[tex]cos^{-1}[cos(\omega)]\implies \omega \\\\[-0.35em] ~\dotfill\\\\ cos\left( -\frac{\pi }{6} \right)\implies \stackrel{symmetry~identity}{cos\left( \frac{\pi }{6} \right)} \\\\\\ cos^{-1}\left[ cos\left( -\frac{\pi }{6} \right) \right]\implies cos^{-1}\left[ cos\left( \frac{\pi }{6} \right) \right]\implies \cfrac{\pi }{6}[/tex]
why did we use the positive version of π/6?
well, the inverse cosine function has a range of [0 , π], and -π/6 is on the IV Quadrant, out of the range for it, however it has a twin due to symmetry on the I Quadrant, that is π/6, thus the reason.
The angle in the interval (0, pi) whose cosine value is √3 / 2 is π/6 radians.
What is Cosine of an Angle?Cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse of a right angled triangle.
We have to find the angle in the interval (0, π) such that the cosine of the angle is √3 / 2.
We know that, ratio of sides of 30-60-90 triangle is 1 : √3 : 2.
Hypotenuse = 2x
Adjacent side to 30° = √3 x
Cos (30°) = Adjacent side / Hypotenuse
= √3 x / 2x
= √3 / 2
30 degrees is equivalent to 30 × (π/180) = π/6 in radians
Hence π/6 is the angle in the interval (0, π) whose cosine value is √3 / 2.
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Let h = number of hours to bike 165 mi. Let m = number of miles biked in 7 hr. Which proportion can be used to determine the value of h?
Answer:
[tex] \frac{m}{h} = \frac{165}{7} [/tex]
<~~• ¥ Pls HELP me!! ¥ • ~~>
Answer:
A = 16
Step-by-step explanation:
Formula b*h/2
b =8
h =4
so
A= 8*4/2
A = 16
a circle has a diameter of 8 m. what is the circumference? use 3.14 for pie
NEED HELP!! 10 POINTS
Answer:
x = 35,000
y = 30,000
Step-by-step explanation:
5x + 2y = 235,000
2x + 3y = 160,000
Have a nice day! :)
7. If VS = 12 meters, find the length of UT.
=
R
127°
V
S
ogmotor
antolles
W
loonsleder
U
T
The length of arc UT in the diagram given, to the nearest tenth, is calculated as: 3.9 meters.
What is the Length of an Arc?Length of arc = ∅/360 × 2πr
Given the following:
Radius = 1/2(VS) = 1/2(12) = 6 meters
∅ = 90 - (180 - 127) = 37°
Length of arc UT = ∅/360 × 2πr = 37/360 × 2π(6) = 3.9 meters
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ΔABC ο ΔQRS
Find the missing side length, m.
Answer:
m=5
Step-by-step explanation:
If the triangles are similar, the ratios of the side lengths are the same
AB AC
----- = -------
QR QS
6 3
---- = -----
10 m
Using cross products
6m = 3*10
6m = 30
Divide each side by 6
6m/6 = 30/6
m = 5
PLEASE HELP, URGENT!!!!
Find M
Answer:
Step-by-step explanation:
cos^-1(√(111))/2√(37) = 30°
m<C = 30°
As the guest was sneaking away, the groundskeeper was 4 feet (or 48 inches) away and pushed an 84-inch ladder onto the suspect. The very top of the ladder hit the guest on the top of the head. Find the height of the guest in inches the convert to feet.
The height of the guest in inches will be 68.93 and in feet is 5.7.
What is the Pythagorean theorem?It states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
By applying the Pythagorean theorem:-
P² = H² - B²
P² = 84² - 48²
P² = 4725
P = √4725
P = 68.73 inches
Now the height in feet will be 68.73 / 12 = 5.7 feet.
Therefore the height of the guest in inches will be 68.93 and in feet is 5.7.
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Jarrett Webster leased a sports car for $299.50 per month for
60 months. He paid a deposit of $250.00, a title fee of $95.00,
and a license fee of $220.00. What is the total least cost?
Answer: 15.095$
Step-by-step explanation:
Really tired and need help 100 points
Answer:
purple
Step-by-step explanation:
A shoreline is eroding at a rate of 1/3 foot per 2 months how many feet are eroding this year
Answer:
2 feet
Step-by-step explanation:
The shoreline is eroding at 1/3 foot per 2 months. There are 12 months in a year so you multiply 1/3 x 6 and you get 2.
PLEASE PLEASE PLEASE HELP ME!!
Answer:
the answer to the question is D
Answer:
The answer is actually B
Step-by-step explanation:
the top layer is 5 x 5 x 2
the bottom layer is 5 x 2 x 10
5 x 5 = 25 and 25 x 2 = 50
5 x 2 = 10 and 10 x 10 = 100
100 + 50 = 150
30% of 210 is what number?
multiply 30% by 210
210 x 0.30 = 63
answer: 63
please help due soon
Answer:
$4742.10
Step-by-step explanation:
Exponential depreciation formula :-
, where y is the value of good after t years , r is rate of depreciation and A is the initial value.
Given : A= $20800 ; r=10.75%=0.1075
The equation models this situation:
Then, the value of car after t=13 years :-
Hence, the value of car after 13 years = $4742.10
1. Let u (1.-3,2), v= (-1.4.2). Then find b) a unit vector in the same direction of 4v.
4v points in the same direction as v, so all you need to do is normalize v.
Simply multiply it by the reciprocal of its magnitude:
[tex]v = (-1, 4, 2) \implies \|v\| = \sqrt{(-1)^2 + 4^2 + 2^2} = \sqrt{21}[/tex]
[tex]\implies \dfrac{v}{\|v\|} = \dfrac{(-1,4,2)}{\sqrt{21}} = \left(-\dfrac1{\sqrt{21}}, \dfrac4{\sqrt{21}}, \dfrac2{\sqrt{21}}\right)[/tex]
The velocity of v in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop h in feet and the velocity v° in feet per second of the coaster at the top of the hill by the formula v°=[tex]\sqrt{v^{2}-64h[/tex] . What velocity must a coaster have at the top of a 50-foot hill to achieve a velocity of 57 feet per second.
The velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.
What is Velocity?Velocity is the rate of change of its position with respect to time.
[tex]V = \dfrac{dy}{dt}[/tex]
Given the velocity(v) in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop(h) in feet and the velocity(v°) in feet per second of the coaster at the top of the hill by the formula v°=√(v²-64h).
Therefore, the velocity of the coaster at the top should be,
[tex]v^o=\sqrt{(v^2-64h)}\\\\v^o=\sqrt{[57^2-(64\times 50)]}\\\\v^o=\sqrt{49}\\\\v^o = 7\rm\ feet/second[/tex]
Hence, the velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.
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50 points
Use the table to identify values of p and q that can be used to facto
x2 + x - 12 as (x + p)(x + 4).
NEED HELP ASAP
Answer:
-3, 4
Explanation:
x² + x - 12
factorize
x² + 4x -3x - 12
take out common terms
x(x + 4) -3(x + 4)
collect into groups
(x-3)(x+4)
p = -3, q = 4
Answer:
C. -3 and 4
Step-by-step explanation:
In order to factor a quadratic equation in the form [tex]ax^2+bx+c[/tex]
we need to find a pair of numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
Therefore, in order to factor [tex]x^2+x-12[/tex] we need to find a pair of numbers that multiply to -12 and sum to 1.
The only pair of numbers in the table that sum to 1 are:
p = -3 and q = 4
Therefore, the solution is option C.
can you please help me I pay you £50
what is the complete factorization of the polynomial below?
x^3 - 4x^2 + x - 4
Answer:
[tex](x-4)(x^2+1)[/tex]
Step-by-step explanation:
[tex]x^3-4x^2+x-4[/tex][tex]=x^2(x-4)+1(x-4)[/tex][tex]=(x-4)(x^2+1)[/tex]Two events can have a strong, weak, or no correlation.
True or false
Find the total amount
$1580 is compounded daily at a rate of 10% for 7 years. Let 1 year = 365 days.
Answer:
$3181.42
Step-by-step explanation:
The balance of an account earning compound interest is given by the formula ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r for t years, compounded n times per year.
__
You have P=1580, r=0.10, n=365, t=7, so the balance is ...
A = $1580(1 +0.10/365)^(365×7) ≈ $3181.42
_____
Additional comment
Your graphing calculator may have a financial function that will calculate this for you.
in the triangle below CFED is a rectangle. If the measure of CFD= 4x and the measure of DFE is 5x, find the value of x
PLEASE ANSWER ALOT OF POINTS
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations or lines A and B have? Explain your answer.
Part B: What is the solution to the equations of lines A and B? Explain your answer.
Answer:
Part A 1 solution
Part B 1,4
Answer:
Part A : It has one solution because the lines intersect at one point
Part B : The solution is the points where the lines intersect
Which is (3,4)
Find the value of x. Geometry Magic 20 set 3
Answer:
The value of x is 64.
Step-by-step explanation:
The base angles of an isoceles triangle are congruent.
[tex]x + 58 + 58 = 180[/tex]
[tex]x + 116 = 180[/tex]
[tex]x = 64[/tex]
Write a recursive formula for the sequence 7, 4, 1, -2, -5, .... Then find the next term.
A. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = -8[/tex]; 7
B. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = 7[/tex]; -8
C. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = -3[/tex]; 22
D. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = 7[/tex]; -8
Answer:
option B
Explanation:
Recursive Formula: aₙ = aₙ₋₁ + d
Given Sequence: 7, 4, 1, -2, -5,....
Identify the common difference:
second term - first term
4 - 7 = -3 or 1 - 4 = -3 or -2 - 1 = -3
So formula:
[tex]\sf a_n = a_{n-1}-3[/tex], where [tex]\sf a_1 = 7[/tex]
Find next term:
[tex]\sf a_6 = a_{6-1}-3 = -5-3 = -8[/tex]
X+8
What is the solution of 5x=T > 0?
XS-8 Or X2 }
L
X <-8 or X › 5
-8≤x<5
-8
PLEASE HELP
Answer:
but good luck with that man
hehe i finished also what is 856 x 925? i'ma take a nap now
Answer:
791,800
Step-by-step explanation:
Answer: 791800
Step-by-step explanation:
HELP PLEASE ILL MARK BRAINLIEST WHEN I CAN
Answer:
216 degrees
Step-by-step explanation:
To convert radian measure to a degree, substitute 180 degrees in for pi.
6(180)/5=216 degrees
Therefore, your answer is 216 degrees
If A is a prime factor of 36, and B is a prime factor of 15, what is the greatest possible difference between A and B?
Answer:
3
Step-by-step explanation:
Prime factorization
36 = 3 * 3 *2 * 2
15 = 3 * 5 The biggest difference is 5 -2 = 3
iris is a sales woman whose base pay plus commissions amounted to $69,464 last year. if her base pay was 39,710 and she made $78,300 in sales last year, what was her rate of commission?
Answer:
Iris is a saleswoman whose base pay plus commissions amounted to $69,464 last year. If her base pay was $39,710 and she made $78,300 in sales last year,
what was her rate of commission?
Commissions were $29,590 against sales of $78,300
Her rate of commission was 37.79%
Step-by-step explanation:
