Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.
sin(2sec^-1 u/10)
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]
Triangle LMN, shown below, is a right triangle.
L
13
5
N
M
12
Which of the following is equivalent to sin L?
PLEASE ANSWER I NEED HELP!!
9514 1404 393
Answer:
D cos(N)
Step-by-step explanation:
In case you haven't remembered the fact that the sine of an angle is equal to the cosine of its complement (the other acute angle in a right triangle), you can always go back to the definitions.
Sin = Opposite/Hypotenuse
sin(L) = NM/NL
and
Cos = Adjacent/Hypotenuse
cos(N) = NM/NL = sin(L)
The equivalent of sin(L) is cos(N).
Use a formula to find the are.
George pass on the way to school distance 200 meters in 165 seconds. What is
his average walking speed in m/s?
Answer:
1.21212121212 or average of basically 1 meter per second
Step-by-step explanation:
Formula: distance over time
Take distance and divide that by time you would get the answer.
Answer 6. Answer ASAP pls pls answer ASAP ASAP pls pls ASAP pls pls ASAP
Answer:
2
Step-by-step explanation:
5x10=50
5x2=10; 10x2=20
10x20=200
find the volume of the cone. use 3.14 for pi. round decimal answers to the nearest tenth. diameter= 24ft height= 8ft
If A is an event that will never happen, then P(A)=
Answer:
0
Step-by-step explanation:
If A is an event that will never happen, then P(A)=0
Please help! What is the volume of the cone?
Answer and explanation please! <3
Answer: V≈804.25
Step-by-step explanation:
V=πr2h
3=π·82·12
3≈804.24772
A rectangular prism has a height of 5 meters a length of 8 meters and a width is 9 meters. What is the volume of the prism
The area of a square can be found using the equation A = s², where A is the area and s is the measure of one side of the square.
Match the equation for how to solve for the side length of a square to its description.
Drag the equation into the box to match the description.
--------------------------------------------------------------------------------------------------------
[ A square has an area of 99 in² ][ - ]
--------------------------------------------------------------------------------------------------------
A.) s=/99in
B.) s=(99)^2in
C.) s=99in
Answer:
s= √99 in.
Step-by-step explanation:
Given the function h(x) = 2.25x, find h(2)
Answer:
h(2)= 4.5
Step-by-step explanation:
h(x)=2.25x
h(2)=2.25(2)
= 4.5
Answer:
Hi! The answer to your question is 4.5
Step-by-step explanation:
To find h(2) we just have to find x in the equation and replace it with a 2
h(x)=2.25(2)
h(x)=2.25(2)=4.5
※※※※※※※※※※※※
⁅Brainliest is greatly appreciated!⁆
- Brooklynn Deka
Hope this helps!!
Hello pls help will give good old BRAINLYEST YAY
Answer:
D
Step-by-step explanation:
The mean, median, and mode all are 3
Someone needs to hear this. So here it is. God will pull you through. You just need to have faith. You just have to keep going. Do not give up. Things will get better. What is important to you is important to the lord. So pray and He will listen.
Answer: thank you
Step-by-step explanation:
Answer:
Thanks!
Step-by-step explanation:
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a prime number a. 0.45 c. 0.71 b. 0.55 d. 0.73 Please select the best answer from the choices provided A B C D
Answer: B
Step-by-step explanation:
The prime numbers here are outcomes 2, 3, and 5.
Therefore, we must add the frequency numbers for these prime numbers:
36 + 44 + 30 = 110
Out of 200 dice rolls, 110 were prime numbers. This can be represented as:
110/200 = 11/20 (fraction form)
= 0.55 (decimal form)
Therefore, the answer is b. 0.55
I will give BRAINLIST Solve the quadratic function by factoring.
2x^2+7x-4=0
Someone please help I will give BRAINLIST please show work I need this for my test
he response times for a random sample of 40 medical emergencies were tabulated. The sample mean is 13.25 minutes. The population standard deviation is believed to be 3.2 minutes. The EMS director wants to perform a hypothesis test, with a .05 level of significance, to determine whether the service goal of 12 minutes or less is being achieved.
Answer:
The calculated value Z = 2.5 > 1.96 at 0.05 level of significance
The null hypothesis is rejected
The Alternative hypothesis is rejected
The EMS director wants to service goal of 12 minutes or less is being achieved
Step-by-step explanation:
Step(i):-
Given that the size of the random sample = 40
Given that the mean of the sample (x ⁻) = 13.25
Given that the standard deviation of the Population = 3.2 minutes
Level of significance = 0.05
The mean of the Population (μ) = 12
Step(ii):-
Null hypothesis:-H₀: (μ) = 12
Alternative Hypothesis: H₁ : μ < 12
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{13.25-12 }{\frac{3.2}{\sqrt{40} } }[/tex]
Z = 2.5
The tabulated value Z₀.₀₅ = 1.96
The calculated value Z = 2.5 > 1.96 at 0.05 level of significance
The null hypothesis is rejected
The Alternative hypothesis is rejected
Final answer:-
The EMS director wants to service goal of 12 minutes or less is being achieved
I have no clue how to do this! please help me!!!
Answer:
The equation has one solution.
A value of x that makes the equation true is 5, which when substituted into the equation and simplified makes the equation turn into 10=10
A value of x that makes the equation false is 6, which when substituted into the equation and simplified makes the equation turn into 12=10
Step-by-step explanation:
2x=10
Divide both sides by two:
2x/2=10/2
x=5. There is no other solution to the equation, because 5 is the only possible answer.
Rachel downloaded a movie at a constant speed.
After she downloaded 40% of the movie, the remaining download time was 40 seconds.
After she downloaded 40 mb, the remaining download time was 16 seconds.
Compute the total size of the movie (in mb) rounded to the nearest mb.
Answer:
The total weight of the file was 64 mb.
Step-by-step explanation:
Given that Rachel downloaded a movie at a constant speed, and after she downloaded 40% of the movie, the remaining download time was 40 seconds, while after she downloaded 40 mb, the remaining download time was 16 seconds, to determine the total size of the movie rounded to the nearest mb, the following calculation must be performed:
100 - 40 = 60
60% = 40 seconds
40 mb = 16 seconds left
16/40 = 4/10
60/40 = 1.5
1.5% for every 1 second of download.
16 x 1.5 = 24
40 + 24 = 64
Thus, the total weight of the file was 64 mb.
Write the number 8.7 x 10^-6 in standard form.
What is another way to describe an equailteral triangel
A=acute
B=obtuse
C=right
D=scalene
Answer:
c
Step-by-step explanation:
Use the elimination method to solve the system of equations.Choose the correct ordered pair. -x + y -2 , 2x -3y = 4
Answer:
To use the elimination method one coefficient of either x or y must be the same number with opposite signs, so the ordered pair is (-10, -8)
Step-by-step explanation:
2(-x+y=2) Make one of the coefficients equal, with opposite signs.
2x-3y=4 Combine equations.
-y=8 Solve, y=-8
Then find x, -x-8=2
-x=10, so x= -10
(-10, -8) is your answer.
I solved the first 2 but can anybody finish it, please?
Answer:
125:200
Step-by-step explanation:
Answer:
the ratio 5 : 8
5/8 - 1/4 simplest form
Answer:
3/8
Step-by-step explanation:
5/8 - 1/4
L.C.M =8
5-2=3
=3/8
The cost of 12 oranges and 7 apples is 5.36. Eight oranges and 5 apples cost 3.68. Find the cost of each
Answer:
Apple costs $0.26
and orange costs $0.32
sorry i don't have time to explain but if u have doubts don't hesitate to ask
Express the confidence interval 0.777
ộHE = +0what is a grid with 4 quadrants and 2 axes?
Answer: The point at which the two axes intersect is called the origin. ... The intersecting x- and y-axes divide the coordinate plane into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.
Step-by-step explanation:
A grid with 4 quadrants and 2 axes is called as cartesian plane.
What is a cartesian plane?The cartesian plane is defined as a two-dimensional coordinate plane, which is formed by the intersection of the x-axis and y-axis.
What is a grid?A grid is a framework of spaced bars that are parallel to or cross each other.
Learn more about grid here
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Please solve this system of equations.
5x-2y=9
12x-8y=4
Answer:
(4,11/2)
Step-by-step explanation:
5x-2y=9
12x-8y=4
A quick look will tell us that neither the x- nor the y- coefficient is the same in both equations, so combining the two by addition or subtraction. We can see that 2 is a multiple of 8, since 2 x 4 = 8. We should multiply the first equation by 4.
4(5x-2y=9)
Now we need to decide if we should add or subtract the equations.
20x-8y=36
12x-8y=4
Since we need to have a -8 and a +8 to eliminate the variables, we should subtract them. Change all the signs of the second equation and combine.
20x-8y=36
-12x-8y=4
----------------
8x=32
Divide both sides by 8 to get the x-value:
[tex]\frac{8x}{8} = \frac{32}{8}[/tex]
x=4
Now that we have our x-value, we need to plug in the y-value.
5x-2y=9
5(4)-2y=9
20-2y=9
-2y=-11
y=11/2
So our solution is (4,11/2)
Let's check our work.
5x-2y=9
5(4)-2(11/2)=9
20-22/2=9
20-11=9
9=9
12x-8y=4
12(4)-8(11/2)=4
48-88/2=4
48-44=4
4=4
Our solution is correct.
Answer:
x=4,y=11/2
Step-by-step explanation:
5x−2y=9
12x−8y=4
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
5x−2y=9,12x−8y=4
To make 5x and 12x equal, multiply all terms on each side of the first equation by 12 and all terms on each side of the second by 5.
12×5x+12(−2)y=12×9,5×12x+5(−8)y=5×4
Simplify.
60x−24y=108,60x−40y=20
Subtract 60x−40y=20 from 60x−24y=108 by subtracting like terms on each side of the equal sign.
60x−60x−24y+40y=108−20
Add 60x to −60x. Terms 60x and −60x cancel out, leaving an equation with only one variable that can be solved.
−24y+40y=108−20
Add −24y to 40y.
16y=108−20
Add 108 to −20.
16y=88
Divide both sides by 16.
y=11/2
Substitute 11/2 for y in 12x−8y=4. Because the resulting equation contains only one variable, you can solve for x directly.
12x−8x11/2=4
Multiply −8 times 11/2.
12x−44=4
Add 44 to both sides of the equation.
12x=48
Divide both sides by 12.
x=4
The system is now solved.
x=4,y=11/2
What would be the final
price of a $59.99 video game
in a state that charges 6.5%
sales tax?
Answer:
$63.89
Step-by-step explanation:
just multiply 59.99 by 1.065
A classroom had 16 computers. If the ratio of computers to ipads was 4 : 5, how many ipads does the classroom have?
Answer:
20 ipads
Step-by-step explanation:
The ratio is 4 : 5
4:5
*4 *4
16c :20i
16 Computers and 20 Ipads.
Harmony thinks 448 is the solution to the equation 8b=56. is harmony correct? explain why or why not.
pls answer quickly my assignment is due tonight
The solution of the equation 8b = 56 is 7. And the solution of Harmony is 448. So, Harmony is incorrect.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
8b = 56
Simplify the equation, then we have
8b = 56
b = 56 / 8
b = 7
The solution of the equation 8b = 56 is 7. And the solution of Harmony is 448. So, Harmony is incorrect.
More about the solution of the equation link is given below.
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