Part 1: Simplify each expression.
Use the trigonometric identities to simplify each expression.
Answers
Answer:
\(\cos ^2\left(x\right)\)
Step-by-step explanation:
You will need to apply some basic trig identities here:
\(\sec ^2\left(\frac{\pi }{2}-x\right) \\\\=> \frac{1}{\cos ^2\left(\frac{\pi }{2}-x\right)}\\\\=> \frac{1}{\sin ^2\left(x\right)}\)
Now we substitute this value back into the given equation:
\(\left(\frac{1}{\sin \left(x\right)}\right)^2\left(\sin ^2\left(x\right)-\sin ^4\left(x\right)\right)\\\\=> \frac{1\cdot \left(\sin ^2\left(x\right)-\sin ^4\left(x\right)\right)}{\sin ^2\left(x\right)}\\\\=> \frac{\sin ^2\left(x\right)-\sin ^4\left(x\right)}{\sin ^2\left(x\right)}\\\\=> \frac{\sin ^2\left(x\right)\left(1-\sin ^2\left(x\right)\right)}{\sin ^2\left(x\right)}\\\\=> 1-\sin ^2\left(x\right)\\\\=> \cos ^2\left(x\right)\)
Hope that helps!
Related Questions
which of the ratios below is equivalent to 8:5? Select all that apply
Answers
\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the Ratio and Proportions.
Thus the equivalent ratio to 8:5 will be,
24:15 , 40:25 and 16:10
because, here if we reduce by common multiple 24:15 , 40:25 and 16:10 both , we will get as 8:5
so the correct answer is c.) 40:25 and e.) 16:10 b.) 24:15
Select all ratios equivalent to 1:2
Step-by-step explanation:
Jughead now earns $10.50 per hour. This is 175% of what he earned last year. How much did he earn last year?
Answers
Answer:
10.5/175*100=6
Step-by-step explanation:
What is the equation in vertex form of the quadratic function with a vertex at (-1,-4) that goes through (1,8)?
Answers
Answer:
G
Step-by-step explanation:
vertex formula = a(x-h)^2 + k
vertex is (h, k) so (-1, -4) means
y = a(x+1)^2-4
passes through (1, 8) so when x = 1 and y = 8
8 = a(1+1)^2-4 = 4a - 4
4a = 4
a = 1
The area of a sector of a circle with a radius measuring 15 cm is 75(pi) cm2. What is the measure of the central angle that forms the
sector?
Answers
The sector of the circle is bounded by 2 radii, and the measure of the central angle that forms the sector is 120 degrees
How to determine the central angle?The given parameters are:
Area = 75π cm^2Radius, r = 15 cmThe area is calculated using
Area = α/360 * πr^2
So, we have:
α/360 * π * 15^2 = 75π
Evaluate the exponent
α/360 * π * 225 = 75π
Divide both sides by 75π
α/360 * 3 = 1
Multiply
α/120 = 1
Multiply both sides by 120
α = 120
Hence, the measure of the central angle that forms the sector is 120 degrees
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Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?
Answer: In total the three teams have won
Optional working
games
Answers
Answer:
38
Step-by-step explanation:
:) hope this helps
What percent of 1800 is 36
Answers
Answer: 2
Step-by-step explanation:
Answer:
2
Step by step explanation:
Which of the following is a counterexample to the given statement?
The name of every month ends in the letter y.
a. January
b. July
C February
d. December
Answers
The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right option is (c) February.
What is a counterexample?
In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.
Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."
Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.
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use differentials to estimate the value of 1.2−−−√4. compare the answer to the exact value of 1.2−−−√4 .
Answers
To use differentials to estimate the value of 1.2√4, we need to first find a suitable function and a point close to the one we want to estimate. Since we are dealing with square roots, we can use the function f(x) = √x. The point closest to 4.2 (1.2 added to 4) that we know the exact value for is 4, as √4 = 2.
1. Find the derivative of f(x) = √x:
f'(x) = (1/2)x^(-1/2)
2. Evaluate the derivative at the known point, x = 4:
f'(4) = (1/2)(4)^(-1/2) = (1/2)(2)^(-1) = 1/4
3. Compute the differential, using Δx = 0.2 (the difference between 4.2 and 4):
Δy = f'(4)Δx = (1/4)(0.2) = 0.05
4. Estimate the value of 1.2√4 by adding Δy to the exact value at x = 4:
1.2√4 ≈ 2 + 0.05 = 2.05
Now, let's compare this to the exact value of 1.2√4:
Exact value: 1.2√4 = 1.2(√4.2) ≈ 1.2(2.0494) ≈ 2.0593
The estimated value using differentials is 2.05, while the exact value is approximately 2.0593. The two values are relatively close, demonstrating the effectiveness of using differentials for estimation.
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Solve for x in the diagram below.
Answers
Answer:
77
Step-by-step explanation:
why because 100+3=103
and this is half a circle so the answer is 180-103 that is 77
Answer:
x = 20°Step-by-step explanation:
From the question it can be seen that all the angles lie on a straight line and
Angles on a straight line add up to 180°
To solve for x add up all the angles and equate them to 180°
That's
x + 3x + 100 = 180
4x + 100 = 180
Subtract 100 from both sides
4x + 100 - 100 = 180 - 100
4x = 80
Divide both sides by 4
We have
\( \frac{4x}{4} = \frac{80}{4} \)We have the final answer as
x = 20°Hope this helps you
can the method of equivalent pipes be used to find a single hypothetical pipe that is equivalent to the pipe system of problem 3.12.6? if your answer is yes, determine an equivalent pipe. if your answer is no, explain your answer.
Answers
No, the method of equivalent pipes cannot be used to find a single hypothetical pipe that is equivalent to the pipe system of problem 3.12.6.
This is because the method of equivalent pipes is used to combine two or more pipes into one pipe to simplify a system. In problem 3.12.6, the given system already consists of only one pipe. Therefore, it is not possible to use the method of equivalent pipes to determine an equivalent pipe.The method of equivalent pipes is used to calculate the head losses for a system of pipes with multiple branches and junctions, using the Loss Coefficient Method and Hazen-Williams Equation. The method of equivalent pipes allows us to convert a complex pipe network into an equivalent pipe with a single diameter and length. However, this method cannot be used for a pipe system with no branches and junctions, such as the one in problem 3.12.6.
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The diameter of a healthy human red blood cell is about 0.007 millimeter. How is this number written in scientific notation?
(A) -7 X 10³
(B) 7 x 10‐³
(C) 7 X 10‐²
(D)7 X 10³
Answers
Answer:
(B) 7 x 10‐³
Step-by-step explanation:
A typical red blood cell in human blood has a diameter of approximately 0.007 mm.
In scientific form = 7 x 10-^3
Determine the time taken when distance is 7150km and the speed is 780 km/hr
Answers
Answer:
denote the time by T , distance by S , and the speed by V. We have that S = 7150km, V = 780 km/hr , T= ?.. T = S:V = 7150 : 780 = 9.17
Answer is T = 9.17 hour
equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)
Answers
The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).
Equation of a circle
A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.
We know that,
Equation of the circle passing through the origin is given by:-
\(x^2+y^2=r^2\)
Where,
r is the radius of the circle, and
(x,y) are the coordinates of each point of the circle.
Hence, we can write,
The radius of the circle will be :-
\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)
Hence, r = 4 units.
Hence, the equation of the circle is given by:-
\(x^2+y^2=16\)
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HELP DUE IN 15 MINS!
Quadrilateral ABCD has vertices A(1, 3), B(2, 0), C(5, 1), and D(4, 4). Find the lengths and slopes of the diagonals. Then classify ABCD. Round answers to the nearest tenth.
1. Length of AC =??
2. Length of DB =??
3. Slope of AC =??
4. Slope of DB =??
5. Classification: Rhombus, Trapezoid, Parallelogram, Isosceles Trapezoid, Rectangle, Kite, Square.
Answers
Answer:
Length of AC = 4.5
Length of DB = 4.5
Slope of AC = \(-\frac{1}{2}\)
Slope of DB = 2
Classification: Square
Hope this helps!
In the figure shown, lines f and g are parallel. Select all angles that are congruent to angle 1.
Answers
\(\\ \sf\longmapsto <1\sim <4(Opposite\:angles)\)
\(\\ \sf\longmapsto <1\sim <5(corresponding \:interior\:angles)\)
\(\\ \sf\longmapsto <1\sim <8(<5\sim <8)\)
Answer:
Step-by-step explanation:
∠1 = ∠4 {Vertically opposite angles}
∠1 = ∠5 {Corresponding angles}
∠1 = ∠8 {Alternate exterior angles}
h(x) = 3x - 5
g(x) = x² - x
Find (h · g)(x)
Answers
Answer: 5/3x
Step-by-step explanation:
add 5 to both sides and divide by 3
How do you know if a function is exponential decay?
Answers
The general form of an exponential decay function is f(a) = P . (1 - r)ᵃ, hence a function is an exponential decay if the factor (1 - r) is less than 1.
The general exponential decay function can be written as:
f(a) = P . (1 - r)ᵃ
Where:
P = initial quantity
f(a) = remaining quantity at time a
a = time period
r = decay rate
(1 - r) = decay factor
On the other hand, the general exponential growth function can be written as:
f(a) = P . (1 + r)ᵃ
Hence, the difference between decay function and growth function is: the factor in decay faction is less than 1, while in growth function, the factor is greater than 1.
Example:
f(a) = 6 . (0.25)ᵃ
This is an exponential decay function because the factor is less than 1, that is 0.25
f(a) = 10 . (3)ᵃ
This is not an exponential decay function, but a growth function, because the factor is greater than 1, that is 3
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which of the following is equivalent to ^3sqrt(4k^2) * ^3sqrt(6jk)
Answers
Explanation
We are asked to find the equivalent of
\(\sqrt[3]{4k^2}.\sqrt[3]{6jk}\)To do so, we will have
\(\begin{gathered} \sqrt[3]{4\times6\times j\times k^2\times k} \\ \\ =\sqrt[3]{24jk^3} \\ \\ =2k\sqrt[3]{3j} \end{gathered}\)Therefore, the answer is
\(undefined\)The goal of building one-to-many relationships between tables is to minimize _____ data. A. misspelled B. rarely used C. numeric D. redundant
Answers
The goal of building one-to-many relationships between tables is to minimize redundant data.
Data redundancy is a regular occurrence in many businesses and occurs when an identical piece of data is stored in two or more different locations. As more businesses switch from using segregated data to a central repository, they discover that their database is full of inconsistent duplicates of the same entry. Understanding how to effectively manage and track data redundancy can help your business avoid long-term inconsistency problems, even though it can be difficult to reconcile — or even benefit from — redundant data entries.
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The goal of building one-to-many relationships between tables is to minimize redundant data.
Redundant data refers to data that is duplicated across multiple tables, which can lead to data inconsistencies and
increase the amount of storage space required.
By creating one-to-many relationships between tables, data is only stored once in the database, and each instance of
the data in other tables refer back to the original source, reducing the need for redundant data storage.
Therefore, The goal of building one-to-many relationships between tables is to minimize redundant data.
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Design DFA {w ∈ Σ ∗ | number of 0’s in w is a multiple of 3 and number of 1’s in w is odd }.
Answers
The resulting DFA will have four states (A, B, C, D) and transitions defined as described above. State D will be the only final state.
To design a DFA that accepts strings where the number of 0's is a multiple of 3 and the number of 1's is odd, we can follow these steps:
1. Define the DFA states:
- We need to keep track of two things: the count of 0's (mod 3) and whether the count of 1's is odd or even.
- Let's define four states: A, B, C, and D.
- State A represents the initial state with a count of 0's = 0 and an even count of 1's.
- State B represents a count of 0's = 1 (mod 3) and an even count of 1's.
- State C represents a count of 0's = 2 (mod 3) and an even count of 1's.
- State D represents any count of 0's (mod 3) and an odd count of 1's.
2. Define the transitions:
- From state A, if we read a 0, we transition to state B (count of 0's = 1 (mod 3)).
- From state A, if we read a 1, we transition to state D (odd count of 1's).
- From state B, if we read a 0, we transition to state C (count of 0's = 2 (mod 3)).
- From state B, if we read a 1, we transition to state D (odd count of 1's).
- From state C, if we read a 0, we transition to state A (count of 0's = 0 (mod 3)).
- From state C, if we read a 1, we transition to state D (odd count of 1's).
- From state D, if we read either a 0 or a 1, we stay in state D.
3. Define the final (accepting) state:
- State D is the final state since it represents the condition of having a count of 0's (mod 3) and an odd count of 1's.
The resulting DFA will have four states (A, B, C, D) and transitions defined as described above. State D will be the only final state.
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Complete question is below
Design DFA {w | w ∈ Σ ∗ | number of 0’s in w is a multiple of 3 and number of 1’s in w is odd }.
Ktkrk rj. Rj4k4k4k krk4ke3k rk3k Ijjkhtjrkrkrnemek3
Answers
what's the question though
Models of inventory systems frequently consider the relationships among a beginning inventory,
a production quantity, a demand or sales, and an ending inventory. For a given
production period j, let
sj-1 = ending inventory from the previous period (beginning inventory for period j)
xj = production quantity in period j
dj = demand in period j
sj = ending inventory for period j
a. Write the mathematical relationship or model that shows ending inventory as a function
of beginning inventory, production, and demand.
b. What constraint should be added if production capacity for period j is given by Cj?
c. What constraint should be added if inventory requirements for period j mandate an
ending inventory of at least Ij?
Answers
a. This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
a. The mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand can be represented as:
sj = sj-1 + xj - dj
This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. If the production capacity for period j is given by Cj, the constraint that should be added is:
xj ≤ Cj
This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. If inventory requirements for period j mandate an ending inventory of at least Ij, the constraint that should be added is:
sj ≥ Ij
This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
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What does negative 9 plus negative 1 and negative 9 times negative 1 equal
Answers
The expression "negative 9 plus negative 1" simplifies to "-10" and the expression "negative 9 times negative 1" simplifies to "9".
In mathematics, when we add two negative numbers, we combine their magnitudes and assign the resulting sum a negative sign. In this case, "-9" plus "-1" equals "-10". When we multiply two negative numbers, the product is positive. Therefore, "-9" times "-1" equals "9". For the expression "negative 9 plus negative 1", we can think of it as subtracting 1 from 9. Since both numbers have a negative sign, their sum will be negative, and the magnitude of the result will be the difference between the magnitudes of the two numbers. In this case, 9 minus 1 equals 8, so the answer is "-10". In the expression "negative 9 times negative 1", we multiply the magnitudes of the two numbers, which are both 9 and 1, respectively. Since both numbers have a negative sign, the product will be positive. Therefore, "-9" times "-1" simplifies to "9".
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Can someone please help me answer this math problem?
Answers
Answer:
50%
Step-by-step explanation:
% increase=increase/ original x 100
increase=end weight-initial weight
=10.2-6.8
=3.4
original=6.8
increase=3.4/6.8 x100
=50
therefore there is a 50% increase?
use the discriminant to determine how many real zeros the quadratic will have. = 5^2− 7 − 6
Answers
Answer:
2
Step-by-step explanation:
f(x) = 5x²− 7x − 6
5x²− 7x − 6 = 0
a = 5, b = -7 , c = -6
the discriminant : D = b²-4ac
=> D = (-7)²-4(5)(-6)
= 49 + 120
= 169
D possitive, it has 2 real zeros
Answer:
2 real zeros seems to be correct
Step-by-step explanation:
just wanted to confirm the finding graphically. give him the brainliest not me
60.5/100 if the denominator is 100 and nominator is 60.5 what is percentage?
Answers
Describe the DOMAIN with Words
Describe the domain of the relationship shown here.
Answers
Answer:
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In other words, the domain of f is the set of real number R (and its set of possible outputs or codomain is also the set of real numbers R)
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Bill makes 30 flags in 3 3/4 hours.
How many flags can he make in 1 hour?
Answers
What is a billion billion in exponential notation.
Answers
Answer:
Step-by-step explanation:
The number of lines that can be drawn perpendicular to a given line at a given point on that line in
space is:
A. not enough information
B. infinitely many
C. 3
D. 0
Answers
The number of lines that can be drawn perpendicular to a given line at a given point in space is infinitely many.The correct answer is option B.
This is a fundamental property of Euclidean geometry.
In three-dimensional space, any line can have an infinite number of lines that are perpendicular to it. This is because for any given line, we can imagine an infinite number of planes that contain the given line and are perpendicular to it.
Each of these planes intersects the given line at a unique point, and from that point, an infinite number of lines can be drawn perpendicular to the given line within the plane.
Therefore, the correct answer is B. infinitely many.
It is important to note that this answer is based on the principles of Euclidean geometry and assumes a standard geometric setting. If the question is referring to a different type of geometry or a specific context that imposes restrictions on the number of perpendicular lines, then the answer may vary.
However, in the absence of such information, the answer remains infinitely many.
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