Answers
Answer:
[tex] \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}[/tex]
Step-by-step explanation:
[tex] \cos( \alpha ) = \frac{ \sqrt{6} }{6} = \frac{1}{ \sqrt{6} } \\ \\ \therefore \: \sin( \alpha ) = \sqrt{1 - { \cos}^{2} ( \alpha ) } \\ \\ = \sqrt{1 - \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} } \\ \\ = \sqrt{1 - {\frac{1}{ {6} }}} \\ \\ = \sqrt{ {\frac{6 - 1}{ {6} }}} \\ \\ \red{\sin( \alpha ) = \sqrt{ { \frac{5}{ {6} }}} } \\ \\ \tan( \alpha ) = \frac{\sin( \alpha ) }{\cos( \alpha ) } = \sqrt{5} \\ \\ \sin( \beta ) = \frac{ \sqrt{2} }{4} \\ \\ \implies \: \cos( \beta ) = \sqrt{ \frac{7}{8} } \\ \\ \tan( \beta ) = \frac{\sin( \beta ) }{\cos( \beta ) } = \frac{1}{ \sqrt{7} } \\ \\ \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha . \tan \beta} \\ \\ = \frac{ \sqrt{5} - \frac{1}{ \sqrt{7} } }{1 + \sqrt{5} . \frac{1}{ \sqrt{7} } } \\ \\ = \frac{ \sqrt{35} - 1 }{ \sqrt{7} + \sqrt{5} } \\ \\ \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}[/tex]
Related Questions
The graphs show the audience, in millions, of two TV shows as a function of the episode number. For the first show (top graph) pick two episode numbers between which the function has a negative average rate of change, if possible. Estimate the average rate of change, or explain why it is not possible.
Answers
Answer:
The slope between two points. The rate at which the dependent variable changes with the independent variable. Yes between episode 5 and episode 6
Step-by-step explanation:
For the function f(x)
8 Vas - 8. find / -'(X).
9
+8
of-'() = (9)
O/(x) = 9(+8)
O!'(x) = (18)
Of(x) = 9(2+8)
8
Submit Answer
Answers
Given:
The function is
[tex]f(x)=\dfrac{8\sqrt[3]{x}-8}{9}[/tex]
To find:
The inverse function [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{8\sqrt[3]{x}-8}{9}[/tex]
Step 1: Putting f(x)=y, we get
[tex]y=\dfrac{8\sqrt[3]{x}-8}{9}[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{8\sqrt[3]{y}-8}{9}[/tex]
Step 3: Isolate variable y.
[tex]9x=8\sqrt[3]{y}-8[/tex]
[tex]9x+8=8\sqrt[3]{y}[/tex]
[tex]\dfrac{9x+8}{8}=\sqrt[3]{y}[/tex]
Taking cube on both sides, we get
[tex]\left(\dfrac{9x+8}{8}\right)^3=y[/tex]
[tex]y=\left(\dfrac{9x+8}{8}\right)^3[/tex]
Step 4: Putting [tex]y=f^{-1}(x)[/tex], we get
[tex]f^{-1}(x)=\left(\dfrac{9x+8}{8}\right)^3[/tex]
Therefore, the correct option is C.
-2x-y=0, where x≤0
Find the 6 trigonometric functions
Answers
Answer:
very hard, why don't you search on internet
Match the reasons with the statements.
Answers
Answer:
top=3, middle=2, bottom= 1
Step-by-step explanation:
Find 2y-6= -6x in slope intercept form and find the slope and y-intercept.
Answers
Answer:
slope=-3
y-intercept=(0, 3)
I need Help, Will give Brainliest to first person to answer
Answers
Answer:
- 26
Step-by-step explanation:
The volume (V) is calculated as
V = lwh ( l is length, w is width, h is height ), then
V = 2x(3x + 1)(5x - 6) ← expand the factors using FOIL
= 2x(15x² - 13x - 6) ← distribute parenthesis by 2x
= 30x³ - 26x² - 12x
The second term is - 26x² with coefficient - 26
Which of the following describes the roots of the polynomial function ix) = (x+2)?(x-4)(x+1)3?
Help fast
Answers
Step-by-step explanation:
2 with multiplicity 2, -4 with multiplicity 1, and 1 with multiplicity 3.
3x +11+7x
Pls help I want to learn this
Answers
Answer:
3x +7x +11=10x+11
Step-by-step explanation:
Answer:
Step-by-step explanation:
Group like terms:
=3x+7x+11
Add similar elements: 3x+7x=10x
=10x+11
Voting in Clarksville's annual school board elections has been going down by 5% from one election to the next. If 440 parents voted this year, how many will vote 3 years from now?
Answers
Answer:
377 parents
Step-by-step explanation:
We start by writing an exponential equation
FV = PV(1 - r)^t
FV is future value = ?
PV is present value = 440
r is rate = 5/100 = 0.05
t = 3
Substituting these values
FV = 440(1 - 0.05)^3
FV = 377.245
This is approximately 377
What is the area of this figure?
Answers
Answer:
[tex]\Huge\boxed {A =859ft^{2} }[/tex]
Step-by-step explanation:
Hello There!
To solve for the area of this figure we need to split the figure into 3 different parts:
A rectangle with a length of 9 ft and a width of 7 ft
a rectangle with a width of 9ft + 7ft and a length of 25 ft
a rectangle with a width of 18 ft and a length of 22 ft
To find the area of a rectangle we use the formula
[tex]A=w*l[/tex] where w = width and l = length
for the first one we plug in the values
A = 9 * 7
9 * 7 = 63 so the area of the smallest rectangle is 63ft²
Now lets find the area of the larger rectangle
The dimensions are l = 25 ft and w = 9 + 7 (16 ft)
Now we can plug in the values into the area formula
A = 16 * 25
16*25=400 so the area of the larger rectangle is 400 ft²
Now lets find the area of the last rectangle
The dimensions are l = 22 ft and w = 18 ft
now lets plug in the values to the formula
A = 22 * 18 =396
so the area of the last rectangle is 396 ft²
Finally we want to add all of the areas together
396 + 400 + 63 = 859
So the area of the figure is 859 ft²
The product of five times p and seven times q is
Answers
Answer:
Step-by-step explanation:
(5p)(7q)=35pq
Answer:
The product of five t imes p and 7 times q is just:
5p(7q), which is 42pq
Let me know if this helps!
I'm doing my homework and I forgot how to do these
Answers
Answer:
9 - 15/2
10 - 9
11 - 16/3
12 - 5/6
Step-by-step explanation:
Please help me with this please!!
Answers
9514 1404 393
Answer:
135°
Step-by-step explanation:
In order to answer the question, we must assume that the black lines are parallel to each other.
The given angles (2, 8) are "same-side (consecutive) exterior" angles, so are supplementary.
∠2 +∠8 = 180°
15x +5x = 180°
x = 180°/20 = 9°
∠2 = 15x = 15(9°) = 135°
Angles 2 and 3 are vertical angles, so angle 3 has the same measure as angle 2.
∠3 = 135°
- Aidan buys used bicycles, fixes them up, and sells them. His average cost to buy and fix each bicycle is $27. He also incurred a one- time cost of $960 to purchase tools and a small shed to use as his workshop. He sells bikes for $67 each. How many bicycles does Aiden have to sell to reach the "break-even" point?
Answers
Answer: Adrian will need to fix 25 bikes to reach a break even point.
The number of bicycles does have to sell to reach the "break-even" point'' will be 24.
What is a break-even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." No net gain or loss has occurred, and one has "broken even,".
Given that Aidan buys used bicycles, fixes them up, and sells them. His average cost to buy and fix each bicycle is $27. He also incurred a one-time cost of $960 to purchase tools and a small shed to use as his workshop. He sells bikes for $67 each.
The number of bicycles will be calculated as:-
27 = ( 67n - 960 ) / n
27n = 67n - 960
40n = 960
n = 960 / 40
n = 24
Therefore, the number of bicycles does have to sell to reach the "break-even" point'' will be 24.
To know more about the break-even point follow
https://brainly.com/question/24233845
#SPJ5
Beth took out a 12-year loan for $35,000 for a new pool. If the interest rate is 10.2%, how much will she pay in interest?
Answers
Answer:
35000×10.2%=3570 Interest will be paid
35000+3570=38570 full amount will be paid in the bank
What is the slope of y = -4x – 3
Answers
Answer:
-4
Step-by-step explanation:
bc the equation is y=mx+b and m is y/x so -4
Which equation represents a line which is parallel to the line 4x-5y=30
Answers
If the length of a rectangle is 16 cm and breadth is 7 cm, the area in square centimetres will be
Answers
Answer:
the answer is 112 mate hope u got ur answer
Please help !! I will give you brainliest!!
Explain each step you took to solve this question.
Given: Angle ^HMA is bisected by MT.
HT = MT
Find the measure of angle ^MAT.
Answers
Answer:
angle MAT=48
Step-by-step explanation:
angle H = 44
angle M = 88
angle A = 48
triangle HTM is an isosceles triangle which means its other two angles are congruent and to find those two measurements we do (180-92)/2=44MT bisects, meaning split equally in half, so we multiply 44 by 2 and now we have angle measures of H&M180-(H+M)= AAn equilateral triangle with side length 9 cm is shown in the diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
Answers
Question:-
Find the area of an equilateral triangle with side length = 9cm correct upto one decimal place.
_______________________________________________
Solution:-
In an equilateral triangle all sides are equal.
Let s = side length = 9 cm
Then, area of equilateral triangle is given as:
A = (√3/4)s²
Putting the value of s here,
A = (√3/4) * (9 cm)²
=> A = (√3/4) * 81 cm²
=> A = √3 * 20.25 cm²
We know that, √3 = 1.732
=> A = 1.732 * 20.25 cm²
=> A = 35.073 cm²
Rounding to one decimal place,
=> A = 35.1 cm²
_______________________________________________
The answer is 35.1 cm².
Hope this helps; have a great day!
Is this a proportional relationship
Answers
Answer:
N o
Step-by-step explanation:
Please does anyone know the answer to this question??
Answers
9514 1404 393
Answer:
126°
Step-by-step explanation:
To find the exterior angle, we need to know one of the acute angles. Those are found using the fact that they are complementary.
(5x -6) +(3x) = 90
8x = 96 . . . . . . . . . . . add 6, collect terms
x = 12 . . . . . . . . . . . . . divide by 8
3x° = 3·12° = 36° . . . . . . find the "remote" acute angle
exterior angle = 90° +36°
exterior angle = 126°
__
The exterior angle is the supplement of the one marked (5x-6)°. It is also the sum of the two remote interior angles, 90° and 3x°. Being lazy, we figure that 90 +3·12 is easier to compute than 180 - (5·12 -6). Either way, the exterior angle is 126°.
factor 5x^3 - 2x^2 using the GCF
Answers
Answer:
x^2(5x-2)
Step-by-step explanation:
The gcf of the whole expression is x^2. You then factor out it from the expression to get x^2(5x-2)
If the equation f(x) = 2* is graphed, which of the following
values of x would produce a value closest to the x-axis?
Answers
Answer:
X=-2
Step-by-step explanation:
Beacuse I got it right
Help me please!! ;okxjda.sdfajskndmf
Answers
Answer:
133
Step-by-step explanation:
2(_9)^2=162
3(-9)=-27
2(-9)^2 +3(-9)-2= 162-27-2=133
Is 121,031 divisible by 3?
Answers
The perimeter of a regular decagon is 363m.
State the length of one of its sides.
Answers
Answer:
36.3 m
Step-by-step explanation:
because a decagon has 10 sides so 363 divided by 10=36.3
3-4(12 divided by 6)
Answers
Answer:
The answer is -2
Step-by-step explanation:
First we divide 12 by 6.
12/6 = 2
Next we subtract 3 by 4.
3 - 4 = -1
Now we solve.
-1 * 2 = -2
So, the answer is -2.
Hope this helps! :)
Answer:
3
Step-by-step explanation:
Do 12/6 first and you get 2 and then you do 3-4 and you get 1
I need some help on this
Answers
Answer:
Step-by-step explanation:
Point of intersections of the graph with x-axis are not clear.
Let these points are x = -a, -b and c
Therefore, function representing the graph will be,
f(x) = p(x + a)(x + b)(x - c)
Since, this graph crosses y-axis at (0, -6),
f(0) = p(0 + a)(0 + b)(0 - c) = -6
-pabc = -6
p = [tex]\frac{6}{abc}[/tex]
Therefore, equation of the given function will be,
f(x) = [tex]\frac{6}{abc}(x+a)(x+b)(x-c)[/tex]
help out for these two questions please
Answers
Answer:
23 - A
24 - x = -3 and x = 1
Step-by-step explanation:
Hey There!
So if you didnt know the " zeroes" are the coordinates of where x=0
For the first one the zeroes would be 1 because that's where the line is at x=0
For the second one the zeroes would be x=-3 and x=1 because that's where x=0 if that makes sense