Answers
If [tex]x[/tex] is positive, then [tex]\tan^{-1}(x)[/tex] is between 0 and π/2, which means [tex]\cos(\tan^{-1}(x))[/tex] is between 1 and 0.
Let [tex]\theta = \tan^{-1}(x)[/tex]. Then [tex]\tan(\theta) = x[/tex], and it follows from the Pythagorean identity that
[tex]\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta) \\\\ ~~~~ \implies \sec(\theta) = \sqrt{1 + \tan^2(\theta)} \\\\ ~~~~ \implies \cos(\theta) = \dfrac1{\sqrt{1+\tan^2(\theta)}} \\\\ ~~~~ \implies \cos(\tan^{-1}(x)) = \boxed{\dfrac1{\sqrt{1+x^2}}}[/tex]
We took the positive square root when solving for [tex]\sec(\theta)[/tex] because we know [tex]\cos(\theta)[/tex] is non-negative, between 0 and 1.
Related Questions
Mrs. Lindeman goes to Dillard's to purchase a new shirt. The price of the shirt is $26
and the sales tax is 8%. What is the total cost of her shirt?
show how to solve problem PLEASE
Answers
Based on the price of the shirt and the sales tax, the total cost of Mrs. Lindeman's shirt is $28.08
How to find the total cost?When given the sales tax and the price of an item, then you are to add the sales tax of that item to the price of the item to find the total cost of the item.
The sales tax on the shirt that Mrs. Lindeman bought is:
= Price of shirt x sales tax rate
= 26 x 8%
= $2.08
The total cost of the shirt to Mrs. Lindeman is:
= 26 + 2.08
= $28.08
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The midpoint of AB is M(1, 3). If the coordinates of A are (-1, 5), what are the coordinates of B?
Answers
EXPLANATION: to get from the midpoint AB to point A, we would get the distance between them to determine the distance from midpoint AB to point B. the distance between the x values 1 and -1 is 2. the distance between the y values 3 and 5 are 2. x values are rising in this case and y values are decreasing. to get to B, we would do 1 + 2 = 3, and 3 - 2 = 1. this would give us (3, 1)
The table below shows the population of a town, recorded in different years.
Use this table to complete the sentence.
Year
2000
2006
2012
Population of
the town
27,488
18,906
22,183
Between 2000 and 2006, the population
of the town increased / decreased
by
%, rounded to the nearest 19.
Answers
From the given table of the population, between 2000 and 2006 the population of the town decreased by 31.2%.
As given in the question,
Population of a town given in the table
Year Population of the town
2000 27,488
2006 18,906
Population of 2006 < population of 2000
Decrease in population = 27,488 - 18,906
= 8,582
Decrease of the population in percentage = (Difference/original) ×100
= ( 8,582 / 27,488 ) × 100
= 31.2%
Therefore, from the given table of the population, between 2000 and 2006 the population of the town decreased by 31.2%
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Answer:
32%
Step-by-step explanation:
27488-18906=8582
27488/8582=3.2
3.2x100=32
decrease by 32
mark me brainliest the other answer is wrong
If g(x) = -f(x), across which axis is f(x) reflected to obtain g(x)?
Answers
To reflect a graph, f(x) over the x-axis, you take -f(x). So if f(x)=x^2, then -f(x) is -x^2. Then g(x)=-x^2 is the reflection of your function f(x) over the x-axis.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
An output variable and one or more input variables are the minimum number of variables in a function. An equation can have any number of variables and declares that two expressions are equal (none, one, or more).
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Find the distance between the points (-4.4 , 9.8 ) and ( -4.4, -6.5).
Answers
Step-by-step explanation:
[tex] = \sqrt{ {x2 - x1)}^{2} + (y2 - y1) } \\ = \sqrt{ {( - 4.4 - ( - 4.4))}^{2} + ( { - 6.5 - 9.8)}^{2} } \\ = \sqrt{ {0}^{2} + 265.69 } \\ = 16.3units[/tex]
HOPE THIS HELPS
Use the formula kilowatt-hour (kWh) = watts x hours used per day / wattage.
To estimate the maximum kilowatt-hour that each appliance uses per day, per month, and per year. write your answers in scientific notation with a single-digit multipler. Assume 30 days per month and 365 days per year.
2. which appliance uses the least amount of energy per day?
3. which appliance uses the most amount of energy per year? Show your work.
Television - Wattage: 300 Hours per day: 6
Clothes dryer - Wattage: 2,790 Hours per day 4
Refrigerator - Wattage: 225 Hours per day: 24
Find the kWh per day, kWh per month, and kWh per year.
Write all of them in scientific notation.
Answers
The clothes dryer uses the maximum energy at 1.018 × 10⁶ kilowatt-hour
Kilowatt-hours are primarily used to sell electrical energy to customers. A device's power consumption in kilowatts, operating time in hours, and price per kilowatt-hour are multiplied to get the cost of running it. Utility companies' charges for power may vary based on the customer's consumption patterns over time. Prices vary widely depending on the location. Prices in the US can differ by a factor of three between states.
A composite energy unit called a kilowatt-hour is defined as one kW sustained for (and multiplied by) one hour. It is equivalent to 3600 kilojoules, or 3.6 MJ, when expressed in the joule (symbol J), the SI's base unit of energy.
So from the given conditions the television uses the least amount of energy per day at 300 kilowatt-hour.
The amount of energy per year:
Television = 300 × 365 = 1.095 × 10⁵ kilowatt-hour
Dryer = 2790 × 365 = 1.018 × 10⁶ kilowatt-hour
Refrigerator = 225 × 365 = 8.213 × 10⁴ kilowatt-hour
Hence the maximum energy is used by the Dryer.
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Jane travels 3 times as fast as Jill. Traveling in opposite directions, they are 256 miles apart after 8 hours. Find their rates of travel.
Answers
Jane is traveling at 26.66 mph
Jill is traveling at 5.33 mph .
let the speed of jane and jill are
Jill = x mph
Jane = 5x mph
where mph= Miles per hour
To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.
we also write as -
Distance = rate x time
8x + 8(5x) = 256
8x + 40 x = 256
48x = 256
x = 256/48
x = 5.33 mph
jill is traveling at 5.33 miles per hour. We can find jane speed by put the value of x
5 x = 5×5.33
5x = 26.66 mph
So Jane is traveling at 26.66 mph
Jill is traveling at 5.33 mph
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Combine like terms to create an equivalent expression.
7.4z-5(-1.6z+2.4)
Answers
The equivalent expression of the expression given as 7.4z - 5(-1.6z + 2.4) is -0.6z + 12
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
7.4z - 5(-1.6z + 2.4)
Open the bracket
7.4z - 5(-1.6z + 2.4) = 7.4z - 8z + 12
Collect the like terms in the above expression
So, we have
7.4z - 5(-1.6z + 2.4) = 7.4z - 8z + 12
Evaluate the like terms in the above expression
So, we have
7.4z - 5(-1.6z + 2.4) = -0.6z + 12
Hence, the equivalent expression of the expression given as 7.4z - 5(-1.6z + 2.4) is -0.6z + 12
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I need help with the following
Answers
Choose the symbol that makes the statement true
A. <
B. =
C. >
PLEASE HELP THANK YOU :)))
Answers
Answer: A. <
Step-by-step explanation:
-2.2 if less than -4
> is the symbol that makes the statement true. Therefore, the correct option is option A.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal symbol ()" to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether they're less than or higher than.
The different inequality symbols, characteristics, and methods for resolving linear inequalities in one variable as well as two variables will all be covered in this article along with examples. > is the symbol that makes the statement true.
Therefore, the correct option is option A.
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Find five solutions of the equation. Select integer values for x, starting with 2 and ending with 2. Complete the table
of values below.
y = 6x-4
...
Complete the table to the right by typing an integer for
the first input and an ordered pair for the second input.
X
-2
-1
0
1
2
y = 6x-4
(x,y)
Answers
The second inputs are -16 , -10 , -4, 2 ,8 an integer.
What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.x y = 6x - 4 (x,y )
-2 6 * -2 - 4 ( -2 , - 16)
______________________________________________________
- 1 - 1 * 6 - 4 ( -1 , -10 )
________________________________________________________
0 0 * 6 -4 ( 0 , -4)
________________________________________________________
1 6 * 1 - 4 ( 1 , 2)
________________________________________________________
2 6 * 2 - 4 ( 2 , 8 )
_______________________________________________________
the second inputs are -16 , -10 , -4, 2 ,8
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The complete question is -
Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below y =6x-4 (x,y) Complete the table to the right by typing an integer for the first input and an ordered pair for the second input. х y = 6x-4 (x,y) -2 - 1 0 1 2 Use two of the given points to graph the equation. Click to enlarge graph
Hey ! I got stuck on this question and really need help
Answers
The solution to the composite functions are;
(q o r)(-2) = 14
(r o q)(-2) = 27
How to Solve Composite Functions?
We are given the functions;
q(x) = 2x - 4
r(x) = -3x + 3
(q o r) simply means; q(r(x)). Thus, it is expressed as;
(q o r) = 2(-3x + 3) - 4
Multiply out the bracket to get;
(q o r) = -6x + 2
(q o r)(-2) = -6(-2) + 2
(q o r)(-2) = 14
(r o q) simply means; r(q(x)). Thus;
(r o q) = -3(2x - 4) + 3
Multiply out the bracket to get;
(r o q) = -6x + 12 + 3
(r o q) = -6x + 15
(r o q)(-2) = -6(-2) + 15
(r o q)(-2) = 27
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ill give points and brainly
Answers
Answer:
400, 440, or 480
Step-by-step explanation:
Without both dots, 400
With one dot, 440
with both dots, 480
Please correct me if I am wrong.
Pls Help!
Find the Greatest Common Factor of 18 and 27, show all your work!
Answers
Answer:
9
Step-by-step explanation:
Factor for 18 are:
1,2,3,6,9,18
Factors for 27 are:
1,3,9,27
Hope I helped <3
NO LINKS!! Please help me with these graphs. Part 4
Answers
Answer:
1. 17.5 units²
2. 16 units²
Step-by-step explanation:
Question 1Given vertices of ΔABC:
A = (-3, 2)B = (4, 2)C = (4, -3)Plot the vertices on the given graph paper and join with line segments to create the triangle.
As point B and C share the same x-coordinate, and points A and B share the same y-coordinate, ΔABC is a right triangle with base AB and height BC.
[tex]\begin{aligned}\textsf{Area of a triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \textsf{Area of $\triangle$ ABC} & = \sf \dfrac{1}{2} \times AB \times BC\\& = \sf \dfrac{1}{2} \times 7 \times 5\\& = \sf \dfrac{35}{2}\\& = \sf 17.5 \:\:units^2\end{aligned}[/tex]
Question 2Given vertices of rectangle WXYZ:
W = (0, 0)X = (2, 2)Y = (6, -2)Z = (4, -4)Plot the vertices on the given graph paper and join with line segments to create the rectangle.
The area of a rectangle is found by multiplying the length by the width. To find the area of rectangle WXYZ, find the length (WZ or XY) and the width (WX or ZY) using the distance formula, then multiply them.
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]
[tex]\begin{aligned}WZ & =\sqrt{(x_Z-x_W)^2+(y_Z-y_W)^2}\\& =\sqrt{(4-0)^2+(-4-0)^2}\\& =\sqrt{(4)^2+(-4)^2}\\& =\sqrt{16+16}\\& =\sqrt{32}\sf \:\:units\\\end{aligned}[/tex]
[tex]\begin{aligned}WX & =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\& =\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}\\& =\sqrt{(2-0)^2+(2-0)^2}\\& =\sqrt{(2)^2+(2)^2}\\& =\sqrt{4+4}\\& =\sqrt{8}\sf \:\:units\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Area $WXYZ$} & = WZ \times WX\\& = \sqrt{32} \times \sqrt{8}\\& = \sqrt{32 \cdot 8}\\& = \sqrt{256}\\& = 16\sf \:\:units^2\end{aligned}[/tex]
Step1: Submit Your Initial Post On the previous page, we learned about Project Implicit and their Implicit Association Tests (IATs). Here we'll discuss whether an IAT (Implicit Association Test) is an observational study or an experiment. To submit your initial post, reply to this discussion and answer the question-to-be-investigated (see below). Be sure to briefly explain your answer.
Question to be investigated: Is an IAT an experiment or an observational study? Explain.
Answers
It should be noted that an IAT is an experiment.
What is an experiment?An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
An experiment is The Implicit Association Tests (IAT). By taking measures, IAT assesses how strongly concepts are associated with one another. According to Carpenter et al. (2019), the IAT, which is an experiment, obtains its findings by meticulously associating things with related answer keys, such as athletic and clumsy.
Therefore, it should be noted that an IAT is an experiment.
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Is this correct?
f(x)=2x+3
Picture is included
Answers
Answer:
Correct
Step-by-step explanation:
Answer: yessir
Step-by-step explanation:
Figure B is a scaled copy of Figure A. Select all of the statements that must be true:
A. Figure B is larger than Figure A.
B. Figure B has the same number of edges as Figure A.
C. Figure B has the same perimeter as Figure A. D. Figure B has the same number of angles as Figure A.
E. Figure B has angles with the same measures as Figure A.
Answers
The required solution of the scaled factored figure is,
B. Figure B has the same number of edges as Figure A.
E. Figure B has angles with the same measures as Figure A.
Given that,
Figure B is a scaled copy of Figure A. We have to select all of the statements that must be true.
Here,
Figure B is similar to figure A but smaller than figure A.
So, Options A, C, and D are false
since the figure is similar, and the number of edges and angles are also equal.
So, Options B and E are correct.
Thus, the required solution of the scaled factored figure is,
B. Figure B has the same number of edges as Figure A.
E. Figure B has angles with the same measures as Figure A.
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√26 in irrational number on the number line using rational approximation
Answers
Answer: your mom
Step-by-step explanation: your dad your brother your sister your uncle your aunt your aaaaauuuuuggggghhhh
Alan ran for president of the chess club and he received 27 votes there were 60 members in the club what percentage of the club members voted for Alan
Answers
Answer:
45%
Step-by-step explanation:
27/60 x 100
.45 x 100
45
A = [- 8, 3] and B = (-6, 2)
A U B=
Answers
Answer:
Step-by-step explanation:NIDIHNG S,AST3RE TIRWACRE
I THINK THAT UR
2/3 of a number plus 1/6 of the same number is equal to 25. What is the number?
Answers
The number is 30.
Step-by-step explanation:
n=number.
2/3n+1/6n=25
Make a common denominator for 2/3 and 1/6 and then combine like terms.
4/6n+1/6n=25
5/6n=25
divide 5/6 on both sides to isolate n.
n=25/(5/6)
oreja.
n=25/1/5/6
nu(25×6)/(5×1)
n=150/5
n=30
OR
multiply the reciprocal instead of dividing.
n=25×(6/5)
n=150/5
n=30
someone help me two qestions 20 points
Answers
11) is 1/2 and 45% and 0.6 and finally 1
12) is 0 then 50% then 0.8 then 4
Amy was scheduled 17 intervals this week.she picked up 4 more intervals during this week
Answers
The commitment adherence percentage for the week will be 53%.
How to compute the percentage?
It was stated that Amy was scheduled to service 17 intervals this week. She picked up 4 more intervals during the week.
The following can be deduced based on the information that are given:
Total intervals = 17
Taken intervals = 4+ 3 + 2 = 9
Therefore, the commitment adherence percentage for the week will be:
= 9/17 × 100
= 53%
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Complete question :
Amy was scheduled to service 17 intervals this week. She picked up 4 more intervals during the week. On Friday, she put 3 intervals up for swap. One of them was picked up by someone else. The other two were not so she released them both during the lockdown period. Amy also had technical issues but never did get a waiver, which resulted in her missing an additional 2 intervals. What was her Commitment Adherence percentage for the week? Enter whole numbers (no decimals)
Simene wants to babysit this weekend to make some extra money. She charges a flat fee then charoes per hout (or part thereof) that she babysits. Saturday afternoon she will babysit for 5 hours. Vanables: f = flat fee m= money Constant: hours =6, Expression: f+6m She has to choose between two families to babysit for.The first family offers her $40 plus $ per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make?
Answers
She should take the offer from the second family as she will make $5 more.
How to calculate the value?First family offers her $40 plus $5 per hour. Therefore, the amount that she can make for 5 hours will be:
= $40 + 5($5)
= $40 + $25
= $65
The second family offers $20 plus $10 per hour. Therefore, the amount that will be made will be:
= $20 + $10(5)
= $70
Therefore, she should take the offer from the second family as she will make $5 more. This was calculated as $70 - $65 = $5.
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Solve the compound inequality.
Answers
The solution to the compound inequality is (-5, infinity) U (-8, infinity)
How to solve the compound inequality?The compound inequality is given as
3x + 2 > 2x - 3 > x - 11
Add 3 to all sides of the inequality
So, we have
3x + 5 > 2x > x - 8
Split the inequality
So, we have
3x + 5 > 2x and 2x > x - 8
Evaluate the like terms
x + 5 > 0 and x > - 8
This gives
x > -5 and x > - 8
As an interval notation, we have
(-5, infinity) U (-8, infinity)
Hence, the solution to the compound inequality is (-5, infinity) U (-8, infinity)
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Solve the given differential equation's particular solution when the curve passes through the point (a = 1, b = 1).
(b^2+7ab+16a^2)da+a^2db=0
Answers
The solution of the given differential equation is;
-1/(b/a + 4) = -㏑|a| - 1/5.
What is defined as the differential equation?A differential equation is a mathematical expression that contains one or even more functions and their derivatives. The function's derivatives characterize the rate of change in a function at a given point.The given differential equation is-
(b² + 7ab + 16a²)da + a²db = 0
Take da common from both;
b² + 7ab + 16a² + a²db/da = 0
The curve passes through the point (a = 1, b = 1).
As, the given differential eq is the homogeneous eq; we can use it as;
Put, b = va
Differentiate above applying product rule.
db/da = (dv/da)a + v
Substitute the value in the main equation;
(va)² + 7a(va) + 16a² + a²( (dv/da)a + v ) = 0
Dividing whole equation by a².
v² + 7v + 16 + (dv/da)a + v = 0
Further simplifying;
(dv/da)a = -(v² + 8v + 16)
(dv/da)a = -(v + 4)²
Bring similar variable together;
dv/(v + 4)² = -da/a
Integrating the equation;
-1/(v + 4) = -㏑|a| + C ; c is the integration constant.
Substitute again the values of v;
-1/(b/a + 4) = -㏑|a| + C ........equation 1
Now use the given points; a = 1; b = 1.
-1/(1/1 + 4) = -㏑|1| + C [㏑|1| = 0]
-1/5 = C
Put the value of C in equation 1.
-1/(b/a + 4) = -㏑|a| - 1/5; is the required differential equation.
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Determine whether
the graph below is that of a function by
using the vertical-line test. If it is, use the graph to find
(a) its domain and range.
(b) the intercepts, if any.
(c) any symmetry with respect to the x-axis, y-axis, or the
origin.
Answers
Answer:
• is the graph that of a function? yes
• the domain is [-π, π] and the range is [-1, 1]
• the intercepts are (π/2, 0), (-π/2, 0), (0, 1)
• determine if the graph is symmetrical: it is symmetrical with respect to the y-axis.
Yes, the graph shows a function.
The domain is [-π, π] and the range is [-1, 1]
The intercepts are (π/2, 0), (-π/2, 0), (0, 1)
It is symmetrical with respect to the y-axis.
We have to given that,
The graph of function is shown in image.
Since, A relation between a set of inputs having one output each is called a function. And, The set of all inputs of the function is called Domain of set.
Hence, By given graph,
It satisfy the vertical line test,
Hence, It shows function.
And, The domain is [-π, π] and the range is [-1, 1]
Here, Graph cut at points (π/2, 0), (-π/2, 0), (0, 1).
Hence, The intercepts are (π/2, 0), (-π/2, 0), (0, 1)
Now, From the graph,
It is symmetrical with respect to the y-axis.
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Previous Problem Problem List Next Problem
(1 point) Let f(z) be the function 10z²-9z+3. Then the quotient
f(4+h)-f(4)
can be simplified to ah + b for:
h. What is the value of a and b
Answers
The value obtained from the given function f(z) = 10z²-9z+3 are-
a = 10h.b = 71h.What defined as the quotient function?A quotient function is a function that consists of two functions isolated by a division sign.The domain of the quotient between two functions, f(x) and g(x), is A ∩ B ("A intersected with B" implies the set among all points that Both A and B have in common), excluding where g(x) = 0.In mathematics, a quotient is the result of dividing one number by another.For the given function;
f(z) = 10z²-9z+3.
The quotient is given as;
Quotient = f(4+h)-f(4)
Put the values (4 + h) and 4 at the place of z in the function.
f(4+h)-f(4) = 10(4 + h)² - 9(4 + h) + 3 -[10(4)² - 9(4) + 3)]
f(4+h)-f(4) = 10h² + 160 -9h + 80h + 3 - 160 + 36 - 3
Cancel the values;
f(4+h)-f(4) = 10h² + 80h - 9h
f(4+h)-f(4) = 10h² + 71h.
Thus, comparing the obtained equation by give form of (ah + b)
a = 10h and b = 71h.
Therefore, the obtained values for the given function f(z) is;
a = 10h and b = 71h.
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What is the difference between the length of the shortest movie and the length of the longest movie?