100.
Looking at the diagram, we can see that the white region takes up about 3/8 of the circle, or 37.5% (since 3/8 is equal to 0.375 or 37.5%). This is closest to answer choice A, which is 38%.
Therefore, the percent that accurately reflects the white section in the circle is 38%.
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Evaluate 23x-1 for x = 1.
2 to the power of 3 not 23
Answers
Answer: = 7 i believe
Step-by-step explanation:
2^3 (2 power by 3) x - 1 for 1 which is 7
plsss help, I've been stuck on this problem for a while
find the measure of each marked angle
Answers
Answer:
x = 8, so the angles measure 60 degrees.
Step-by-step explanation:
Alternate exterior angles are congruent, so we have:
\(10x - 20 = 7x + 4\)
\(3x = 24\)
\(x = 8\)
\(10(8) - 20 = 80 - 20 = 60\)
\(7(8) + 4 = 56 + 4 = 60\)
A spherical water tank holds 12,000 ft^3 of water. What is the diameter of the tank? Hint: V = pi/6 d^3
Answers
Answer:
Step-by-step explanation:
It's 28.40ft by the way.
Answer:
The answer is 28.80
is a transformation involving the addition, subtraction, multiplication, or division of or by a constant.
Answers
Yes, a transformation can involve the addition, subtraction, multiplication, or division of or by a constant. In fact, these operations are commonly used in mathematical transformations.
For example, adding a constant to each value in a set of data is a common way to shift the entire set of values up or down. Multiplying each value in a set of data by a constant is a common way to stretch or shrink the data. Subtraction and division can also be used in transformations, depending on the context. However, it is important to note that not all transformations involve these operations.
Some transformations may involve more complex operations, such as exponentiation or logarithmic transformations. So, the short answer is yes, but the long answer is that it depends on the specific transformation being used.
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Find the surface area of the composite figure
5 cm
6 cm
4 cm
20 cm
12 cm
K6 cm
5 cm 4 cm
Answers
The surface area of the composite figure is 1160 cm².
How to find the surface area of the composite figure?To find the surface area of the composite figure, we need to determine the individual surface areas of each component and then sum them up.
The composite figure consists of multiple rectangular prisms. Let's calculate the surface area of each component:
Rectangular prism with dimensions 5 cm x 6 cm x 4 cm:
Surface area = 2(5 cm x 6 cm) + 2(5 cm x 4 cm) + 2(6 cm x 4 cm)
= 60 cm² + 40 cm² + 48 cm²
= 148 cm²
Rectangular prism with dimensions 20 cm x 12 cm x 6 cm:
Surface area = 2(20 cm x 12 cm) + 2(20 cm x 6 cm) + 2(12 cm x 6 cm)
= 480 cm² + 240 cm² + 144 cm²
= 864 cm²
Rectangular prism with dimensions 6 cm x 5 cm x 4 cm:
Surface area = 2(6 cm x 5 cm) + 2(6 cm x 4 cm) + 2(5 cm x 4 cm)
= 60 cm² + 48 cm² + 40 cm²
= 148 cm²
To find the total surface area of the composite figure, we add up the surface areas of each component:
Total surface area = 148 cm² + 864 cm² + 148 cm²
= 1160 cm²
Therefore, the surface area of the composite figure is 1160 cm².
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Find the component form of the vector that translates A(-4,8) to A'(7,-9)
Answers
The component form of the vector that translates A to A' is (11, -17)
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
In translation, the shape of the figure does not change but its size may change.
Other transformation processes are reflection and rotation.
The component form of the vector is governed by the rule; A' - A
so we subtract corresponding x- coordinates and corresponding y- coordinates
A' - A = (7, -9) - (-4, 8)
= ( 7 - - 4, -9 - 8)
-= ( 11, -17)
In conclusion, the vector that translates A to A' is ( 11, -17 )
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An animal shelter conducts an annual fundraising drive. The animal shelter must raise at least enough money to cover their annual rental of $2,500 and weekly expenses of $450. So far, the shelter has received a one-time donation of $125 and pledged donations of $680 per week. Which inequality can be used to find w, the number of weeks it can take for the shelter to meet the goal?
Answers
The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10
To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.
Let's break down the expenses and donations:
Expenses:
Annual rental = $2,500
Weekly expenses = $450
Donations:
One-time donation = $125
Pledged donations per week = $680
Let w represent the number of weeks it takes for the shelter to meet its goal.
Total expenses for w weeks = Annual rental + Weekly expenses * w
Total expenses = $2,500 + $450w
Total donations for w weeks = One-time donation + Pledged donations per week * w
Total donations = $125 + $680w
To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:
Total donations ≥ Total expenses
$125 + $680w ≥ $2,500 + $450w
Simplifying the inequality, we have:
$230w ≥ $2,375
Dividing both sides of the inequality by 230, we get:
w ≥ $2,375 / $230
Rounding the result to the nearest whole number, we have:
w ≥ 10
Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:
w ≥ 10
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Stuck with these two probabilities! Please help
Answers
The probability of line from F to B = 25% and the probability of the second line from A to F = 75%
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 20
event of the first line = 5
event of the second line = 15
probability of line from F to B = 5/20
(5 × 100)/20 = 25%
probability of the second line from A to F = 15/20
(15 × 100)/20 = 75%
Therefore, the probability of line from F to B is 25 percent (25%) while the probability of the second line from A to F is 75 percent (75%)
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The probability of line from F to B = 25% and the probability of the second line from A to F = 75%
What is probability
The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 20
event of the first line = 5
event of the second line = 15
probability of line from F to B = 5/20
(5 × 100)/20 = 25%
probability of the second line from A to F = 15/20
(15 × 100)/20 = 75%
Therefore, the probability of line from F to B is 25 percent (25%) while the probability of the second line from A to F is 75 percent (75%)
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in tests about a population proportion, p0 represents the . a. observed p-value b. probability of c. hypothesized population proportion d. observed sample proportion
Answers
The correct answer is c. hypothesized population proportion. In tests about a population proportion, p0 (pronounced as "p-naught") represents the hypothesized population proportion.
Which is the proportion of individuals in the population who possess a particular characteristic or exhibit a particular behavior. The hypothesized population proportion is typically derived from prior knowledge or information about the population or based on theoretical considerations.
It is used as a reference value to compare against the sample proportion (phat) to determine whether there is evidence of a statistically significant difference between the sample and population proportions.
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Quetlon 21 of 28Which of the following represents the ratio of the hypotenuse to the short legfor the triangle shown below?30°60°A. 2:1B. 1: 5C. 3:1D. 1:2
Answers
In order to determine the ratio of the hypotenuse to the short leg, use the sine of angle 30°:
sin 30° = opposite side / hypotenuse
Take intop account that sin30° is jsut the same the required ratio.
Moreover, consider that sin 30° = 1/2, which is the same that:
opposite side / hypotenuse = 1/2
or
hypotenuse / opposite
Which of the following is/are correct? (Select all that apply. You have only one submission for this question.) If u and v are parallel, then either u.v=jul lvl or u. V-lul lvl. The vector projuv is parallel to v If u and v are orthogonal, then u xv = 0. The expression u. (vw) is meaningful and the result is a scalar. Suppose u: O. If u xv=uxw, it follows that vw. If u and v are parallel, then u xv = 0. The expression u u can be negative
Answers
The correct statements are If u and v are orthogonal, then u × v = 0. The vector proj_v u is parallel to v. If u and v are parallel, then u × v = 0.
The statement "If u and v are parallel, then either u · v = |u||v|" is incorrect. The correct statement is "If u and v are parallel, then u · v = |u||v|".
The statement "The expression u.(vw) is meaningful and the result is a scalar" is incorrect. The expression u.(vw) is not meaningful because the dot product is only defined for vectors of the same dimension.
The statement "Suppose u: O. If u × v = u × w, it follows that v = w" is incorrect. The correct statement is "Suppose u ≠ 0. If u × v = u × w, it follows that v - w is parallel to u".
Finally, the statement "The expression u · u can be negative" is incorrect. The dot product u · u is always non-negative, and is only equal to zero if and only if u = 0
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Eduardo rides his bike for 5 miles. Claudia runs of the distance Eduardo
bikes.
How many miles does Claudia run?
Answers
Answer:
5 miles
Step-by-step explanation:
Give the equation of the line, perpendicular to the line with equation y=2x+1, that passes
through the point (8,-2)
Answers
Answer:
y=-1/2x+2
Explanation:
Find the area of the chape giving… pls help me
Answers
Answer:
Area = 8 sq cm
Step-by-step explanation:
This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:
base × height.
We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.
Area = b × h
= 4 × 2
= 8
The area is 8 sq cm.
If a population is not normally distributed, the distribution of the sample means for a given sample size n will
A. take the same shape as the population.
B. approach a normal distribution as n increases.
C. be positively skewed.
D. be negatively skewed.
E. None of the above
Answers
If a population is not normally distributed, the distribution of the sample means for a given sample size n will (B) approach a normal distribution as n increases.
The correct answer is B.
As per the central limit theorem, regardless of the shape of the population, the distribution of the sample means for a given sample size n will approach a normal distribution as n increases.
This is because as sample size increases, the sample means become more representative of the population, and the effects of any skewness or non-normality in the population become less significant.
Therefore, option B is the correct answer.
Option A is incorrect because the distribution of sample means does not necessarily take the same shape as the population.
Options C and D are incorrect because the skewness of the population does not necessarily translate to the skewness of the distribution of sample means.
Finally, option E is also incorrect because option B is the correct answer.
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Consider the following generic C comparison function and its assembly language representation C code: byte compbyte a,byte b)/a in rdi,b in rsi Assembly code cmpb %rsi,%rdi set_inst %a1 ret Your jobs(fill-in blank):now sh given values of a and b g SET instruction and the A.5 points set CI SF OF %al setg 47 23 B.5 points set h SF OF %a setl 23 47 C.5 points ZA SF OF %al set sete 23 23 D.5 points CF ZF SF OF 00%1 set b setne 23 47
Answers
The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:
A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.
B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.
C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.
D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.
Therefore, the correct answer is D. setne 23 47
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Use the graph of the piecewise function to answer the question.
Over which intervals is the function decreasing?
Select all that apply.
x > 6
x ≤ -6
1 < x ≤ 5
-5 < x ≤ 1
5 < x ≤ 6
-6 < x ≤ -5
Answers
The decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6
How to determine the decreasing interval?From the given graph, the function value decrease at the following x values
Negative infinity to x = -6x = 1 to x = 5x = 6 to x = infinityThis can be properly represented as:
x ≤ -6, 1 < x ≤ 5 and x > 6
Hence, the decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6
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"Can someone please help me match the vocab words in the box to
the correct meanings of what they do? Thank you.
ET574 Homework Data Visualization Q1 - 10: 1/2 point each Q11 & 12 1 point each Total homework score = 7 points Choose from these terms to answer question 1-10 (not all are used) pip bar chart numpy s"
Answers
Match the Data Visualisation terms as follows:
1. Numpy: Working with arrays and matrices.
2. Bar chart: Representing categorical data with rectangular bars.
3. Pip: Package installer for Python.
4. S: Statistical library for Python.
The following are the meanings of the given terms:
Numpy: It is a Python library used for working with arrays and matrices.Bar chart: It is a chart that represents categorical data with rectangular bars with heights or lengths proportionate to the values they represent.Pip: It is a package installer for Python.S: It is a statistical library for Python.To know more about Data Visualisation, visit:
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I need help with this question
Answers
Answer:
I thinks its F because you cant factor it
Step-by-step explanation:
Answer:
F) The expression does not have a real factor