If tan a = x + 1 and tan ß = x - 1, then verify that: 2cot(a - B) = x²
Answers
[tex]
\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]
Hence verifying that 2cot(α - β) = x².
Related Questions
Nigel is going from London, UK, to Moscow, Russia, by train. He goes 296 miles on a train from London to Paris, France. He takes another train 500 miles to Munich, Germany, and switches trains in Munich to ride 256 miles on a train to Vienna, Austria. His last train ride carries him 1,298 miles from Vienna to Moscow. Find his total distance by first rounding each distance to the nearest hundred miles before adding.
Answers
Answer: 2400 miles
Step-by-step explanation:
Round;
256 to 300
500 to 500
296 to 300
1,298 to 1,300
Add; 300 + 300 + 500 + 1,300 to get your 2,400 miles.
the equation sin(40)=b/20can be used to determine the length of segment ac . what is the length of ac? round to the nearest tenth
Answers
If the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
Given,
The equation,
sin 40 = [tex]\frac{b}{20}[/tex]
We know,
According to trigonometric equation
sin θ= Opposite side / Hypotenuse.
Length of the segment AC = b
Then,
sin 40 = [tex]\frac{b}{20}[/tex]
b= sin 40 × 20
b= 12.85 units
Hence, if the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
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A rectangular room is 15 ft long and 10 ft wide. A scale drawing of the room had a width of 5 inches.What is the length of the room in the drawing?
Answers
Answer:
7.5 inches
Step-by-step explanation:
15 ft long and 10 ft wide becomes 3/2 when converted into a ratio
we now have 3/2 and five inches
3 is 1.5*2
5*1.5 is 7.5
Answer:
7.5in
Step-by-step explanation:
If the original room's dimensions are (15ft x 10ft). Then the new scaled-down version is (?ft x 5in) we can set up a ratio of 10/5 = 2 to find that the scale from the room to the drawing is being shrunk by a factor of 2. So if you take 15/2 you will get your final answer of the new length of 7.5in!
Simplify the complex fraction below.
Answers
Answer: 6
:)
___________________________________
Answer:
[tex] \sf \large \: \frac{2}{27} [/tex]
Step-by-step explanation:
Let's solve this equation step by step
2/3/1/9
= 2/3/9/1
= 2/27
The owners of an apartment building bought it new and then 5 years later sold it for $165000. They calculated that the building appreciated $2000 per year
while they owned it.
ind a linear function that describes the value of the building over time, if a is the age of the apartment building.
Answers
f(a)= 2000a +155000 is a linear function that describes the value of the building over time, if a is the age of the apartment building
The owners of an apartment building bought it new and then 5 years later sold it for $165000. They calculated that the building appreciated $2000 per year while they owned it.
we have to find a linear function that describes the value of the building over time, if a is the age of the apartment building
write a linear function is in slope-intercept form:
y= mx+b
Here, x is the independent variable, and y is the dependent variable. Also, the slope of the line, m, represents some kind of constant rate. Finally, b, the y-intercept represents some sort of starting value for our dependent variable.
165000= $2000*5+b
$165000= $10000+b
$155000=b
f(a)=2000a+155000
therefore f(a)= 2000a +155000 is a linear function that describes the value of the building over time, if a is the age of the apartment building
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can someone help me with this domain and function question :)
Answers
Answer: (-∞, ∞)
Step-by-step explanation:
|2x+5|+3 can't equal 0. The denominator can't equal 0.
|2x+5|+3[tex]\neq[/tex]0
|2x+5|[tex]\neq[/tex]-3 ==> Absolute value functions can't be negative, so the denominator will never equal 0.
Hence, domain is x equals all real numbers: (-∞, ∞)
A mural measures 145 feet long by 190 feet high. Find the ratio of the height to the perimeter of this mural.
Answers
The ratio of height to perimeter of mural is 19:67.
The perimeter of mural will be calculated by the formula -
Perimeter = 2 × (length + breadth)
So, finding the perimeter using the mentioned formula. Keep the values of length and breadth in formula to calculate the perimeter of mural.
Perimeter = 2 × (145 + 190)
Performing addition of values in bracket
Perimeter = 2 × 335
Performing multiplication
Perimeter = 670 feet
Ratio = Height : Perimeter
Ratio = 190 : 670
Cancelling zero to find the ratio
Ratio = 19 : 67
Hence, the ratio of the height to the perimeter of this mural is 19:67.
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Please help me solve this problems.
Answers
Answer:
[tex] \sqrt{54 {x}^{5}yw {}^{8} } \\ \sqrt{7 \times 8 {x}^{5}yw {}^{8} } \\ = 2x {}^{2} {w}^{4} \sqrt{14xy} [/tex]
XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.
Answers
2(6m+12)=180
12m+24=180
12m=156
m=13
Help please it’s geometry
Answers
Answer:
RA = RB because the base angels of isosceles are equal and their measurement are equal too
Step-by-step explanation:
angle RAB=180(sum of angels of a triangle)
180/2=90
90/3=30
Angle R= 90
Angle A=30
Angle B= 30
So,It is proved that RA=RB
I tried my best to answer hope it is accurate.
Use the formula for the area of a trapezoid A = h (bi+b²), 2 where A is area, b₁ and b₂ are the length of the bases, and h is the height, to answer the question. How many square feet of grass are there on a trapezoidal field with a height of 75 ft and bases of 125 ft and 81 ft?
Answers
Answer:
7725 ft³===================
Use the given numbers and formula to calculate the area:
[tex]A = h(b_1+b_2)/2[/tex][tex]A = 75(125+81)/2=75(206)/2=75(103)=7725[/tex]Between what two integers does square root of -19 lies
Answers
Answer:
4 and 5
Step-by-step explanation:
4^2=4xx4=16,
5^2=5xx5=25, and 19 is between those two squares
-2x-y=1 in slope intercept form
Answers
Move the variable to the right
-y=1+2x
Change the signs
y=-1-2x
Reorder the terms
Solution
y=-2x-1
Hope this helps
How many degrees must figure A be rotated counterclockwise around the origin in order to line up with Figure B?
Answers
Answer:
270
Step-by-step explanation:
One turn would put you in quadrant 2 and would be 90. A second turn would put you in quadrant 3 and that would be 180. A third turn would put you in quadrant 4 and that would be 270. I know that it is hard to see what I mean by a turn. It would be if you had a piece of tracing paper with the figure drawn on it and you turn the paper at the origin so that the lines at the corners would like up, each turn would be 90 more degrees.
write an equation in slope-intercept form of the line that bisects the angle formed by ED and EF.
Answers
Answer:
ok
Step-by-step explanation:
the answer is (2,4)
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NEED HELP ASAP
Which ordered pairs are solutions to the system of inequalities?
{x−3y≥1
{2x+y≤4
Select each correct answer.
(0, 3)
(−1, 1)
(3, −2)
(4, 0)
(2, 3)
(1, −1)
Answers
BEST ANSWER GETS BRAINLIEST PLEASE HELP FAST [35 POINTS]
The vertices of Figure A are located at (-9,4), (-3,6), (-2,3) and (-8,1) on a coordinate plane. Figure A is transformed to Figure B by rotating the figure 90º clockwise about the origin, translating it 8 units left and 4 units down, and then dilating from the origin by a scale factor of 2. Which ordered pair will be a vertex in Figure B?
A. (-8,10)
B. (−2, 5/2)
C. (-9/2 −6)
D. (-22,-12)
Answers
Answer:
a
Step-by-step explanation:
what does a sqiggley equal sign mean.
Answers
Answer:
Approximately ≈
Step-by-step explanation:
Answer:
approximately equal to
or
Approximate equality
Is this true
4. When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. For example, 12 – 4 is 8 and 11 – 4 is 7
Answers
Answer:
The answer is True
Step-by-step explanation:
In the substraction, if you reduce or increase the substrahend by a number, the result is the same number less or more
Eighty meters of fencing is available to enclose the rectangular garden of Mang
Gustin. Give a function A that can represent the area that can be enclosed in
terms of x.
Answers
A function that can represent the area that can be enclosed in terms of x is 40x-x².
Given that Eighty meters of fencing is available to enclose the rectangular garden of Mang Gustin.
Area is defined as the amount of space that can be used within a flat surface or the surface of a solid. Perimeter is defined as a continuous line that forms a boundary to define a two-dimensional shape.
Let the length of garden, l=x
and the given perimeter, p=80
As we know, perimeter of rectangle is P=2(l+b).
Now, we will substitute the values and find the value of b, we get
80=2(x+b)
Now, we will divide both sides by 2, we get
80/2=2(x+b)/2
40=x+b
Further, subtract x from both sides, we get
40-x=x+b-x
40-x=b
Now, we will find the area of rectangle by using the formula A=lb.
Substitute the values in above formula, we get
A=x(40-x)
A=40x-x²
Hence, the area that can be enclosed in terms of x is 40x-x².
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Please solve this, thank you
Answers
Answer:
2.62 x 10^16
Step-by-step explanation:
Let look at the numerator:
(3.1 x 10^6)(6.97 x 10^4)
= (3.1 x 6.97) x 10^(6+4)
= 21.607 x 10^10
So 21.607 x 10^10
_______________
8.245 x 10^-6
= (21.607/8.245) x 10^(10 - -6)
= 2.62 x 10^(10 + 6)
= 2.62 x 10^16
I hope this helps
:
Uncle Choo sold 580 reams of printing paper in January and 755
reams of printing paper in February.
He sold 2100 reams of printing paper from January to March.
How many reams of printing paper did he sell in March?
Answers
Step-by-step explanation:
2100-(580+755)
2100-1335
=835
Answer=
January=580
February=755
January+February=
580+755=1335
March=2100-1335
=765
so March is 765 reams
January+February+March
580+755+765=2100reams
ASAP, yk the pain too, help me out!!! begging
2x+p/q=2x+q/p, p DOESNt equal to 0, q doesn’t equal to 0
Answer: If p=q, ______. If p doesn’t equal q, _______.
Answers
The equation, [tex] \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} [/tex], gives;
When p = q, the number of solutions is infinite.
When p ≠ q, the equation has no solution
How can the given equation be evaluated?The given equation is presented as follows;
[tex] \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} [/tex]
If p = q, we have;
[tex] \frac{2 \cdot x + q}{q} = \frac{2 \cdot x + q}{q} [/tex]
[tex] \frac{2 \cdot x + p}{p} = \frac{2 \cdot x + p}{p} [/tex]
Therefore, the equation has an infinite number of solutions when p = Q
If p ≠ q, and x = 3, we have;
[tex] \frac{2 \cdot x + p}{q} = \frac{2 \times 3 + p}{q} = \frac{6 + p}{q} [/tex]
[tex] \frac{2 \cdot x + q}{p} = \frac{6 + q}{p} [/tex]
[tex] \frac{6 + p}{q} [/tex] = \frac{6 + q}{p} [/tex]
6•p + p² = 6•q + q²
However;
p ≠ q
Therefore;
6•p ≠ 6•q
p² ≠ q²
6•p + p² ≠ 6•q + q²
Which gives;
[tex] \frac{6 + p}{q} \neq \frac{6 + q}{p} [/tex]
The equation is not defined when p ≠ q
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What is the value of 8 in each number? 389
Answers
Answer:80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
its just 80
The graph of f(x) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1.75, 4), has a vertex of (negative 0.25, negative 3), and goes through (1.4, 4). Solid circles appear on the parabola at (negative 1.6, 3.1), (negative 1.2, 0), (negative 0.25, negative 3), (0.8, 0), (1.2, 3.1).
Over which interval on the x-axis is there a negative rate of change in the function?
–2 to –1
–1.5 to 0.5
0 to 1
0.5 to 1.5
Answers
Answer:
The answer is A. –2 to –1
Step-by-step explanation:
Answer: A on edge
Step-by-step explanation:
.............................
Answers
Answer: yes i get it
Step-by-step explanation:
Find a solution to the linear equation 13x +y =26 by filling in the bows with a valid value of x and y.
Answers
The solution to the linear equation are x = 2 - y/13 and y = 26 - 13x.
It is required to find the solution to the linear equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The equation is
13x + y = 26
We have to find the value of x and y .
According to given question we have
13x + y = 26
Subtract 13x from both sides we get,
y = 26 - 13x
Subtract y from both sides
13x = 26 - y
Divide through by 13
x = 2 - y/13
Therefore, the solution to the linear equation are x = 2 - y/13 and y = 26 - 13x.
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Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f passes through (-9,-8) and is perpendicular to the line whose equation is x = 8.
The equation of the function is
Answers
Answer:
y = -8
Step-by-step explanation:
line x = 8 is a vertical line so the line perpendicular has slope of 0
Using m = 0, x = -9, y = -8
y = mx + b
-8 = 0(-9) + b
b = -8
so y = -8
Step-by-step explanation:
y = 8, the one above is correct, we both are.
what is the direction of vector v if it ends at (-3,-10)
Answers
The direction of the vector v in standard position is approximately 253.301°.
What is the direction of a given vector?
Vectors in rectangular form present the change of each of the two variables parallel to orthogonal axes. Each point is described by the following definition:
v = (Δx, Δy) (1)
And the direction of a vector is equal to this inverse trigonometric function:
θ = tan⁻¹ (Δy / Δx) (2)
If we know that Δx = - 3 and Δy = - 10, then the direction of the vector is:
θ = tan⁻¹ (- 10 / - 3)
θ = tan⁻¹ (10 / 3)
θ ≈ 253.301°
The direction of the vector v in standard position is approximately 253.301°.
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a bouquet has 10 flowers.among them,3 are red. at the same ratio, how many red flowers are needed to prepare two bouquets
Answers
Answer:
in one bouquet there are 3 red so in two bouquets there must be 6