Answers
The simplified trigonometric expression is given as follows:
[tex]-sin{\theta}\tan{\theta}(1 - \csc{\theta})[/tex]
How to simplify the given trigonometric expression?The expression is given by:
[tex]\frac{\cos{\theta}}{1 + \csc{\theta}} \times \frac{1 - \csc{\theta}}{1 - \csc{\theta}}[/tex]
Applying the subtraction of perfect squares at the denominator, we have that the expression is given by:
[tex]\frac{\cos{\theta}(1 - \csc{\theta})}{1 - \csc^2{\theta}}[/tex]
Applying an identity, we have that:
[tex]1 - \csc^2{\theta} = -\cot^2{\theta}[/tex]
Hence the expression is:
[tex]-\frac{\cos{\theta}(1 - \csc{\theta})}{\cot^2{\theta}}[/tex]
cot = cos/sin, hence:
[tex]-\frac{sin^2{\theta}(1 - \csc{\theta})}{\cos{\theta}}[/tex]
tan = sin/cos, hence the simplified expression is:
[tex]-sin{\theta}\tan{\theta}(1 - \csc{\theta})[/tex]
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Related Questions
You want to put a 2 inch thick layer of topsoil for a new 20 ft by 24 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answers
3.0 CUBIC YARDS I WILL NEED TO ORDER TO PUT A 2 INCH THICK LAYER OF TOPSOIL
HOW TO FIND VOLUME OF SOIL ?As a result, the problem gives you the volume of the space you are trying to fill with soil ( 20ft by 24ft by 2 in). Let's measure everything in feet first, and then we can measure the volume in yards. You may acquire a volume of approximately (rounding to two decimal places)80.00 cubic feet by converting 2 inches to feet, or 2/12. Then, to obtain your volume, multiply that by 20 times 24. Since there are 3 feet in 1 yard, we divide this volume in yards by 3, giving us 3.0 cubic yards. You will need 3.0 cubic yards if the business only sells in 1/4 cubic yard increments.
CALCULATIONV = (20')(24')(2'/12)
V = 80f[tex]t^{3}[/tex]
1 [tex]yd^{3}[/tex] = 27 [tex]ft3[/tex]
80[tex]ft3[/tex] / 27[tex]ft3[/tex] ≈ 3.0
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1. |x - 7] + 8 < 11
How do u solve
Answers
The solution of the given inequality |x - 7| + 8 < 11 is 4 < x < 10.
What is meant by the term inequality?In mathematics, an inequality is an interaction between two expressions as well as values which are not equitable to each other. Inequality results from a lack of balance.
Rule 1: Once inequalities are linked, they can be crossed. As a result, if an is greater than b and b is greater than c, a will indeed be greater than c as well.If a > b > c, a > c, we can skip b and get to the relationship between a and c directly.Rule 2: When you swap the values, this same sign reverses.If p > q, then q < pIf p < q, then q > pAs per the given relation;
|x - 7| + 8 < 11
Subtract both side by -8.
|x - 7| + 8 - 8 < 11 - 8
|x - 7| < 3
Removing modulus will give the relation as;
- 3 < x - 7 < 3
Add 7 on both side.
- 3 + 7 < x - 7 + 7 < 3 + 7
4 < x < 10
Thus, the solution of the x lied between 4 and 10 with the condition that;
4 < x < 10.
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Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 1
(2) take the square root
(3) subtract 4
(4) divide into 7
Find an expression for f(x).
f(x) =
X
State the domain of f using interval notation.
Answers
Answer:
Expression for f(x) = [tex]\frac{\sqrt{x + 1} - 4}{7}[/tex]
Domain in interval notation: [tex]\:[-1,\:\infty \:)[/tex]
Step-by-step explanation:
[tex]\textrm{Let }f(x)\text{ represent the function}[/tex]
Step 1: Add 1 to [tex]x[/tex] ==> x + 1
Step 2: Take square root ==> [tex]\sqrt{x+1}[/tex]
Step 3: Subtract 4: ==> [tex]\sqrt{x+1} - 4[/tex]
Step 4: Divide by 7 ==> [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]
The expression for f(x) is [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]
The domain of a function is the set of all inputs for which the function is real and defined
[tex]\sqrt{x+1}[/tex] is real only for positive values of the square root
This means
[tex]\sqrt{x+1} \ge 0[/tex]
Squaring both sides we get
[tex]x + 1 \ge 0[/tex]
Subtracting 1 from both sides we get
[tex]x \ge -1[/tex]
This is the lower limit for [tex]x.[/tex] There is no upper limit
The domain of[tex]f(x)[/tex] is therefore
[tex]x \ge -1[/tex]
In interval notation it is expressed as
[tex][-1,\infty)[/tex]
Note the square bracket on the left and parenthesis on the right. This notation means that -1 is part of the domain but [tex]\infty[/tex] is not included since at [tex]\infty[/tex] the function is not defined
Jill and Frank decided to take a long weekend in New York. City Hotel has a special getaway weekend for $79.95. The price is per
person per night, based on double occupancy. The hotel has a minimum two-night stay. For this price, Jill and Frank will receive $50
credit toward their dinners at City's Skylight Restaurant. Also included in the package is a $3.99 credit per person toward breakfast for
two each morning.
Since Jill and Frank do not own a car, they plan to rent a car. The car rental agency charges $19.95 a day with an additional charge of
$.22 a mile and $1.19 per gallon of gas used. The gas tank holds 24 gallons.
From the following facts, calculate the total expenses of Jill and Frank (round all answers to nearest hundredth or cent as appropriate).
Assume no taxes.
Answers
Answer:
$560.33
Step-by-step explanation:
Hotel: 79.95*2*2=$319.8
Dinner: 182-50=$132
Breakfast:
24.17+26.88=$51.0551.05-3.99*4=$35.09Rental:
19.95*2=$39.94940-4820=120 120*0.22=$26.41/2=2/4 3/4-2/4=1/4 ---> so they used 1/4 of the tank which is 1/4*24=6 6*1.19=$7.1439.9+26.4+7.14=$73.44Hotel+dinner+breakfast+rental: 319.8+132+35.09+73.44=$560.33
If a driver uses 1/ 10 of gas every day what fraction of a tank will he use in 3 days.
Answers
Answer:
3/10
Step-by-step explanation:
it is really simple just do 1/10+1/10+1/10=3/10
Helpppp pls now asap
Answers
18+6/3•2
Ik it’s easy
Answers
Answer:
4
Step-by-step explanation:
First let's begin at the top of the fraction, 18+6
18+6
24
Now let's look at the bottom of the fraction, 3*2
3*2
6
We now have 24/6, so we will simplify the fraction to get our answer by dividing 24 by 6
24/6
4
15. The weight of a trout varies jointly as its length and the square of its girth. One angler
caught a trout that weighed 10.5 pounds and measured 26 inches long with an 18-inch
girth. Find the weight of a trout that is 22 inches long with a 15-inch girth. (Girth is the
distance around the body of a fish.)
Answers
The weight of the trout is 6.17 pounds.
How to find the weight of the trout?
We know that the weight of a trout varies jointly as its length and the square of its girth.
If W is the weight, x is the length and y is the girth, then:
W = k*x*y^2
Where k is a constant.
We know that one trout with:
x = 26 in
y = 18in
Has a weight of 10.5, then we can write:
10.5 = k*(26)*(18)^2 = k*8,424
Solving for k we get:
10.5/8,424 = k
Then the equation is:
W = (10.5/8,424)*x*y^2
Now, our trout has:
x = 22 in
y = 15 in
Then the weight is:
W = (10.5/8,424)*22*15^2 = 6.17
The weight of the trout is 6.17 pounds.
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what is the limit of the equation?
Answers
answer:
[tex] \frac{6}{5} [/tex]
solve the quadratic equation
Make sure the equations equal 0
4w^2 - 42w + 20 = 0
PLEASE SHOW YOUR WORK!
Answers
Answer:
hello! it's all explained in the photo :)
Step-by-step explanation:
write a number to represent the situation: A withdrawal of $36
Answers
The number which represents the situation of a withdrawal of $36 is -$36.
In this question, we have to find out the number or integer which represents the situation of a withdrawal of $36. This question is from integers topic and for that we should have the definition of integers in our mind. So, an integer is defined as number which can be represented without the fractional form. It contains whole numbers and negative of natural numbers. The integers are generally denoted by the symbol 'Ζ'. And, the integers can be negative or positive.
In this question we have asked withdrawal of $36 from any source. So, withdrawal basically means money will decrease, so it will become negative.
To represent a withdrawal of $36, we will use the negative sign.
Hence, -$36 is the correct representation of the situation of a withdrawal of $36.
Therefore, -$36 is the required answer.
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Which two inequalities can be used to find the solution to this absolute value inequality?
Answers
The two inequalities that can be used to find the solution are x-1 < 3 and x-1 > -3.
The given inequality is 3 + 2|x-1| < 9.
The absolute value |x-1| can be (x-1) or -(x-1).
We need to solve this inequality for this two cases.
So first if |x-1| = (x-1), then,
3 + 2|x-1| < 9
⇒ 3 + 2(x-1) < 9
⇒ 2(x-1) < 6
⇒ x-1 < 3
⇒ x < 4 is the solution.
Now if |x-1| = -(x-1), then,
3 + 2|x-1| < 9
⇒ 3 - 2(x-1) < 9
⇒ -2(x-1) < 6
⇒ -(x-1) < 3
⇒ x-1 > -3 [When multiplied with (-1), the inequality reverses]
⇒ x > -2 is the solution.
Going through these steps, we can conclude that the two inequalities that can be used to find the solution to the absolute value inequality,
3 + 2|x-1| < 9 are x-1 < 3 and x-1 > -3.
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Use the tests for divisibility to determine which numbers divide evenly into the given number.
648
Answers
The numbers that can divide 648 evenly, using the divisibility tests, include 1, 2, 3, 4, 6, 8, 9, 12, and 18 and some multiples of any two numbers.
What is the divisibility test?A divisibility test is performed to identify whether a number can be divided evenly by a fixed divisor without a remainder and without actually performing the division process.
Divisibility by 1: Every number is divisible by 1 = 648 (648/1).
Divisibility by 2: 648 is an even number and divisible by 2 = 324.
Divisibility by 3: Sum the digits (18). 18 is divisible by 3 = 6 (18/3).
Divisibility by 4: The last two digits (4 and 8) form a number (12) that is divisible by 4
Divisibility by 6: It is divisible by 2 and by 3
Divisibility by 8: If the hundreds digit is even, the number formed by the last two digits must be divisible by 8.
Divisibility by 9: Sum the digits (18). 18 is divisible by 9
Divisibility by 12: 648 is divisible by 3 and by 4.
Divisibility by 18: 648 is divisible by 2 and by 9.
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Which of the following does not describe a rigid motion transformation?
Answers
Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.
What is meant by the term rigid motion transformation?The term rigid motion transformation has to do with the fact that when an object is moved the size and the shape of the object would still have to stay the same. This is different for the non rigid motion. This because the size and the shape would have to increase in this case.
When the object is moved from one area to the other and it remains the same then we would have to say that the rigid transformation has occurred.
Hence we would have to say that Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.
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Felicia decided to invest $17,000 of her retirement fund
Answers
Simplify negative three fifths times m times quantity negative two sevenths times m minus one fourth end quantity.
A: 6 over 35 times m squared plus 3 over 20 times m
B: negative 6 over 35 times m squared minus 3 over 20 times m
C: 6 over 35 times m squared plus one fourth
D: negative 6 over 35 times m squared plus 3 over 20 times m
Answers
The required simplified value of the given expression is 6 / 35m² - 1/4. Option C is correct.
To determine the simplified value of the negative three-fifths times m times quantity negative two-sevenths times m minus one-fourth end quantity.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
negative three-fifths times m times quantity negative two-sevenths times m minus one-fourth can be interpreted as,
= -3/5m * - 2/7m - 1/4
= 6 / 35m² - 1/4
Thus, the required simplified value of the given expression is 6 / 35m² - 1/4. Option C is correct.
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Can someone provide an example and counter example of a function ?
Answers
An example of a function is: The area of a square is a always a function of the length and width.
A counterexample of the function is: The area of a square is a function of the diagonal.
What is a function?This a term used in mathematics to represent a mathematical relations. This is usually of three parts: the inputs, the output, and the relationship between them.
In the example the sides of the square is the input, the area is the output while the formula is the relationship.
what is a counter example?Counter example is used to show a flaw in a mathematical statement where the conclusion is not in agreement with the statement.
In the given example providing a method of calculating area of squares using the diagonals counters the initial statement that has it that area of a square is a always a function of the length and width.
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What number is 56.5 % of 305
Answers
Answer:
172.63
Step-by-step explanation:
First let's write the problem as an expression
56.6% * 305
Let's convert 56.6 to a decimal
0.566% * 305
Now finish by multiplying
0.566% * 305
172.63
The difference between two numbers is 69. Four times the smaller is equal to 3 more than the larger. What are the numbers?
Answers
smaller number = y
larger number = x
x - y = 69
4y = x + 3
you can solve this using substitution
x = 69 + y
(isolating one of the variables)
4y = 69 + y + 3
(substituting 69 + y for x into the other equation)
4y = 72 + y
3y = 72
y = 24
(simplify)
x - 24 = 69
x = 93
(substituting 24 into one of the original equations)
Greg must choose a number between 67 and 113 that is a multiple 4,6 of and 9 . Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Answers
A number between 67 and 113 which is a multiple 4, 6 and 9 is 108
In this question, Greg must choose a number between 67 and 113 that is a multiple 4, 6 and 9.
We need to find the numbers which follow above conditions.
First we find the numbers between 67 and 113 that is a multiple 4.
68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112
the numbers between 67 and 113 that is a multiple 6 are:
72, 78, 84, 90, 96, 102, 108
the numbers between 67 and 113 that is a multiple 9 are:
72, 81, 90, 99, 108
We can observe that a common number between 67 and 113 which is a multiple 4, 6 and 9 is 108
Therefore, a number between 67 and 113 which is a multiple 4, 6 and 9 is 108
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square root of 36/9 help please!
Answers
Answer: 2
Step-by-step explanation:
[tex]\sqrt{\frac{36}{9} }[/tex]=
[tex]\frac{\sqrt{36}}{\sqrt{9}}[/tex]=
6/3=2
The answer is 2. I have no explanation because I searched it up at a website.
x+[tex]\sqrt{x}[/tex]x=90
Answers
Answer:
x=3 and her is right
Answer whyyyy
Step-by-step explanation:
A daily newspaper has a circulation of 3679000 copies per day. If 1 days papers are distributed evenly among 13 cities, how many copies would each city recipe?
Answers
283,000 newspaper copies will be distributed among the 13 cities evenly.
How is simple division calculation done?Out of the four basic mathematical operations, division is frequently regarded as the most challenging. Once we fully comprehend the procedure and guidelines, we can use a calculator without error to perform increasingly challenging calculations.
We can divide or "share" numbers using division to arrive at an answer. Take 10 ÷ 2 as an example. How would we arrive at the solution? (ten divided by two). This is equivalent to "sharing" 10 candies between 2 kids. The total quantity of candies that each child receives must be the same. The solution in this instance is 5.
No. of newspaper circulated a day = 3,679,000
No. of cities to be distributes among = 13
No. of newspaper a city will receive = 3,679,000/ 13
= 283,000
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I don't really understand this, how to set it up etc and i cant figure out how to get the actual answer. Im sorry i make no sense
Answers
Answer:
i also can't at all
Step-by-step explanation:
This is hard for me
The stemplot displays 26 students’ scores on a 90-point statistics test.
A stemplot titled Test scores has values 43, 45, 46, 51, 52, 53, 55, 57, 60, 63, 63, 65, 66, 67, 67, 69, 69, 71, 71, 72, 74, 76, 77, 79, 84, 85.
Which of the following best describes the center and variability of the distribution?
The scores on the test are centered around 63 and vary from 45 to 85.
The scores on the test are centered around 66 and vary from 43 to 85.
The scores on the test are centered around 66 and vary from 40 to 80.
The scores on the test are centered around 69 and vary from 45 to 85.
Answers
Answer:
The answer is B
Step-by-step explanation:
Just look at the numbers, that is the only one with the correct range.
The scores on the test are centered around 66 and vary from 43 to 85. Therefore, the correct option is option B.
What is mathematical distribution?
Distributions are objects that generalise the traditional idea of functions used for mathematical analysis. They are often referred to as Schwartz distributions or generalised functions. Functions with no classically defined derivatives can be distinguished using distributions.
In the theory of partial differential equations, distributions are frequently utilised because it may be simpler to prove the existence of distributional solutions (weak solutions) rather classical solutions or because there may not be any suitable classical solutions. The scores on the test are centered around 66 and vary from 43 to 85.
Therefore, the correct option is option B.
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Find an expression which represents the sum of (-9x + 3y) and (-3x + 5y) in simplest terms.
Answers
Answer: -12x+8y
Step-by-step explanation:
Based on the given conditions, formulate: (-9x+3y)+(-3x+5y)
Determine the sign: -9x+3y-3x+5Y
Combine like terms: -12x+8y
help me please help helpfnfbdbdbdbdbdb
Answers
Answer: The location of P is -9
Step-by-step explanation:
90 items to ship full case and 8 items per case
Answers
Answer:
That means you would only be able to fit 11 cases since 8 × 11 = 88. Any more cases would exceed 90 items.
Step-by-step explanation:
PV = nRT Solve for R
Answers
Answer: R=PV/nT
Step-by-step explanation:
PV=nRT
divide both sides by nT
PV/nT =nRT/nT
R=PV/nT
i hope this was helpful
The given equation solved for R has R=PV/nT.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is PV=nRT.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, R=PV/nT
Therefore, the given equation solved for R has R=PV/nT.
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Winter Fun Ski Resort sells only 2 types of tickets - adult and student. On Monday, the resort sold 200 tickets. The price of an adult ticket is $50 and the price of a student ticket is $25. How many adult and student tickets were sold on Monday?
Answers
Answer:
Step-by-step explanation: you have to tell us how much money was made in order to find out how many of each