arccos(2x) + arccos(x) = π/2
Apply cos to both sides, then expand the right side using the identity I mentioned in a comment:
cos(arccos(2x) + arccos(x)) = cos(π/2)
cos(arccos(2x)) cos(arccos(x)) - sin(arccos(2x)) sin(arccos(x)) = 0
Now think of arccos(2x) and arccos(x) as angles in two right triangles. Let θ = arccos(2x) and φ = arccos(x) (and let's also assume that both have measure between 0 and π/2). These are angles such that
cos(θ) = 2x
cos(φ) = x
In these triangles, you then have
sin(θ) = sin(arccos(2x)) = √(1 - 4x ²)
sin(φ) = sin(arccos(x)) = √(1 - x ²)
while
cos(θ) = cos(arccos(2x)) = 2x
cos(φ) = cos(arccos(x)) = x
So the original equation is transformed to
2x ² - √(1 - 4x ²) √(1 - x ²) = 0
Solve for x :
2x ² = √(1 - 4x ²) √(1 - x ²)
(2x ²)² = (√(1 - 4x ²) √(1 - x ²))²
4x ⁴ = (1 - 4x ²) (1 - x ²)
4x ⁴ = 1 - 5x ² + 4x ⁴
0 = 1 - 5x ²
x ² = 1/5
x = ± 1/√5
Now bearing in mind that we assume 0 < φ < π/2, we should have cos(φ) = x > 0, so we take the positive solution,
x = 1/√5
The Boeing777-300ER flies between Auckland and Los Angeles. It has 246 Economy
class seats, 50 Premium Economy seats and 44 Business Premier seats. Out of the 340
seats in total, what percentage are Economy seats?
Answer:
72.35%
Step-by-step explanation:
246/340 = .723529
Just multiply it by 100 to get the percentage
.723529 x 100 = 72.3529
Not looking for answer but does anyone know this specific topic in math
Answer:
This is called system of equations.
Step-by-step explanation:
This combines two equations and then lines them up to a system.
Answer:
Step-by-step explanation:
matrix
or
vector geometry
I need help make sure to round it to the nearest 10th
Answer:
10.52
Step-by-step explanation
Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.
A. 13
B. 15
C. 16
D. 25
Answer:
A. 13
Step-by-step explanation:
2(x - 3) + 3y
2(5 - 3) + 3×3
2× 2 + 3×3
4 + 9
13
Answer:
The correct answer is A
Step-by-step explanation:
2(x-3) + 3y so you replace them and get 2( 5 - 3) +3(3)
next,
you would solve it
2 x 5 and 2 x 3 you get 10-6 + 9, the 9 is from multiplying 3 by 3
finally you solve it
10-6 = 4 +9
= 13!
Solve for x: -5 < 8x + 11 < 19
Answer:
-2<x<1
Step-by-step explanation:
-5 < 8x + 11 < 19
Subtract 11 from all sides
-5-11 < 8x + 11-11 < 19-11
-16 < 8x<8
Divide by 8
-16/8 < 8x/8 <8/8
-2<x<1
find the area of the following composite figure
find the ratio in lowest term b 750m and 1km
Answer:
4m/3m
Step-by-step explanation:
1km = 1000m
750m : 1km
750m : 1000m
Reduce ratio in simplest form.
HCF of 1000 and 750 is 250
750 ÷ 250 / 1000 ÷ 250
= 4/3
Hence, the simplest form of the ratio 750m : 1km is 4m/3m
Factorize no g, h, j, k, m, n
answer =
=3a²-16ab+13b²
=3a²-(13+3)ab+13b²
=3a²-13ab-3ab+13b²
=a(3a-13b)-b(3a-b)
=(3a-13b)(a-b)
Answer:
even I got confused in question no. j
no worry rest all are solved .
all the questions are solved by middle term splitting method .
1/5 of a certain number is added to 5½ the same as when ⅙ of the number that is subtracted from 30⅖find the number
Step-by-step explanation:
1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n
make the 3rd term an improper fraction
1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n
multiply equation by 30, cancel the denominators, resulting in:
6n + 6(51) = 6(152) - 5n
6n + 306 = 912 - 5n
6n + 5n = 912 - 306
11n = 606 is the number
n = 606/11
n = 55 1/11
Answer:
68
Step-by-step explanation:
let unknown number be x
⅕x + 5½= 30⅖ - ⅙x
⅕x + 11/2= 152/5 - ⅙x
collect like terms
⅕x+⅙x= 152/5 - 11/2
[tex] \frac{11}{30}x = \frac{249}{10} [/tex]
cross multiply
30 * 249=(11 * 10)x
7470=110x
x=7470/110
x= 68
which inequality is represented on the number line shown?
Answer:
A
Step-by-step explanation:
b/ of shaded region can make to closed inequality & it's not closed to make open inequality.
This two-way frequency table shows the results of a survey of users of the mass-transit system in a city. People were asked their age and whether they used the system regularly (three or more times per week).
Answer:
if Q={1,3,5,7,9}Express it in description methods
Answer: With the condition that age is 30 or under, the sample space is restricted to the first column. This simplifies the problem to:
P(uses mass transit |age is 30 or under) = 125/575=0.217
Step-by-step explanation:
edmentum
our of 1000 new born
babies, there are 514
boys, what will be the
empirical probability
the newly born baby is
(i) a boy (ii) a girl
Look a view at this picture
. Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world. It rises 450 ft over a horizontal distance of 1,000 ft. a. What is the percentage grade of this hill? Round to the nearest tenth of a percent.
Answer: 50%
Step-by-step explanation:
From the question, we're given the information that Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world and that it rises 450 ft over a horizontal distance of 1,000 ft.
Therefore, the percentage grade of this hill will be calculated as the height over the length and this will be:
= 450/1000 × 100
= 45%
= 0.45
= 0.5 to nearest tenth
= 50% to nearest tenth.
Someone help me on this, thats my illustration for it its a lil long
The uppercase letters are the angles, while the lowercase letters are the sides. We have side 'a' opposite angle A, side b opposite angle B, side c opposite angle C.
We have this given info:
A = 25a = 13.2b = 25.5Let's use the law of sines to find angle B
sin(B)/b = sin(A)/a
sin(B)/25.5 = sin(25)/13.2
sin(B) = 25.5*sin(25)/13.2
sin(B) = 0.81642164
B = arcsin(0.81642164) or B = 180 - arcsin(0.81642164)
B = 54.72817392 or B = 180 - 54.72817392
B = 54.72817392 or B = 125.27182608
When rounded to the nearest whole degree, we get B = 55 or B = 125.
However, I'll use the slightly more accurate values of B for the next two sections.
---------------------------------------
Let's consider the case that B = 54.72817392
This would have to mean
A+B+C = 180
C = 180-A-B
C = 180-25-54.72817392
C = 100.27182608 which rounds to C = 100
Through the law of sines we can say
c/sin(C) = a/sin(A)
c = sin(C)*a/sin(A)
c = sin(100.2718 2608)*13.2/sin(25)
c = 30.73327084 which rounds to c = 30.7
One solution is
A = 25, B = 55, C = 100
a = 13.2, b = 25.5, c = 30.7
As you can probably guess, the phrasing "solve the triangle" means find all sides and angle measures.
---------------------------------------
Now we'll consider the case that B = 125.27182608
We follow the same steps as the previous section
A+B+C = 180
C = 180-A-B
C = 180-25-125.27182608
C = 29.72817392 which rounds to C = 30
and
c/sin(C) = a/sin(A)
c = sin(C)*a/sin(A)
c = sin(29.72817392)*13.2/sin(25)
c = 15.48842618 which rounds to c = 15.5
The other solution is
A = 25, B = 125, C = 30
a = 13.2, b = 25.5, c = 15.5
Check out the diagrams below.
Match all the part of the circle to their correct name.
1. YW
2. Q
3. WX
4. W
5. ST
6. VQ
7. TW
a. Center
b. Secant Line
c. Chord
d. Radius
e. Point of Tangency
f. Diameter
g. Tangent Line
Answer:
halo
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
please mark brainliest???
The correct matches are,
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
What is diameter?In geometry, a diameter of a circle exists as any straight line segment that passes via the center of the circle and whose endpoints lie on the circle. It can also be described as the longest chord of the circle. Both descriptions exist also valid for the diameter of a sphere.
The correct matches are,
1. YW - chord
2. Q - center
3. WX - tangent line
4. W - point of tangency
5. ST - secant line
6. VQ - radius
7. TW - diameter
To learn more about diameter refer to:
https://brainly.com/question/23220731
#SPJ2
Hello! I have an algebra 1 dba tomorrow (flvs). I am just a little nervous and want to be a little more prepared. Does anybody know what questions I will be asked? Btw this is for algebra 1 module 4. Thank you :)
Answer:
Im not sure what is in the algebra 1 module 4 but for algebra 1 you should study how to graph equations, solve system of equations with substitution and elimination. those topics, at least for e, have been a little tricky
Step-by-step explanation:
Trong mặt phẳng tọa độ cho tam giác ABC biết các đỉnh A(-1,2), B(4,7) và trọng tâm tam giác G(3,2). Viết phương trinh đường thẳng d chứa đường cao đi qua A của tam giác ABC
What is the value of the expression below when w=2 and x=2
9w - x
Here, all we need to do is subtitute w = 2 and x = 2 into the expression, by multiplying and adding. First, we will muliply 9w:
9w
9 · w =
9 · 2 =
18
Now, all we have to do is use our answer for 9w, and subtract x from it:
9w - x
18 - (2) =
18 - 2 =
16
So, our answer is 16.
Let me know if you have any other questions! :)
what is the electrical work done in a circuit
Answer:
a open and close switch and a condentation out put.
find x. A. 21√2 B. 7 C. 21√3 over 2 D. 21√2 over 2
Answer:
D
Step-by-step explanation:
for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio
sin60=opposite/hypotenuse
sin60=a/7√3
a=10.5
then after you have found the adjacent you can use the cos ratio
cos45=adjacent/hypotenuse
cos45=10.5/x
cos45x/cos45=10.5/cos45
x=14.849
which is the same as 21√2 over 2
I hope this helps
Answer:
D
Step-by-step explanation:
Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2a = 21 ( divide both sides by 2 )
a = [tex]\frac{21}{2}[/tex]
Using the cosine ratio in the right side triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{a}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = [tex]\sqrt{2}[/tex] a = [tex]\sqrt{2}[/tex] × [tex]\frac{21}{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → D
Use the parabola tool to graph the quadratic function f(x)=(x−5)2+1 . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
Vertex (5, 1)
Example of second point (4, 2)
Step-by-step explanation:
THe equation given is in vertex form so it will be easy to find the vertex
(x-5)^2+1
Vertex is at h,k and vertex form is y = a(x−h)^2 + k
x coordinate will be 5
y coordinate will be 1
vertex - (5, 1)
You can plot a second point by plugging in any number into the x or y
For example, if you set x to be 4,
(4-5)^2+1
1^2+1
1+1=2
which is the graph of g(x) = sqrt x-16
Answer:
Step-by-step explanation:
I am not sure if you are asking for the graph of
√(x-16) that has a x intercept at (16,0)
or
√ x -16 that has a y intercept at (0, -16)
Best answer gets brainliest and 5 stars
Answer:
No, because 6² + 8² ≠ 12²
Step-by-step explanation:
In a right angled triangle,
Perpendicular² + Base² = Hypotenuse² (pythagoras theorem)
But in the given triangle; 6² + 8² ≠ 12²
36 + 64 ≠ 144
100 ≠ 144
Perpendicular² + base² ≠ hypotenuse²
Thus the given triangle is not right angled.
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
Find the approximate side length of a square game board with an area of 128 in2. HELP PLZ
Answer:
The side length is approximately 11.3 inches
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
128 = s^2
Take the square root of each side
sqrt(128) = sqrt(s^2)
11.3137085= s
The side length is approximately 11.3 inches
Answer:
11.3
Step-by-step explanation:
Formula for square: x^2 = A
Plug in:
x^2 = 128
√x^2 = √128
x = 11.3
Hope this helped.
plz help me to slove this
Answer:
50
Step-by-step explanation:
= 3^3 + (2 x 2 x 3) + 2^2 + ( 3 + 2)^5
= 3^3 + (12) + 2^2 + (3 + 2)^5
= 3^3 + 12 + 2^2 + (5)^5
= 9 + 12 + 2^2 + 5^5
= 9 + 12 + 4 + 5^5
= 9 + 12 + 4 + 25
= 50
Write the polynomial in standard form 8-5x+x^3-2x^4
Answer:
-2x^4+x^3-5x+8
Step-by-step explanation:
8-5x+x^3-2x^4
Write the polynomial from highest powers of x to lowest
-2x^4+x^3-5x+8
If g(x) = 2(x − 4), find the value of x if g(x) = 20
Answer:
x=14
Step-by-step explanation:
g(x) = 2(x − 4)
Let g(x) = 20
20 = 2(x − 4)
Divide each side by 2
20/2 = 2(x-4)/2
10 = x-4
Add 4 to each side
10+4 = x-4+4
14 =x
PLS HELP ME ON THIS QUESTION!!!
Answer:
210 in³
Step-by-step explanation:
length = 10 in
Width = 7 in
Height = 3 in
Volume of rectangular prism = length * width * height
= 10 * 7 * 3
= 210 in³
Answer: Option D
210 in³
Volume of Rectangular prism = lwh
Height = 3in
Width = 7in
Length = 10in
Volume = 10(7)(3)
Volume = 210 in³
Must click thanks and mark brainliest
Mr.Swanson drove 150 miles in 4 hours how many miles will he drive in 1 hour
Answer:
37.5 miles
Step-by-step explanation:
Distance covered in 4 hours = 150 miles
Distance covered in 1 hour = 150/4 = 37.5 miles
