Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.
sin(2sec^-1 u/10)
Answers
Answer:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Step-by-step explanation:
We want to write the trignometric expression:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]
As an algebraic equation.
First, we can focus on the inner expression. Let θ equal the expression:
[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]
Take the secant of both sides:
[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]
Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:
[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]
By substitutition:
[tex]\displaystyle= \sin(2\theta)[/tex]
Using an double-angle identity:
[tex]=2\sin(\theta)\cos(\theta)[/tex]
We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:
[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]
Simplify. Therefore:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Related Questions
Water in a 14mm diameter pipe flows at 2m/s. How many liters flow along the pipe in 1 minute
Answers
Answer:
The flow rate will be say around 10000 liters per hour. Or 180 liters per minute.
Step-by-step explanation:
PLEASE HELP ME FAST, I ASKED THIS ALREADY AND ALL I GOT WAS ONE OF THOSE SCAM LINKS :( IF YOU GIVE AN EXPLANATION I CAN GIVE YOU BRAINLIEST!
Two angle measures in a triangle are 47° and 43°. What type of triangle is it?
Also, I just wanted to say that I can only give brainliest if two people answer. Thank you!
Answers
Answer:
Right triangle
Step-by-step explanation:
Answer:
Right triangle
Step-by-step explanation:
To find the third angle, we add the two known angles.
47 + 43 = 90
The sum of all the angles of a triangle is always 180.
Therefore, we subtract 90 from 180 to find the third, unknown angle.
180 - 90 = 90
Because 90 degrees is the third angle, and 90 degrees is a right angle, this is a right triangle.
Find the measure of <4.
{{
24
158°
KE
* 4 = [?]
Answers
<4=22°
Answer:
<4+158=180 co interior angle
<4=180-158=22°
Answer:
solution given:
<4+<158°=180°[co- interior angle]
<4=180°-<158°=22°
<4=22° is your answer
What is the solution set for this inequality?
-8x + 32 -16
x < 6
x > 6
x > -2
x < -2
Answers
Answer:
x>-2
Step-by-step explanation:
-8x+32-16<0
-8x<16
divide both sides by -8
x>-2
that's because when you divide by a negative your inequality sign changes
Find the product. 2 (-5)
Answers
Answer:
-10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
a positive times a negative is a negative number
and 2 x 5 is 10
so it`s -10
What is the value of 3x + 5y, when x = 12 and y = 4? 24 А B В 48 C 56 D 72
Answers
Answer:
C is the answer
Step-by-step explanation:
All you have to do is plug 12 in for x and 4 in for y
3(12) + 5(4) = solve
36 + 20 = 56
Hope that helps
x
What are the perimeter and area
of a square with side length of 12 in.?
A. P= 24 in., A = 24 in.?
B. P= 144 in., A = 48 in.2
O
C. P = 24 in., A = 144 in.2
O
D. P= 48 in., A = 144 in.2
Answers
Answer: P = 48 in, A = 144 in.2
Step-by-step explanation: Since a square has equal sides and we know one side length is 12 inches, then all the sides are 12 inches. For perimeter, we add all sides, which would equal 48 and for area, we multiply 2 of the sides, which would be 144.
A picture of Margo's garden is shown below. It is made of 2 rectangular prisms. She wants to fill it with dirt. She needs to find the volume of the garden to know how much dirt to buy.
9 cubic feet
10 cubic feet
98 cubic feet
107 cubic feet
Answers
Answer:
9 cubic feet
Step-by-step explanation: You multiply them all then divide 9 by the greatest number that fits in 10710111011/111 binary division
Answers
Answer:
91090.1891892
Step-by-step explanation:
rounded it would be 91090
The sum of 9 and a number is less than 12. Which of the following inequalities expresses the solutions ?
Answers
Mrs. Wilson Shared 63 stickers equally among 4 girls and 5 boys.How many stickers were in each share?
Answers
Answer:
7 stickers for each kid
Step-by-step explanation:
Maria is 4 ft 2in tall. To find the height of a flagpole, she measured her shadow and the pole's shadow . What is the height h of the flagpole?
Answers
Answer:
25 ft
Step-by-step explanation:
The height of the flagpole, using trigonometric ratio is 25feet.
The tangent of angle C will be the ratio of Maria's height to her shadow.
What is the tangent of an angle?The tangent of an angle is the ratio of opposite side to the adjacent side.
It is given that,
Her height = 4 ft 2 inch = 25/6 feet
Length of her shadow =10/3 feet
So, tan C = (25/6)/(10/3)
tan C = 5/4
We know that ∠C and ∠T will be equal
So, tan C = tan T = h/20
5/4 = h/20
h =25
Therefore, The height of the flagpole, using is 25feet.
To get more about trigonometric ratios visit:
https://brainly.com/question/24349828
6x+2+11x+8=180 what's the value of x?
Answers
-10 -10
——————-
17x=170
————
17 17
x=10
Answer:
x=10
Step-by-step explanation:
If we roll 40 times, how many rolls would you expect to win?
Answers
Answer:
what
Step-by-step explanation:
ok first of all roll what. If its a coin you will expect to win 20 times . if its a dice than it will be around 6.67 times.
The lengths of nails produced in a factory are normally distributed with a mean of 4.95 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 5% and the bottom 5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answers
Answer:
The length that separates the bottom 5% is of 4.87 centimeters.
The length that separates the top 5% is of 5.03 centimeters.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 4.95 centimeters and a standard deviation of 0.05 centimeters.
This means that [tex]\mu = 4.95, \sigma = 0.05[/tex]
Bottom 5%:
The 5th percentile, which is X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 4.95}{0.05}[/tex]
[tex]X - 4.95 = -1.645*0.05[/tex]
[tex]X = 4.87[/tex]
The length that separates the bottom 5% is of 4.87 centimeters.
Top 5%:
The 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 4.95}{0.05}[/tex]
[tex]X - 4.95 = 1.645*0.05[/tex]
[tex]X = 5.03[/tex]
The length that separates the top 5% is of 5.03 centimeters.
I need help on number 26
Answers
Answer:
The number of required shelves is 5
You have to find the HCF of 45, 105, and 75.
footballs=21
small cars=15
For Howards science experiment he needs 69 blocks that each have a mass of 0.5 kilograms. Is the total mass of the blocks 3.45 kilograms, 34.5 kilograms, or 345 kilograms?
Answers
Just take 69 blocks and times by 0.5
The list shows the number of pages in various novels: 286,295,307,241,396,368 what is the range
Answers
Answer:
155
Step-by-step explanation:
You must first subtract the lowest number (241) from the highest number (396) Then you get 155! I hope this helps!
Consider the following number line:
B
C
A+
11
=>
1
0
Drag the following cards to match each point to its value.
Point Value
А
1
5
B
0.8
3
5
Answers
Answer:
The pink A goes to the Green C on the number line. the green C goes to the pink A on the number line. The Blue B goes to the Blue B in the number line.
Step-by-step explanation:
hope it helped ;)
Andrew has $550 in a savings account that earns 5 % annually. How much will he earn in interest in 4 years?
Use the formula = , where is the interest earned, is the principal (starting amount), is the interest rate expressed as a decimal, and is the time in years.
Answers
$110
Step-by-step explanation:
formula= P×T×R ÷ 100
550×4×5÷100
55×4×5÷10
1100÷10
$110
Darren has traveled
2/3
of his total trip. He has traveled 21 miles so far. How many more miles does he have to travel?
Answers
Answer:
The answer is 7 miles
Step-by-step explanation:
2/3 × 21 = 14
21-14 = 7
WILL MARK BRAINLIST!!
simplify: 3/4 × 2x/5
Answers
Answer:
(3/10)x or if you didn’t undertsand that
[tex]\frac{3}{10}x\\[/tex]
Step-by-step explanation:
So multiplynormally, if theres an x in the numerator or denominator , it doesn’t matter since the variable is going to end up in the middle. Multiply it normally, simplify and then you would have (3/10)x
on the first one shows you how to solve it then second one is the problem just tell me the answer pls have a good day bye
Answers
Answer:
1/2 + 10/12. = 1/2 × 6/6 =6/12. 6/12 + 10/12 =16/12. 16/12 = 1 4/12 = 1 1/3
The LCM of 5 and 6 is ______. Numerical Answers Expected!
Answers
Answer:
30
Step-by-step explanation:
Answer:
30.
Step-by-step explanation:
2 x 3 x 5 = 30
Where does the graph of cosine begin?
Answers
9514 1404 393
Answer:
wherever you want it to
Step-by-step explanation:
The cosine function is defined for all real numbers. A graph of it can exist on any interval from -∞ to +∞. Since you make the graph, and it is impossible for you to graph x = -∞, the left side of the graph (where it "begins") will be the point you decide to use to start graphing.
HELP FAST PLZ
The same house costing $500,000 with the 15-year mortgage and the APR of
4.5% would have what amount for its first month's principal payment?
Answers
Answer:
Step-by-step explanation:
How much would the mortgage payment be on a $500K house? Assuming you have a 20% down payment ($100,000), your total mortgage on a $500,000 home would be $400,000. For a 30-year fixed mortgage with a 3.5% interest rate, you would be looking at a $1,796 monthly payment.
Help with number two please:)
Answers
Well 6x3=18
So 5x3=15
How many ways can you arrange the letters in the word MARBLE if the letters B and L have to
stay together?
Answers
Answer:
I thought of 10
Step-by-step explanation:
Ambler, blamer, ramble, amble, blame, abler, blare, blear, blam, blae
Find x and y thank you for you’re help
Answers
Answer:
y = 18
x = 15.588
May I have some help with this please?
Answers
f(x) = |7m + 4| = 1
First equation by taking positive modules
7m + 4 = 1
7m = -3
m = -3/7 . Ans.
Second equation by taking negative modules
-7m - 4 = 1
-7m = 5
m = -5/7 . Ans.
∴ m = [ -5/7 U -3/7 ] Ans .