Answers
Answer:
(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)
From trigonometric identities, we have;
1 + cot²θ = cosec²θ
On the Left Hand Side of the equation, we get;
cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)
On the Right Hand Side of the equation, we have;
√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)
∴ √(cosec²θ - 1) = cot(θ)
By transitive property of equality, therefore;
cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)
(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A
sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³
(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))
∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))
sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))
sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))
(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1
(sinA - cosecA)² = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A
(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A
∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A
Where;
sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A - 2 - 2 + cosec²A + sec²A
sin²A + cos²A - 2 - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A
1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3
Where;
cosec²A = cot²A + 1
sec²A = tan²A + 1
∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation
∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1
(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA
Squaring the Right Hand Side of the equation, we get;
(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA
sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA
∴ (sinA - cosA)² = 1 - 2·sinA·cosA
Taking the square root of both sides gives;
√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]
∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]
By symmetric property of equality, we have;
[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA
Step-by-step explanation:
Related Questions
What is the length of leg s of the triangle below?
90°
45
6
172
45
O
A. 72
B. 5
C. 3
O O O O a
D. 6
E. 3.2
F. 36
Answers
Answer:
6
Step-by-step explanation:
It's a 45-45-90 triangle, it has two similar sides, since it has two similar angles, which are both 45°
so, side = s = 6
Answered by GAUTHMATH
The length of the leg s of the triangle below is 6.
Option D is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Applying the Pythagorean theorem in the triangle.
√72² = s² + 6²
72 = s² + 36
s² = 72 - 36
s² = 36
s = √36
s = 6
We can also say that,
Opposite angles of equal sides are equal
So,
s = 6.
Thus,
The length of the leg s of the triangle below is 6.
Learn more about the Pythagorean theorem here:
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ok so this... is confusing the hell outta me any help?
Answers
Answer:
y = 24
Step-by-step explanation:
The sum of the angles of a triangle is 180
A+B+C = 180
ABC = 60
We know 2x-4 = 60
2x -4+4 = 60+4
2x = 64
x = 64/2 = 32
A = 3x = 3(32) = 962x-4 = 60
B = 60
Using the first equation
96+ 60 +y = 180
156 +y =180
y = 180-156
y = 24
determine the quadratic equation in standard form of a parabola with a zero at x=5 and vertex ar (-3, 32). start with factored form
a)find the other zero
b) create your factored form equation
c) create your standard form equation
Answers
Answer:
see image...
start with Graphing Form: y = a(x-h)²+ k
knowing that h is the x value (negative of it) of the vertex , and k is the y value of the vertex
Graphing Form Equation: y = a(x+3)²+32
you are also given that when the x value is 5 the y value has to be 0
0 = a(4)^2 + 32
a has to be - 1/2
Step-by-step explanation:
Cho đa thức f(x) = biết rằng f(1)=f(-1); f(2)=f(-2).
Chọn câu đúng :
A. f ( x ) = f ( −x) với mọi x
B. f ( x ) = − f ( −x) với mọi x
C. f ( x ) = 2 f ( −x) với mọi x
D. f ( x ) = 3 f ( −x) với mọi x
Answers
Answer:
A
Giải thích:
f(1)=f(x)
f(-1) và f(-2)= f(-x)
=> f(1)=f(-1) =A. f(x)=f(-x)
Name three collinear points.
Answers
Answer: l,j,k
Step-by-step explanation:
need help with number 8
Answers
Answer:
x = 14 2/3
Step-by-step explanation:
it is a parallelogram.
that means AB is parallel to CD, and AD to BC.
it also means that the total angles at B and D must be equal. and the total angles at A and C.
and the sum of all angles in a parallelogram is 360 degrees.
so, we have
360 = 2×(4x + 4x + 8) + 2×(x + 10 + 2x + 8) =
= 8x + 7x + 16 + 2x + 20 + 4x + 16 =
= 21x + 52
308 = 21x
x = 14.666666666.... = 14 2/3
What is the product of the fractions below?
Answers
Answer:
B
Step-by-step explanation:
6/11 * 7/3 = 6*7/11*3 = 42/33
We can simplify this by dividing both by 3.
42/3 = 14
33/3 = 11
So we get 14/11
i am having problems with this problem.
Answers
Answer:
-70
Step-by-step explanation:
keep adding -4 until you reach the 18th term for example
-2
-6
-10
-14
-18
-22
-26
-30
-34
-38
-42
-46
-50
-54
-58
-62
-66
-70
find the mean value of the following. 5, 11, 4, 10, 8, 6
Answers
44/6 = 7.33….
answer: 7.33…..
5. At a wedding reception, an equal
number of guests were seated at
12 round tables. The 13 people in
the wedding party were seated at
a rectangular table. There were 121
people at the reception altogether.
Which equation could you use to find
the number of guests, n, seated at each
round table?
A 12 + 13n = 121
B 12n + 13= 121
C 121 = 12n - 13
D 121 = 13n - 12
Answers
Answer:
b i think
Step-by-step explanation:
Pippa had 35 stickers. She gave an equal number of stickers to 8 friends. She gave each friend as many stickers as possible and kept the rest for herself. How many stickers did Pippa keep for herself? What is the misconception which might lead some to select D) 27 A) 3 B) 4 C) 11 D) 27
Answers
Answer:
The answer is (A), Pipa kept 3 stickers to herself
Step-by-step explanation:
Use what you know about sine, cosine, and tangent to calculate the height of the buildings in the diagram below.
Answers
Answer:
x = 32 feet
Step-by-step explanation:
By applying tangent rule in ΔACD,
tan(40°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AB+AC}{CD}[/tex]
= [tex]\frac{x+BC}{87}[/tex]
x + BC = 73 -----(1)
By applying tangent rule in ΔBCD,
tan(25°) = [tex]\frac{BC}{CD}[/tex]
= [tex]\frac{BC}{87}[/tex]
BC = 40.57
By substituting the value of BC in equation (1),
x + 40.57 = 73
x = 32.43
x ≈ 32 feet
15. Mary was given data comparing students’ mark in math class and the number of classes missed. She plotted the data on the graph below and drew a line of best fit. Do you agree with Mary’s drawing of the line of best fit? Justify your answer. PLEASE HELP ITS RLLY IMPORTANT
Answers
Answer:
No
Step-by-step explanation:
The line of best fit should follow the correlation of the data and it should go through as many of the plotted data as possible.
The Data is showing a negative correlation but she has drawn on a positive correlation and it also only goes through 1 point.
Hope this helps :)
describe the rule that describes the relationship between the numbers in the top row (x) and the bottom row (y) in the following table
Answers
Answer:
y(x) = 2x+3
Step-by-step explanation:
the rule is y(x) = 2x+3
If f(x) = x3 – 1, what is the ordered pair for x = -2.?
Answers
Answer:
(-2, -9)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x³ - 1
x = -2
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-2) = (-2)³ - 1Exponents: f(-2) = -8 - 1Subtract: f(-2) = -9Rewrite: (-2, -9)rachel rides her bicycle due east at 9 miles per hour amos rides his bicycle due north at 12 miles per hour if they left from the same point at the same time how far apart will they be after 1 hour
Answers
The distance between Rachel and Amos after one hour is 15 miles.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Distance travelled by Rachel after one hour = 9 mph * 1 h = 9 miles
Distance travelled by Amos after one hour = 12 mph * 1 h = 12 miles
Let x represent the distance between Rachel and Amos, hence:
x² = 9² + 12²
x = 15
The distance between Rachel and Amos after one hour is 15 miles.
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Using the Pythagorean Theorem, they will be 15 miles apart after one hour.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, considering their directions, their distance is the hypotenuse of a right triangle of legs 9 miles and 12 miles, hence:
[tex]d^2 = 9^2 + 12^2[/tex]
[tex]d = \sqrt{9^2 + 12^2}[/tex]
d = 15 miles
More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982
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Find the value of c so that the polynomial p(x) is divisible by (x-3).
p(x) = -x^3 + cx^2 -4x + 3
Answers
Answer:
c = 4.
Step-by-step explanation:
If p(x) is divisible by (x-3) then p(3) = 0 (By the Factor Theorem), so
-(3)^3 + (3)^2c - 4(3) + 3 = 0
-27 + 9c - 12 + 3 = 0
9c = 27 + 12 - 3
9c = 36
c = 4.
Answer:
4
Step-by-step explanation:
help
1) find the value of x
2)find length of a side of the square
Answers
Answer:
x = 12 , s = 41
Step-by-step explanation:
The sides of a square are equal , so
4x - 7 = 3x + 5 ( subtract 3x from both sides )
x - 7 = 5 ( add 7 to both sides )
x = 12
Then
length of side s is
s = 4x - 7 = 4(12) - 7 = 48 - 7 = 41
A man invested a certain amount of money in a bank at a simple interest rate of 5percent per annum. At the end of the year, his total amount un the bank was GHC 840,000.00. How much sid he invest in the bank.
Answers
Answer: He invested 8,00,000.
Step-by-step explanation:
R = 5%
A = 840,000
T = 1 year
so
so
I = A-P
so
I = PTR/100
or, A-P = (p*1*5)/100
or, 840,000-P = 5p/100
or, 8,40,00,000-100P = 5p
or, 8,40,00,000 = 105P
so, p = 8,40,8,40,00,000
so, P = 8,00,000
Graph the line that has a slope of -7/4 and includes the point (0,10).
Answers
Answer:
y=-7/4x +10
Step-by-step explanation:
that the graph, you can plug the equation in desmos,
hope it helps! :)
Can someone please explain this step by step.
Answers
Answer:
-5 and 2
-3 and 0
-2 and -1
...gives -3
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-5,2), (-2,-1), (-3,0)
all pairs add up to -3
Urgently need help step by step explanation needed
Answers
Answer:
p=8
Step-by-step explanation:
-5log(p+1)+2=-8
-5log(p+1)=-10
log(p+1)=2
p+1=9, p=8
Carrie is asked to draw a triangle with the following specification
• at least two angles measuring 60°
Which of the following statements about this triangle is true?
A. One and only one triangle exists with the given condition, and it must be an equilateral triangle
В.
More than one triangle exists with the given condition, and all instances must be equilateral triangles
C
One and only one triangle exists with the given condition, and it must be an isosceles triangle
D
More than one triangle exists with the given condition, and all instances must be isosceles triangles
Answers
Answer:
just put in the cheat codes of life its not that hard
Answer:
answers is B
(Study island)
Step-by-step explanation:
Last question, thank you guys a lot for helping me out
Answers
Answer: Her earnings after taxes will be $415.80 (choice C)
How?
PER 1 HOUR: 0.77 x (13.50 x 1) = 0.77 x $13.50 = $10.395
PER 40 HOURS: 0.77 x (13.50 x 40h) = 0.77 x 13.50 x 40 = $415.80
please help meeeeeeeeeeeeee
Answers
Answer:
a)-2x(x+4x²)+3(x²+2x)
-2x²-8x³+3x²+6x
-2x²+3x²+6x-8x³
x²-8x³+6x
in descending order
-8x³+x²+6x
b)(4x-3)(4x+3)
4x(4x+3)-3(4x+3)
16x²+12x-12x-9
16x²-9
I hope this helps and sorry if it's wrong
|Area of a square field is 617796cm² . Find length of its each side.
Answers
Answer:
length of its each side is 786 cm
Step-by-step explanation:
l² = 617796cm²
l = √617796
l = 786cm
Answer:
[tex]area \: of \: square = {l}^{2} [/tex]
[tex]617796 = {l}^{2} [/tex]
[tex] \sqrt{617796 } = l[/tex]
[tex]786 = l[/tex]
therefore ,l=786cm
If 5 is added to the difference of 3 times of 4 and 7 find the number
Answers
Answer:
14
Step-by-step explanation:
3*4=12
3*7=21
Diff= 21-12
Diff= 9
Plus 5=9+5
The number is 14
Choose the complete predicate for the sentence below. My friend from school is going to a football game tomorrow. My friend My friend from school going to a football game tomorrow is going to a football game tomorrow
Answers
Answer:
The complete predicate is the following: "is going to a football game tomorrow."
Step-by-step explanation:
A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.
Answer:
The complete predicate is the following: "is going to a football game tomorrow."
Step-by-step explanation:
A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.
the train regularly travels 135 miles in 60 minutes.
What is the speed, in miles per minute, on this portion of the route?
Answers
Answer:
2.25 miles per minute
Step-by-step explanation:
Speed = Distance/Time
135/60
2.25 miles per minute
Answer from Gauthmath
A rectangle has side lengths 2x + 3 and 5x - 2.
Write an expression without brackets for the area of the rectangle
Answers
Answer:
10x² + 11x - 6
Step-by-step explanation:
The area (A) is the product of the sides, that is
A = (2x + 3)(5x - 2) ← expand using FOIL
= 10x² - 4x + 15x - 6 ← collect like terms
= 10x² + 11x - 6
