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
A triangle and a parallelogram have the same base and the same area.
If the sides of the triangle are 26 cm, 28 cm and 30 cm and the
parallelogram stands on the base 28 cm. Find the height of the
parallelogram.
Answers
Height of parallelogram =12cm
Select the correct answer.
The product of two numbers, x and x+ 3, is 550. Which equation could be solved to find the value of the smaller number, x?
Answers
Answer:
C) x^2 + 3x
Step-by-step explanation:
The equation that could be solved to find the value of the smaller number, x is x^2 + 3x = 550
How to determine the equation?The numbers are given as: x and x + 3
The product of these numbers is 550.
So, we have:
x * (x + 3) = 550
Expand
x^2 + 3x = 550
Hence, the equation that could be solved to find the value of the smaller number, x is x^2 + 3x = 550
Read more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ2
Find the missing segment in the image below
Answers
Answer:
20.4
Step-by-step explanation:
that is the procedure above
Answer:
Step-by-step explanation:
Help
I really need help pls
Answers
Answer
Mandisa uses more balloon per animal.
Amira and Mandisa made the same amount of balloon animals.
Explanation
Mandisa uses 5 balloons per animal.
You can find this out by putting the difference between two of the y values (output, dependent variable, in this case balloons) over the difference between two of the x values (input, independent variable, in this case animals). Let's take 225 and 125 from the y value and 20 and 40 from the x value. Mandisa uses 225-125=100 balloons per 40-20=20 animals. Mandisa uses 5 balloons per animal. 5 is more than 4 (how many balloons Amira uses for each animal), so Mandisa uses more balloons per animal.
Amira and Mandisa made the same amount of balloon animals.
Now you can divide the number of balloons they had at the beginning by the number of balloons per animal to find out how many animals each person made. Amira started with 260 balloons and used 4 balloons for each animal. Amira made 260/4=65 animals.
If Mandisa used 100 balloons to make 20 animals, she would have had 225+100=325 balloons at the beginning. Mandisa made 325/5=65 animals.
Find the number of unique permutations of the word ALGEBRA.
Answers
Answer:
= 2520
Step-by-step explanation:
In 2520 distinct way the letter "ALGEBRA " can be Arranged
I think it's the answer
A line segment has one endpoint of A (-3,2) and a slope of (-3/5). Find coordinates for B
Answers
Answer:
Step-by-step explanation:
This is a very interesting problem. We are given the slope and one point, which makes this funner than normal ;)
Filling in the slope formula with what we are given:
[tex]-\frac{3}{5}=\frac{y-2}{x-(-3)}[/tex] which simplifies to
[tex]-\frac{3}{5}=\frac{y-2}{x+3}[/tex]
Since slope is rise over run, the rise number is -3; the run number is 5. That means that the equation to find the y coordinate comes from -3 = y - 2; the equation to find the x coordinate comes from 5 = x + 3 (keep in mind that you could have made the x coordinate the negative one; it doesn't matter. You will get the same answer regardless...promise).
Solving for y:
-3 = y - 2 and
y = -1
Solving for x:
5 = x + 3 and
x = 2
Let's check those coordinates in the slope formula and see if our slope is in fact -3/5:
[tex]m=\frac{-1-2}{2-(-3)}=-\frac{3}{5}[/tex] so we're all good!
The coordinates of B are (2, -1)
x + y = 3 . If y = 3, find the value of x
Answers
Answer:
0
Step-by-step explanation:
x + y = 3
y = 3
=> x + 3 = 3
=> x = 3 - 3
=> x = 0
solve h(x)=x^2-2x-8>7
Answers
Answer:
x < -3 and x > 5
Step-by-step explanation:
x² - 2x - 8 > 7
~Rewrite in standard form
x² - 2x - 15 > 0
~Factor
(x + 3)(x - 5) = 0
~Solve for both factors
x + 3 = 0
x = -3
x - 5 = 0
x = 5
Best of Luck!
the table shows the ratio between the number of books ordered and their cost. 7,14 8,16 9,18. find equivalent ratios when the number of books ordered is 1,2, and 3. write them as ordered pairs in the form (x-coordinate, y-coordinate). starting from the origin explain how to plot three equivalent ratios on a coordinate grid.
Answers
Answer:
Number of Books. Cost (dollars). 7 14. 8 16. 9 18. Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form...
FOR BRAINLIEST ASAP!!!
Jean bought an mp3 player and a calculator for a total of $208. the mp3 player cost $140 more than the calculator, what did the calculator cost
Answers
Answer:
Calculator cost = $34
Step-by-step explanation:
x + (x+140) = 208
2x + 140 = 208
x=34
Need help ASAP !!! Am I correct? Just checking….
Answers
Answer:
Yes you are
Step-by-step explanation:
If you multiply the first equation by 3 , y becomes 3y and so you can eliminate from there.
Please help me with this question.
Answers
LB= 55.5/9.15= 6.06557377
The value of the expression 2x^2/x(100-15x) when x=5 is
Answers
Answer:
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
[tex]2({5}^{2}) \div 5(100 - 5(15))[/tex]
[tex]50 \div 25 \times 5[/tex]
[tex]50 \div 125[/tex]
[tex]2 \div 5[/tex]
What does the question mean? For the blank
Answers
Answer:
Absolute value.
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \sqrt{s^2}[/tex]
The square root and the square will cancel. This yields:
[tex]=|s|[/tex]
We need the absolute value because any value squared is positive. The square root of a positive value will also be positive.
In other words, if we only simplified the expression down to s without the absolute value, if s was originally negative, our simplification will have also been negative.
For instance, say s = -7, then:
[tex]\displaystyle \sqrt{(-7)^2}=\sqrt{49}=7[/tex]
However, if we let √s² = s, then s = -7. By having the absolute value, we have that |s| = |-7| = 7, which is the correct statement.
(a) 88.83 is what percent of 21?
(b) 25.83 is 52.5% of what number?
Thanks!!!
Answers
B is 0.492
what is the 13mm = to
Answers
Find the coefficient of x^4 in the expansion of
(2x+1)^12
Answers
Answer:
7920
Step-by-step explanation:
you can use the binomial theorem obviously but you can also use symbolabs or wolframalpha and just solve it like that.
please help, ill give 69 points <33
Answers
Which shows the equation below written in the form ax2 + bx+c = 0?
x*2+7x+ 9 = 3
Answers
Hi!
x² + 7x + 9 = 3
x² + 7x + 9 - 3 = 0
x² + 7x + 6 = 0
Answer:
x^2+7x+ 6 = 0
Step-by-step explanation:
x^2+7x+ 9 = 3
Subtract 3 from each side
x^2+7x+ 9-3 = 3-3
x^2+7x+ 6 = 0
Which algebraic expression is a difference with two terms?
A. 3y+1
B.-2y+5+3
C. 5y-7
D.5(y-6)
Answers
Answer:
1.
C. 5y -7 is an algebraic expression difference with two terms.
Percentage change
….
Answers
Answer:
80%
Step-by-step explanation:
Change is (45-25)/25*100=(20/25)*100=80%
Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4
Answers
What is the equation of a line that passes through the points, (-2, 2) and is parallel to a line with an equation of y = 2x + 5
Answers
Answer:
y = 2x+6
Step-by-step explanation:
y = 2x + 5
This line is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 2. Parallel lines have the same slope
y = 2x+b
Using the given point and substituting it into the equation
2 = 2(-2) +b
2 =-4+b
Add 4 to each side
2+4 = -4+b+4
6 = b
y = 2x+6
Can someone help me please with this math homework!!!
Answers
Answer:
-2x + 3y = -19
Step-by-step explanation:
y + 1 = 2/3(x-8)
multiply by 3 to get rid of the fraction
3(y + 1 = 2/3(x-8)
3y + 3 = 2(x-8)
simplify
3y + 3 = 2x - 16
3y - 2x = -19
-2x + 3y = -19
[tex]\sqrt{x^{2} +2x+2\\}[/tex]
Answers
Answer:
[tex]{ \tt{ \sqrt{ {x}^{2} } + 2x + 2}} \\ { \tt{ = x + 2x + 2}} \\ = { \tt{3x + 2}}[/tex]
(URGENT PLEASE HELP)
The vertex of this parabola is at (5, 5). When the x-value is 6, the
y-value is -1. What is the coefficient of the squared expression in the parabola's equation?
a) 4
b) -6
c) 6
d) -4
Answers
Answer:
-6
Step-by-step explanation:
A parabola is vertex form is written as
y = a(x-h)^2 +k where (h,k) is the vertex
Substituting in the vertex
y = a(x-5)^2 +5
We know a point on the parabola so we can find a
-1 = a( 6-5)^2 +5
-1 =a(1)^2+5
-1 = a +5
Subtract 5 from each side
-1-5 = a
-6 =a
Derrick's dad bought new tires for $900 using a credit card. His card has an
interest rate of 19%. How much interest will he accrue after 4 months?
Answers
Answer:
$57 interest
Step-by-step explanation:
For an interest rate of 19% ; the monthly interest will be 19/100 = 0.19
4 months interest will be (0.19 * 4)/12 = 0.0633
so now, the value of the interest will be
0.0633 * 900 = $57
in a right triangle ABC, C is the right angle. What does cos A equal
1: cos(B)
2: both A and C
3: Cos(90-A)
4: sin(90-A)
Answers
Answer:
4
Step-by-step explanation:
A+B+C = 180
C = 90
A+B = 90
A=90-B
Cos (A) = Sin(90-A)
Find the value of the expression 8x^3 if x= -1
Answers
Answer:
- 8
Step-by-step explanation:
Substitute x = - 1 into the expression , that is
8x³
= 8(- 1)³ = 8(- 1) = - 8
Triangle ABC has vertices A(0, 2), B(5, 4), and C(5,0). Triangle A'B'C'has
corresponding vertices A'(-5, -1), B'(0, 1), and C'(0, -3). Which of the following
describes a translation that would produce triangle A'B'C' from the pre-image of
triangle ABC?
A) To the left five units, up three units.
B) To the left five units, down three units.
C) To the right five units, up three units.
D) To the right five units, down three units.
Answers
Answer:
B) To the left five units, down three units
Answer:
( B ) To the left five units, down three units.
