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
Question 15 of 26
A triangular portion of a baseball field is marked as shown below. To the
nearest tenth, what is the length of the side labeled c?
B
с
4 yds
329
28
С
A
'
Triangle not drawn to scale
O A. 3.5 yds
O B. 4.1 yds
C. 2.8 yds
D. 4.5 yds
Answer:
3.5 yards
Step-by-step explanation:
The value of c in the triangle ABC is 3.5 yds, Option A is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is ABC.
We have to find the length c in the triangle.
Now let us use sine rule to find the value of c.
c / sin 28° = 4 / sin 32°
The value of sin 28° is 0.4695 and sin 32° is 0.5299
c / 0.4695 = 4 / 0.5299
Apply cross multiplication
c × 0.5299 = 4 × 0.4695
c × 0.5299 = 1.8636
Divide both sides by 0.5299
c = 1.8636/0.5299
c = 3.516
= 3.5 yds
Hence, the value of c in the triangle ABC is 3.5 yds, Option A is correct.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ7.
Which of the following questions is a statistical question
Hi there!
»»————- ★ ————-««
I believe your answer is:
The first question.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
Statistical questions have answers in which data varies. The first question, "How many sticks of gum can you chew at one time?" can be statistical because not all people can chew the same number at one time. Some can chew 2 sticks, others can chew 3 or 4.The other three questions can be answered with a fixed number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Determine if the expression 3c^5+7c^-1-c is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer: It's not a polynomial
It's not a polynomial because the exponent of -1 in the second term. The exponents for any polynomial must be nonnegative whole numbers {0,1,2,3,...}
Lai Yee and Khadijah have 60 stamps. When Lai Yee gives 5 stamps to Khadijah, the number of Lai Yee's stamps is twice the number of Khadijah's stamps. How many stamps does each of them have at first?
Answer:
Lai yee : 45
Khadijah : 15
Step-by-step explanation:
Here is the Explanation
Find the 6th term of the arithmetic sequence – 2 – 2,-43 +1, -72 +4, ...
Answer:
Sum = 9a + 45d = 108. Or a + 5d = 12. Hence 6th term = 12. SUFFICIENT.
46 x 53 please show with work or something
Answer:
2,438
Step-by-step explanation:
53
46
______
318
212
_______
2438
6 times 3 is 18. Put the 8 in the ones place and carry the 1 ~ 6 times 5 is 30. Add the carried 1 and you have 31. Put that next to the 8. ~ 4 times 3 is 12. put the 2 under the 1 in 318 and carry the 1. ~ 4 times 5 is 20. Add the carried 1 and you have 21. ~ Put that next to the 2. Now add 318 to 2120 and you have the answer of 12438.
please help asap it's important!!!
Answer:
486cm^2
Step-by-step explanation:
Surface area of cube = (6a^2)
6×9×9=486.
Solve this system of equations with matrices. x – 5y – 4z = 15 -3x +2y + 3z = -6 4x + 8y – 2z = 3
Answer:
x = 59/10, z = 237/70, and y = -121/70
Step-by-step explanation:
____________ show the frequency of data.
A. dot plots
B. bar graphs
C. all of these
D. line plots
2 square5 + 5 square5
Answer:
=2^5+5^5
=32+3125
=3157
I need help ASAP!! Please explain how to solve the question
Answer:
318
Step-by-step explanation:
Let's divide this shape into 2 triangles & 3 rectangles.
Area of Triangle = 1/2 (bh)
(1/2 (9x6) ) x 2 = 54
Area of Rectangles = (9x11) + (8x11) + (7x11)
= 264
264 + 54 = 318km^2
Answered by g a u t h m a t h
Mary can do a job in 80 minutes, Working with Jané, both can do the job in 30
minutes. How long will it take Jane to do the job alone?
Answer:
see below
Step-by-step explanation:
The equation to determine the work time is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/80 + 1/30 = 1/c
Multiply by the least common denominator to clear the fractions, which is 240c
240c(1/80 + 1/30 = 1/c)
3c+8c = 240
11c = 240
Divide by 11
11c/11 =240/11
c = 240/11 minutes
c=21.81818
Approximately 22 minutes
If you have to invest in an account that pays 5.3 compound annually, after 10 years how much interest is earned
[tex]\\ \sf\longmapsto Interest=Rate\times Time[/tex]
[tex]\\ \sf\longmapsto Interest=5.3(10)[/tex]
[tex]\\ \sf\longmapsto Interest =53[/tex]
It means that if your principal is $100 after 10years you will receive $53 as interest
Step-by-step explanation:
[tex]thank \: you[/tex]
Question 3 of 10
Which method for calculating credit card balances is best for consumers who
make large payments?
A. Average monthly balance method
B. Previous balance method
ОООО
C. Average daily balance method
D. Adjusted balance method
SUBMIT
Answer:
D. Adjusted balance method
Step-by-step explanation:
1)An average American human lives about 78.74 years. A survey gave an average time spent going to the bathroom to be 102 minutes per week. If there are 52 weeks in a year, 7 days in a week and 1 day is 24 hours, then how many minutes do Americans spend on the toilet in their life time?
2)How many minutes have you spent on going to the bathroom if you are at the age of 16?
HELP ILL GIVE BRAINLIEST
Answer:
C. 4
Step-by-step explanation:
The graph seems to start at y=4, and decreases.
multiple the following
[tex] \frac{18}{15} \times \frac{25}{12} [/tex]
Answer:
5/2
Step-by-step explanation:
(18/15)*(25/12)=(18*25)/(15*12)=450/180=5/2
It is Keke’s birthday, and her parents want to surprise her with a room full of balloons. Use the Fermi process
to estimate the number of balloons needed to fill Keke’s living room. Assume the living room is a rectangular
prism with a length of 30 feet, a width of 45 feet, and a height of 11 feet. Assume the balloons are spheres
with a radius of 0.45 feet. Show your work
Answer:
im not sure sorry .
Step-by-step explanation:
a boy rode his bike at an average speed of 11 kilometers per hour . how much far did he ride in four hours
Step-by-step explanation:
The answer is mentioned above.
Hope it helps.
An athlete throws her javelin 9.5 yards. She throws it this distance 2 times. How far she throw her javelin in total
Answer: 19 yards
Step-by-step explanation: 9.5x2=19
What is the height of the building?
(33.85307637623) = 33.9m
the answer is option d
Evaluate the expression for c = 11.
-1 - C=
Answer:
c=-12
Step-by-step explanation:
place 11 in for C > -1-11=
subtract 11 from -1. -12
A school bus has seating for 75 students. There are 13 buses at a school. What is the maximum number of students
the buses can seat
225 students
750 students
975 students
985 students
Help
Answer:
75 students and 13 buses are just 75 x 13
975 students
Step-by-step explanation:
75 x 13 = 975
Find the number if 20% of 64 is 10% of it?
Answer:
128
Step-by-step explanation:
20% of 64
= 0.2 × 64 = 12.8
10% = 12.8 , then
100% = 12.8 × 10 = 128
Answer:
The number is 128
Step-by-step explanation:
Let the number be represented by X
Therefore
20/100*64=10/100*X
---10X=1280
Now dividing both sides of the equation by 10 it will be
=10X/10=1280/10 which is
---X=128
Therefore the number is 128
please help asap don't give me the wrong answers.
Answer: 340cm^
Step-by-step explanation:
you have to multiply them to find out
Write the mixed numbers as fractions.
-1\1/2
Answer:
3/2
Step-by-step explanation:
1 1/2= 1 x 2 + 1
= 3/2
Which classification describes the following system of equations?
(12x+5y-32= 36
x-2y + 4z = 3
9x-10y + 5z = 27
Answer:
(12x+5y-32=36
12x-x+5y-2y-32=36
4 is a square number and also an even number. How many other whole numbers less than 50 are an even, square number?
Find the area of the region bounded by y=1/x^2, y=4, and x=5. Use any method/
Answer:
81/5
Step-by-step explanation:
See image.
I always think drawing these out helps.
I had to find lower limit for x by finding when 1/x^2=4
x^2=1/4
This implies x=1/2 since in the picture x is positive.
We need to evaluate
Integral( 4 - 1/x^2 , from x=1/2 to x=5)
Or
Integral( 4 - x^-2 , from x=1/2 to x=5)
=4x+x^-1 ] from x=1/2 to x=5
(4×5+5^-1)-(4×1/2+(1/2)^-1)
(20+1/5)-(2+2)
20-(2+2)+1/5
20-4+1/5
16+1/5
81/5
If a state issued license plates using the scheme of two letters followed by four digits, how many plates could it issue?
Answer:
Combining these results, it follows that there are 676 x 1000 = 676,000 different license plates possible.
