if sin(θ)=7/25, when π/2<θ<π, use the given information about θ to find the exact value of sin(θ/2)
we know that π/2 < θ < π, which is another way of saying that θ is in the II Quadrant, so half that angle will most likely be located on the I Quadrant, where cosine as well as sine are both positive.
Now, let's keep in mind that θ itself is in the II Quadrant, where the cosine is negative whilst the sine is positive.
[tex]\textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{25}}\qquad \textit{let's now find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{25^2-7^2}=a\implies \pm\sqrt{576}=a\implies \pm 24=a\implies \stackrel{II~Quadrant}{-24=a} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{-24}}{\underset{hypotenuse}{25}} \\\\\\ sin\left(\cfrac{\theta}{2}\right)\implies \pm \sqrt{\cfrac{1-\left( -\frac{24}{25} \right)}{2}}\implies \pm \sqrt{\cfrac{1 +\frac{24}{25} }{2}}[/tex]
[tex]\pm\sqrt{\cfrac{~~\frac{49}{25} ~~}{2}}\implies \pm\sqrt{\cfrac{49}{50}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{49}{50}}}\implies \cfrac{\sqrt{49}}{\sqrt{50}}\implies \cfrac{7}{5\sqrt{2}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{\cfrac{7}{5\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{7\sqrt{2}}{5\sqrt{2^2}}}\implies \cfrac{7\sqrt{2}}{10}[/tex]
Hello Can Someone Please Answer This Math Question
Step-by-step explanation:
the answer is in the picture
Find the equation of the line that is parallel to the line y = 3x + 1 and passes through
the point (1, 2).
(Show Work and steps)
Answer:
[tex]y=3x-1[/tex]
Step-by-step explanation:
lines that are parallel have the same gradient
using this fact we can create the equation:
[tex]y=3x+c[/tex]
and substitute in our values
[tex]2=3+c[/tex]
[tex]c=-1[/tex]
so the equation of the line is [tex]y=3x-1[/tex]
Find the value of xx, yy, and zz in the parallelogram below..
Answer:
36, y = 10, and z = -25
Step-by-step explanation:
99 and -3z +6 are same side interior angles, so they sum to 180 degrees.
99 -3z + 6 = 180
-3z = 75
z = -25
Opposite angles of a parallelogram are congruent
2x + 9 = -3x + 6
2x + 9 = 75 + 6
2x = 81 - 9
2x = 72
x = 36
9y + 9 = 99
9y = 90
y = 10
Translate the following expression:
5 less than 4 times a number(use n), squared
due in 1 hour
Step-by-step explanation:
[tex](4n - 5) {}^{2} [/tex]
4 times a number implies it's multiplied by 4
5 less is simply -5
and square all that to get (4n-5)²
This is my best guess
If the payans make a 15% down payment of $ their monthly payment will be $
Answer:
If the Payans make a 15% down payment of $1,237.18, their monthly payment will be $35.
Hope this helps!
A robot can complete 5 tasks in 3/4
hour. Each task takes the same amount of time.
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
Answer:
[A] 9 minutes to complete one task
[B] 6 tasks completed, with 2/3rds of another task completed.
Step-by-step explanation:
5 tasks in 45 mins is equal to one task in 9 minutes
60 minutes in an hour, 9 minutes per task = 6 tasks completed, with 2/3rds of another task completed.
(HELP) What is the perimeter of the figure?
28 m
20 m
22 m
14 m
Answer:
20m
Step-by-step explanation:
Perimeter is the sum of all the sides.
Perimeter = 3+5+1+7+4 = 20m
I need help please please
Answer:
A
Step-by-step explanation:
Reflects across the y axis then rotates 180 degrees.
Answer:
reflection then rotation
Step-by-step explanation:
because to get 2 you reflect then 3 is rotated
Here is 3 & 4 I NEED DONE ASAP!
Given matrices are from here
https://brainly.com/question/18267865
=====================================================
Problem 3
a)
B - C = DNE
We cannot subtract matrices of different sizes. Matrix B is 2x2 while C is 3x2. Both matrices must have the same number of rows, and they must also have the same number of columns. The matrices don't have to be square.
------------------------------
b)
[tex]A+B = \begin{bmatrix}-5 & 6\\7 & 4\end{bmatrix}[/tex]
You add the corresponding elements. For instance, in the top left corner we have -1+(-4) = -5. The other entries are treated in a similar manner.
------------------------------
c)
[tex]-2E = \begin{bmatrix}6 & -4 & 8\\-12 & 14 & -16\\-10 & -18 & 20\end{bmatrix}[/tex]
You get this from multiplying each entry in matrix E by -2. Eg: top left corner has -2*(-3) = 6
------------------------------
d)
[tex]CD = \begin{bmatrix}4 & 7 & 8\\ 1 & 3 & 4\\14 & 17 & 16\end{bmatrix}[/tex]
Matrix C has 3 rows and D has 3 columns. The final answer will be size 3x3
To generate each value in the answer matrix, you'll highlight rows of C to pair with columns of D. Then you'll multiply out the corresponding values, after which you add those products. This is done for every entry in the answer shown above.
For example, the first row of C is highlighted and the second column of D is highlighted. Those values pair up and multiply getting -1*(-1) + 2*3 = 1+6 = 7, which goes in the first row and second column of the answer matrix. The other entries are handled in a similar fashion.
------------------------------
e)
[tex]\det(B) = -46[/tex]
The 2x2 matrix determinant formula is [tex]\begin{vmatrix}a & b\\c & d\end{vmatrix} = a*d - b*c[/tex]
In this case, a = -4, b = 6, c = 5, d = 4.
------------------------------
f)
[tex]B^{-1} = \begin{bmatrix}-2/23 & 3/23\\ 5/46 & 2/23\end{bmatrix}[/tex]
Swap the top left and bottom right corners of matrix B. Change the sign of the other two corner values. Then multiply each entry by 1/d where d is the determinant found back in part (e) above. Be sure to reduce any fraction as much as possible.
=====================================================
Problem 4
Answers: x = 2 and y = -10
-----------------
Work Shown:
[tex]\begin{bmatrix}2x & 4\\-5 & -2\end{bmatrix}+\begin{bmatrix}3 & -7\\11 & y-1\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & 4+(-7)\\-5+11 & -2+(y-1)\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & -3\\6 & y-3\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\[/tex]
In the top left corners of each matrix, in line 3, we have 2x+3 = 7 which solves to...
2x+3 = 7
2x = 7-3
2x = 4
x = 4/2
x = 2
In the bottom right corners, we have y-3 = -13 which solves to....
y-3 = -13
y = -13+3
y = -10
The diagram shows squares arranged around the edge of a right triangle. What is the area of square B
Step-by-step explanation:
take the right triangle
15^2 = 9^2 + x^2
225 = 81 + x^2
x = 12
area of square b = 144
In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(14x)°.
What is the value of x?
Enter your answer in the box.
In a straight line, all angles sum up to 180°
====================================
[tex]\hookrightarrow \sf x +\dfrac{1}{4} x = 180[/tex]
[tex]\hookrightarrow \sf \dfrac{4x}{4} +\dfrac{1}{4} x = 180[/tex]
[tex]\hookrightarrow \sf \dfrac{4x+x}{4} = 180[/tex]
[tex]\hookrightarrow \sf 4x+x= 180(4)[/tex]
[tex]\hookrightarrow \sf 5x= 720[/tex]
[tex]\sf \hookrightarrow x = 144[/tex]
Answer:
x = 144°
Step-by-step explanation:
Since the larger line is a straight line, ∠1 and ∠2 are a linear pair. A linear pair is such a pair where two angles sum up to 180°.
⇒ ∠A + ∠B = 180°
Substitute the measure of ∠A and ∠B
⇒ x + x/4 = 180° [∠A = x; ∠B = x/4]
⇒ 4x/4 + x/4 = 180° [Rewrote x as 4x/4]
⇒ 5x/4 = 180°
Using cross multiplication
⇒ 5x = 180 × 4 = 720
⇒ x = 720/5 = 144°
Which of the following shows figure T rotated 90° clockwise around the Orgin ?
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
It's the 4th one because it's the only one that rotated at 90° clockwise and around the origin.
ANSWER QUESTION FOR A BRAINLIEST ANSWER
An airplane on autopilot took 5 hours to travel 3,475 kilometers. What is the unit rate for kilometers per hour?
The floor of a NYC subway car measures approximately 12 feet. How many cubic feet of space are there in a subway car?
The cubic feet of space that is in the subway car is the volume of the subway car which is 5,502.
How many cubic feet of space are there in a subway car?The shape of a subway car is in the form of a rectangular prism. In order to determine the cubic feet of space, the volume of the car has to be determined. The formula for the volume of a rectangular prism would be used.
Volume = width x height x length
12 x 51 x 8.5 = 5205
Here is the complete question:
The floor of an NYC subway car measures approximately 51 feet by 8.5 feet. The height of the NYC subway car measures approximately 12 feet. How many cubic feet of space are there in a subway car?
To learn more about the volume of a cuboid, please check: https://brainly.com/question/26406747
Slove for x
Show all work
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex](x)(y)=9(4)[/tex]
[tex]\sqrt{x^2} =\sqrt{36}[/tex]
[tex]x=6[/tex]
~
Need help asap!!!!
i will mark brainliest
Answer:
41
Step-by-step explanation:
Answer:
the value of x is 41°
Step-by-step explanation:
x + 76°+63° = 180°{being straight angle}
or, x+139° = 180°
or, x = 180° - 139°
or, x = 41°
estimate -12 4/9 multiplied by 5 7/8
A. -72
B. 78
C. -78
D. 72
I need help please ASAP ?!!! ANYONE PLS HELP
Answer:
1. 3/6
2. 2/4
3. 4/6
4. 3/6
Step-by-step explanation:
multiple each fraction by the number of parts I pretty sure
Please help me find the missing angle measures. :(
Answer:
M<1 = 120° therefore, M<7 = 120°
M<1 = 120° therefore, M<5 = 120°
Find the area can i get the answer ASAP pls......................
Which describes the slope of the given line?
A) positive
B) zero
C) negative
D) undefined
Answer:
C) Negative
Step-by-step explanation:
This is because the top is left and going right
Answer:
negative
Step-by-step explanation:
Show that ln(x^3 -4x) − ln(x^2 -2x)= ln(x + 2).
determine whether the ordered pair is a solution of the linear equation. thanks in advance!!
Answer:
no
Step-by-step explanation:
because it is nor a solution
I need to know this very hard question!
Answer:
8 [tex]\frac{3}{4} \\[/tex]
Step-by-step explanation:
Going from left to right on the number line we see that k is between 8 and 9. So 8 will be your whole number. The number line is divided into 8 sections between each whole number and k is located 6/8 between 8 and 9.
This mixed number is 8 6/8. We can reduce the 6/8 to 3/4 by dividing by 2 on the top and bottom. So your final answer is 8 3/4.
PRECAL EDGE HELPPPPP
The water level at a pier is modeled by the function y= 2.5 cos(2pi/12.5) +12, where y represents the water level
measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water
first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.
Answer:
3.1
Step-by-step explanation:
Answer:
3.1
Step-by-step explanation:
edg 2021
6(x-1)=9(x+2) what's the answer?
Answer:
x=-8
Step-by-step explanation:
For each part, first decide which of the three methods sections will most easily enable you to sketch the surface. These are the generalized cylinder method, the surface of revolution method, and the method of slices (traces) for general quadric surfaces. Then apply that method to sketch the surface.
a. x^2 = 4z +8
b. x^2 - 4y^2 – 4z^2 = 16
c. y^2 = x^2 + 2z^2
Answer:
Step-by-step explanation:
We use these three methods
1. Generalized cylinder method
2. Surface of revolution method
3. Method of slices general quadratic
1. For A = x² = 4z + 8
We use the method of slices for general quadratic
2. X²-4y²-4z² = 16
We use the generalized cylinder method
3. Y² = z² + 2z²
We use surface of revolution
Please check attachment for answers
If 4 gal of premium unleaded gasoline costs $15.04, how much would it cost to completely fill a tank whose capacity is 9-gal?
The cost to completely fill the tank is $
Answer:
$33.84 cents
Step-by-step explanation:
Given the following question:
4 gallons = 15.04
1 gallon = ?
How much for 9 gallons?
To find the answer we have to find how much one-gallon costs since we already know how much it costs for 4 gallons of this unleaded gasoline.
[tex]15.04\div4[/tex]
[tex]15.04\div4=3.76[/tex]
[tex]=3.76[/tex]
One gallon of this gasoline costs $3.76 now we need to find how much it costs for 9 gallons.
[tex]3.76\times9=33.84[/tex]
[tex]=33.84[/tex]
For nine gallons of gasoline it will cost you "$33.84 cents."
Hope this helps.
A car manufacturer claims that the company’s newest model has a peak power of exactly 329 horsepower. Katherine is a reporter for an automotive magazine. She is testing the manufacturer's claim and says that the population mean peak power is less than the advertised amount. She measures the peak horsepower of 42 randomly selected cars of the new model. The sample mean is 327.74 horsepower with a standard deviation of 2.41 horsepower. Should Katherine reject or fail to reject the null hypothesis given the sample data below? H0:μ=329 versus Ha:μ<329 α=0.05 (significance level) t≈−3.39 with 41 degrees of freedom p-value<0.005
Answer: Katherine should reject the null hypothesis.
Step-by-step explanation:
We reject the null hypothesis when p-value is less than the significance level.
here, H0:μ=329 versus Ha:μ<329
α=0.05 (significance level)
p-value<0.005
so , we should reject the null hypothesis as p-value is less than the significance level.
Hence, Katherine should reject the null hypothesis.