Step-by-step explanation:
You want to demonstrate the identity ...
(1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)
Working with the left side, we have ...
[tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]
__
Additional comment
The referenced identities are ...
tan = sin/cos
cos² = 1 -sin²
and the factorization of the difference of squares:
a² -b² = (a +b)(a -b).
A water tank discharges at the rate of 80 L/min. How long would it take to
discharge 4800 L?
Step-by-step explanation:
so, 80 L can get out of the tank every minute.
how long for 4800 L ?
that simply means "how many minutes for 4800 L ?"
and this we get by dividing 4800 by 80 (to see how often 80 fits into 4800) :
4800 / 80 = 60 minutes
so, it takes 60 minutes or 1 hour to discharge 4800 L.
When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee 14 cups = 1 qt2. how many kg of coffee are required to produce 200 cups of coffee?
1.738 kg of coffee are required to produce 200 cups of coffee.
What is Proportion?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.
Now it is given that,
1 pound of coffee yield 50 cups.
Since 1 pound = 0.4535 kg
Therefore, 0.4535 kg of coffee yield 50 cups.
Let x be the kgs of coffee that yields 200 cups of coffee.
Thus by proportion we can write,
0.4345 / 50 = x / 200
By cross multiplication we get,
50 x = 0.4345 * 200
⇒ 50x = 86.9
⇒ x = 86.9 / 50
⇒ x = 1.738 kgs
which is the required amount of coffee need to yield 200 cups.
Thus, 1.738 kg of coffee are required to produce 200 cups of coffee.
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The graph shows the percentage of garbage that was recycled between 1991 and
2013
Answer:
Step-by-step explanation:
the amount of garbage started to increase around 2005 or 2007
Just plot a point anywhere they graph is straight
For the following relation, provide the domain and range.
Domain: [A, B] Range: [C, D]
A=
B=
C=
D=
Answer:
Domain: [-4,2]
Range: [-3,3]
Step-by-step explanation:
A = -4
B = 2
C = -3
D = 3
the image i attached is the question
Answer:
D
Step-by-step explanation:
Solve for X:
3x-8≥7
3x≥15
x≥5
Any value of x is greater than or equal to 5
This is represented by answer D
whats 9 and 4 exponent time negative 1/3 and 4 exponent?
1. 1.371742E−3
2. 256 .
What is an Exponent?
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2³) means: 2 x 2 x 2 = 8.
It is written as a small number to the right and above the base number.
Here in the question we find out (9)∧-3 and (4)∧4
1. (9)∧-3 =x∧n=9−1
x∧n=9-³
=1/9³
=1/9×9×9
=1/729
=0.0013717421124829
=1.371742E−3
2. (4)∧4 =x∧n=4∧4
=4×4×4×4
=256
The meaning of exponent is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.
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Is the statement the solution set of a linear system involving variables is a list of numbers that makes each equation in the system a true statement when the values are substituted for respectively true or false? explain.
False, because The singles answer fits the description. All potential solutions are included in the solution set.
There might not be a solution to a set of linear equations that makes sense. False. There is at least one answer for a consistent system.What makes up a linear system's solution set?
The answer to a system of equations is a set of values for a variable that concurrently satisfy each equation. Finding every feasible combination of the variable values that make up the system's solutions is necessary to solve an equation system.Is it true that a linear system's existence and uniqueness are two key issues? False or true?
In a linear system, existence and uniqueness are crucial considerations. Both conceptually and practically, it is frequently essential to know whether a system has a solution (exists) and, if it does, whether this solution is the only one available (uniqueness).Learn more about linear system.
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it's me again can someone solve this question i'm really bad at fractions
Answer:
it would be A since the plus sign is canceled by the minus sign for the equation.
How to right 730,812 in word form
Step-by-step explanation:
seven-hundred thirty thousand eight-hundred twelve
Is the graph increasing, decreasing, or constant?
O A. Increasing
• B. Decreasing
C. Constant
Answer:
b decreasing its korrect now
If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, measure of angle 1 = 133 degrees, find the measures of angle 2 and angle 3
If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, The measure of ∠2 = 47° and ∠3 = 133°.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are supplementary angles as the total of these two angles is 180°. The sum of complimentary angles is 90 degrees.
Given,
the measure of angle 1 = 133°
As, ∠1 + ∠2 are supplementary angles,
⇒ ∠1 + ∠2 = 180° ......(1)
∠2 + ∠3 are supplementary angles,
⇒ ∠2 + ∠3 = 180° .......(2)
From (1),
⇒ 133° + ∠2 = 180°
⇒ ∠2 = 47°
From (2),
47° + ∠3 = 180°
∠3 = 133°
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Evan wants to leave an 18% tip for the server at a restaurant. Which expression does not show how to calculate the tip if b is the total bill?
Answer:
(b*.18)
Step-by-step explanation:
In terms of tips, 18% of $1.00 is $0.18. So for every dollar in the total (b) we can assume that it is going to be 18% of the overall total. 18% is 18/100 or .18, so we know the tip will be .18 of b (b*.18).
Answer:
7 major of system units defination and function
[tex]y \geq \frac{1}{3}x+4\\[/tex]
In linear equation, y ≥ x + 12/3 is simple version .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.y ≥ 1/3 x + 4
y ≥ x/3 + 4
y ≥ x + 12/3
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The endpoint of the line segment is (4,6) and (-6,2). Point G divides the segment into two equal parts?
What are the coordinates of point of G?
Answer:
G = (-1,4)
I drew it and work it out tho
PLS HELPPP ive been stuck on this for so long
Answer:
1. 15.17ft 2. 18.57ft 3. 22.41%
Step-by-step explanation:
1. What was the length of one side of the garage originally?
Area of a square = s × s which is also equal to s²
s means one side of the square, as it is a square, all sides are equal.
so
230 = s²
s = √230 = 15.17
2. What is the length of one side of the garage now?
The original area of the garage was 230ft²
But now, the area has increased by 50%
Increased Area = 230 × 50% = 115ft²
Total Area = 230 + 115 = 345ft²
In the question, they are saying that after the area is increased, the garage is still a square which means that the side lengths have equal values.
Area = s²
345 = s²
s = √345 = 18.57
3. What was the percentage increase of the length of one side?
Length : Percentage
15.17 : 100
18.57 : x
When the length of one side was 15.17, the percentage was 100% as that is what the original length was, we can use ratio and proportion to find what the percentage will be when the length is 18.57.
Now cross multiply
18.57 × 100 = 15.17x
1857 = 15.17x
1857/15.17 = x
x = 122. 41
The new percentage is 122.41%
The difference between both percentages is:
122.41 - 100 = 22.41
And 22.41 is the percentage increase.
Find all the integer solutions of each system of inequalities {y>=0 {72-y>=4
The integer solutions of each of the system of inequalities are 0, 1, 2, 3, .....65, 66, 67, 68. There are total 69 integer values that y can take.
In the question, we are given the inequalities:-
y ≥ 0 and 72 - y ≥ 4
We have to find the integer solutions of each of the system of inequalities.
From 72 - y ≥ 4, we can write,
72-4 ≥ y
68 ≥ y
Hence, from 68 ≥ y and y ≥ 0, we can write,
68 ≥ y ≥ 0
Hence, y can take 69 integer values from 0 to 68, both included.
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Find four relations from {a, b} to {x, y} that are not func- tions from {a, b} to {x, y}.
Definition of Relation:
Let A and B be sets. A relation R from A to B is a subset of Ax B
Definition of Function:
A function f from a set A (domain) to a set B (codomain) is a relation that satisfies the following properties:
1) Every element in A there is an element y in B such that (x,y) F
2) For all elements z in A there exist a unique element y in B.
The cartesian product of the sets A (a, b) and B (r,y) is
A x B {(a,z) (a,y).(b,),(b,s)}
Step 2
1. T ((a,x), (a,y))
Since T-((a,z), (a,y)) is a subset of (a, b) x (x,y).
so T is a relation from (a,b) to (x,y).
But for the element a in domain, there exist two different images x and y in co-domain.
This violates the definition of function.
Therefore, T_{1} = \{(a, x), (a, y)\} is a relation but not a function.
Step 3
2. T_{2} = \{(b, x), (b, y)\}
Since T_{2} - \{(b, x), (b, y)\} is a subset of \{a, b\}\{x, y\} .
so T_{1} is a relation from \{a, b\} to \{x, y\}
But for the element b in domain, there exist two different images x and y in co-domain
This violates the definition of function
Therefore, T_{2} = \{(b, x), (b, y)\} is a relation but not a function.
Step 4
,T 1 =\ (a,z)\
Since 7-((a,z)) is a subset of \{a, b\}\{x, y\}
so Ty is a relation from \{a, b\} * to (x,y\
But the element & in domain does not map with any element in co-domain
This violates the definition of function
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Question 1 (10 points)
Berry Ice charges $6.25 a cup and $0.60 for each topping (x) you add. Layla wants a cup with 3 toppings.
Which expression best represents the situation, and how much will the cup cost Layla?
Answer: Total cost for her would be $8.05
Step-by-step explanation:
Given:
Berry Ice charges $6.25 a cup
$0.60 for each topping (x) you add
since she wants a cup with 3 toppings.
then
total cost = 6.25 (cost of 1 cup) + 0.60*3 ($0.60 for each topping then for 3 topping 3*cost of 1 topping)
=$8.05
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30g to the 5th power/6g to the 9th power
Answer:
5.0 × 1012 kg-4. I'm pretty sure this is the answer
Answer:
2.41
Step-by-step explanation:
We needed split up 30 into 2 factors where one of them had to be the same number on the bottom. Since 6 is on the bottom we need to find a number that multiples with 6 to get to 30 and 30/6 gives us 5. So then we can split up 30g into 5g *6g and with the exponents of course. Now since 5g and 6g are multiplying, we can just take 5g out of the equation. If they were adding or subtracting we couldn't.So that gives us 5g^5 * (6g^5/6g^9). According to exponent laws or whatever they're called, if 2 numbers have the same base and have exponents, we can add or subtract the exponents if they are being multiplied or divided by each other. Therefore our final answer is 2.41.
PLEASE SOLVE ITS FOR A TEST I NEED IT
Answer:
The answer is Option C
Answer:
I think the answer would be C
Step-by-step explanation:
In the diagram, roads a and b are parallel.
Solve for x and find the measure of VTU.
Answer:
102
Step-by-step explanation:
<QRT and <VTU are alternate exterior angles, so they are congruent.
m<QRT = m<VTU
x + 40 = 2x -22
62 = x
m<QRT = x + 40 = 62 + 40 = 102
m<VTU = 2x - 22 = 62*2 - 22 = 124 - 22 = 102
solve the equation2 ( x-4 ) = -22
Answer:9
Step-by-step explanation:
9
Answer:
x = -7
Step-by-step explanation:
2(x-4) = -22
2*x + 2*-4 = -22
2x - 8 = -22
2x = -22 + 8
2x = -14
x = -14/2
x = -7
Check:
2(-7-4) = -22
2*-11 = -22
Given the functions f and g, EXPLAIN why you canNOT find f * g.
f = {(-1, 7), (1, 3), (3, 4), (6, 8), (7, 0)}
g = {(0, 10), (2, "-6)," (4, 7), (8, "-1)}
You cannot find f * g because the functions have different domains
How to explain why you cannot find f * g?The functions are given as:
f = {(-1, 7), (1, 3), (3, 4), (6, 8), (7, 0)}
g = {(0, 10), (2, "-6)," (4, 7), (8, "-1)}
In the above function definitions. we have
Domain of f(x): -1, 1, 3, 6, 7
Domain of g(x): 0, 2, 4, 8
See that both functions have different domains
This means that you cannot find f * g because the functions have different domains
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Help please I will mark you as a brainliest.
Answer:
(5² - 8) x 2 doesn't belong
Step-by-step explanation:
this is because this answer is the only one with parintisies around the 5²
Help me please, no joke answers
Answer:
Starting from the left, the points plotted are:
-√9, -1.75, -3/2, -5/3, √4
How many quarters are in four and a half pizzas?
Draw a diagram to justify your answer.
The expression 17n+11 represents the perimeter of the triangle. What is the length of the third side? Please Answer as soon as posable. Thank you.
Answer:the answer is 8n hope that helps!
7.) A bag of 8 apples costs $1.00at Sam's Orchard, a. At this same rate, how much would 18 apples cost?
The cost of 18 Apples at the same rate is $2.25
cost for 8 apples = $1.00
cost of 1 apple = 1.00/8
$0.125 for one apple
cost of 18 apples = 18*0.125 =$ 2.2 5
Here in the given sum we have used simple unitary method concept like in the 1st line we noted the cost of 8 apples that is given in the question that is equall to $1.00. In the next step we found the cost of 1 apple simply by dividing 1.00/8 that amouted to $0.125. In the last stage we have calculated the amount for 18 apples that amouted to $2.25 . We have simply multiplied 18 apples with the cost of 1 apple that is $0.125 which amouted to $2.25
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The irreversible loss of an island from over 100 acres in size to less than 3 acres is an example of?
The irreversible loss of an island from over 100 acres in size to less than 3 acres is an example of the irreversible nature of human change.
Human activity has lead to the change of Earth's climate in unimaginable ways over the last thousand years. Some of these changes are so significant that they are practically inevitable and irreversible.
Due to global warming, the planet's temperature is increasing gradually every year. This change in climate causes polar ice caps to melt and increases the water level.
Islands, which are pieces of land in between water bodies, are reducing in size due to this. The increased water level submerges some or all parts of an island. This is especially threatening for small islands.
This is not only dangerous for the human and wildlife population of these islands, but also for the general habitability. Due to frequent flooding, soil salinity increases and this makes it difficult to cultivate these islands.
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The difference between two positive numbers is 2 and the difference between their squares is 40. Work out the two numbers.
