Answers
Answer:
y = [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
using the addition formula for sine
sin(x + y) = sinxcosy + cosxsiny
then
sinxcosy + cosxsiny = [tex]\frac{1}{2}[/tex] sinx + [tex]\frac{\sqrt{3} }{2}[/tex] cosx
for the 2 sides to be equal , then
cosy = [tex]\frac{1}{2}[/tex] and siny = [tex]\frac{\sqrt{3} }{2}[/tex]
then
y = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex]
and
y = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex]
thus y = [tex]\frac{\pi }{3}[/tex]
[tex]\\ \rm\Rrightarrow sin(x+y)=\dfrac{1}{2}sinx+\dfrac{\sqrt{3}}{2}cosx[/tex]
[tex]\\ \rm\Rrightarrow sinxcosy+cosxsiny=\dfrac{1}{2}sinx+\dfrac{\sqrt{3}}{2}cosx[/tex]
Cancel sin and cos[tex]\\ \rm\Rrightarrow cosy+siny=\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}[/tex]
[tex]\\ \rm\Rrightarrow cos\dfrac{\pi}{3}+sin\dfrac{\pi}{3}=\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}[/tex]
y=π/3Option B
Related Questions
Sam ran 2 5/4 miles last weekend. This weekend he ran 3 5/1 miles. How many miles did he run in all?
Answers
Answer:
11 1/4
Step-by-step explanation:
2 5/4 = 3 1/4
3 5/1 = 8
8 + 3 1/4 = 11 1/4
A pistol is accidentally discharged vertically upward at a height of 3 feet
above the ground. If the bullet has an initial muzzle velocity of 200 feet
per second the path of the bullet is modeled by
h (t) = -16t² + 200t + 3.
A. How long does it take for the bullet to reach its maximum height.
Round to nearest hundredth.
B. What is the maximum height?
C. How long will it take for it to hit the ground?
D. When will the bullet be 403 feet above the ground?
Answers
The maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.
How to obtain the maximum value of a function?To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, the height of the bullet from the ground is modeled by the equation:
[tex]h(t) = -16t^2 + 200t + 3[/tex]
where height is in meters and time is in seconds. And t is the time in seconds passed from the point of time when the bullet was fired.
A) Finding maximum height reached by the bullet:Finding its first and second rate with respect to the variable 't', we get:
[tex]\dfrac{d(h(t))}{dt} = h'(t) = -32t + 200\\\\\dfrac{d^2(h(t))}{dt^2} = h''(t) = -32 < 0[/tex]
Thus, the second rate is negative no matter what the value of 't' is. So all the critical points would be corresponding to maxima.
Now, finding the critical points by equating the first rate = 0, we get:
[tex]h'(t) = 0\\\\-32t + 200 = 0\\\\t = \dfrac{200}{32} = 6.25 \: \rm sec.[/tex]
Due to only one critical point, and that each critical point is maxima, we have the value of h(t) globally maximum when t = 6.25
Putting t = 6.25 in the function h(t), we get the maximum height achieved by the bullet as:
[tex]h(t) = -16t^2 + 200t + 3\\h(6.5) = -16(6.5)^2 + 200(6.5) + 3 = 627 \: \rm ft[/tex]
B) Finding the time it will take the bullet to fall on the groundWhen the bullet will fall on the ground, the value of h(t) would be 0.
Putting h(t) = 0, and finding the values of 't' for which this is true, we get:
[tex]h(t) = -16t^2 + 200t + 3\\0 = -16t^2 + 200t + 3\\\\16t^2 -200t -3 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(-3)}}{2(16)}\\\\t \approx \dfrac{200 \pm 200.479}{32}\\\\t \approx -0.0149 \: \rm sec., t \approx 12.51 \: sec.[/tex]
Bullet will fall only after it is shot, so time taken for the bullet to fall compared to the time when its shot would be greater, so time passed (t here) would be positive.
Thus, at approx t = 12.51 sec, the bullet will fall on the ground.
C) When will the bullet be at 400 ft of height from the ground?At t = 0, bullet was at 3 ft, and therefore, whenever bullet will reach 400 ft, the time t would be > 0.
Putting h(t) = 400, we get:
[tex]h(t) = -16t^2 + 200t + 3\\400 = -16t^2 + 200t + 3\\\\16t^2 -200t +397 =0\\\\t = \dfrac{-(-200) \pm \sqrt{ (-200)^2 - 4(16)(397)}}{2(16)}\\\\t \approx \dfrac{200 \pm 120.797}{32}\\\\t \approx 2.475\: \rm sec., t \approx 10.02\: sec.[/tex]
These both values are true. The time when t = 2.475 approx, the bullet would be going up, passing by 400 ft height, and when t = 10.02 approx, the bullet would be coming down, passing by 400 ft height.
Thus, the maximum height the bullet will reach is 627 ft. The time(from the point when bullet was fired) it will take the bullet to hit the ground is 12.51 sec approx. The time when the bullet will be 403 ft above the ground are 2.475 sec and 10.02 sec approx.
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Solve. 5y + 42 − y = 34
Answers
Answer:
The answer is y= -2
Step-by-step explanation:
(Arrange according to the like terms first)
5y-y+42= 34
4y+ 42-34= 0
4y+ 8= 0
4y= -8
∴ y= -8/4=-2
So, y= -2
Hope it will help.
Answer:
y = -2
Step-by-step explanation:
question : 5y + 42 − y = 34
⇒ 5y + 42 − y = 34
•shifting the +42 to the right side :
⇒ 5y - y = 34 - 42
⇒ 4y = -8
•shifting the 4 to the right side :
⇒ y = -8/4
⇒ y = -2 Answer...
hope that helps...
I NEED THIS ASAP PLEASEEach unit on the graph is equal to 1 block. How many blocks does Ben need to walk from his house to reach the museum? A. 7 blocks B. 9 blocks C. 10 blocks D. 13 blocks
Answers
EXPLANATION:
Consider the diagram below. where h represents height and l represents length. Which of the following represents the approximate area of both figures?
Answers
Answer:
Both figures have an area of (6hl) by Cavalieri's Principle for two-dimensional figures.
Step-by-step explanation:
Answer:
option a
Step-by-step explanation:
because of his province duh
What two-dimensional shape iS formed by the cross section
shown below?
Answers
Answer:
pentagon
Step-by-step explanation:
it has 5 sides
Answer:
The 2 dimensional shape that is formed by the cross section below is a triangle.
Move a symbol to each box to compare the fractions.
5/6 10/12
12/100 10/12
<>=
Answers
Answer:
See below ~
Step-by-step explanation:
Question 1
5/6 _ 10/12
Take LCM as 125/6 x 2/2 _ 10/1210/12 _ 10/1210/12 = 10/12Question 2
12/100 _ 10/12
Simplify both sides3/25 = 5/6Take LCM as 1503/25 x 6/6 = 5/6 x 25/2518/150 _ 125/150125 is greater than 1812/100 < 10/12Please help me, I feel so idiotic right now
Answers
Answer:
a) $8.80
b) 40%
Step-by-step explanation:
Part (a)
Given:
Original price = $22Discounted price = $13.20Original price - discounted price
= $22 - $13.20
= $8.80
Part (b)
percentage = (amount discounted ÷ original price) x 100
= (8.80 ÷ 22) x 100
= 40%
The population of a small village has fallen by 6% to 658. What was the population of the village before the decrease?
Answers
Answer: answer below
Step-by-step explanation:
5 objects of any size that are in
the shape of a rectangular prism.
You can find these items anywhere
around your house. You could use a
tissue box, shoe box, cereal box,
any snack food box, etc.
Ruler that has inches.
help
Answers
To make a triangular prism we need cardboard, glue and scissors.
What is a triangular prism?A triangular prism is a geometric shape characterized by:
It has three sides.It is a polyhedron.It has a triangular base and three faces that join it with another base.Its sides are rectangular.How to make a triangular prism out of cardboard?To make a triangular prism out of cardboard we must draw two equilateral triangles on the cardboard.Then we must draw three rectangles that have the same height as the length of the sides of the triangle.Subsequently, we must cut out all the shapes we draw, a total of five figures.Then we must paste the three rectangles on each side of the triangles.Once we glue the three rectangles to one of the triangles, we assemble the prism by joining the other side of the rectangles to the other triangle.Learn more about prism in: https://brainly.com/question/12649592
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The box-and-whisker plot below shows the number of points each member of the middle school basketball team made during the game on Saturday.
Answers
What is the value of x2(7−x)+2 when x=5?
Answers
(5)^2(7-5)+2
square 5 to get 25(7-5)+2
minus 7 and 5 to get 25(2)+2
multiply 25 and 2 to get 50 + 2
add the equation to get 52
so, the value of the equation is 52
hope this helped!
Please help!!!!!
Two chords intersect within a circle to form an angle whose measure is 53 degrees. If the intercepted arcs are represented by 3x + 3 and 10x -14, find the measure of the LARGER of these two arcs.
A. 106
B. 76
C. 9
D. 30
Answers
Answer:
76degrees
Step-by-step explanation:
Using the theorem which states that the vertex of the angle inside a circle is half the sum of the measured intercepted arcs. Hence;
Angle at the vertex = 53 degrees
Half the sum of intercepted arcs = 1/2(3x+3+10x-14)
Half the sum of intercepted arcs = 1/2(13x-11)
Equating to the vertex to find x
1/2(13x-11) = 53
13x - 11 = 2 * 53
13x - 11 = 106
13x = 106 + 11
13x = 117
x = 117/13
x = 9
For the arc 3x + 3
= 3(9) + 3
= 27 + 3
= 30degrees
For the arc 10x - 14
= 10(9) - 14
= 90 - 14
= 76degrees
Hence the measure of the larger of the two arcs is 76degrees
PLease help me w this q.8
Answers
Answer:
B
Step-by-step explanation:
Angle 1 and angle 3 are alternate interior angles.
anyone know the answer i really need help?
Answers
Answer:
8
Step-by-step explanation:
HOPE THIS HELPS! PLS GIVE ME BRAINILIEST PLSSSSSSSSSSSSSSSSSSS!
what is the volume of the triangular prism
A) 12 cm
B) 18
C) 24
D) 48
Answers
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h
Graph =−2+5 y = − 2 x + 5 and =−12−3 y = − 1 2 x − 3 . Are the lines parallel, perpendicular, or neither?
Answers
Answer:
They are neither,they intersect but not at a 90 degree angleStep-by-step
explanation: hope this helps :)
What is the area of the unshaded part of the
rectangle to the right?
A. 19,000 ft²
B. 45,000 ft²
C. 28,000 ft²
D. 26,000 ft²
Answers
the answer is 82 million
HELP I REALLY NEED HELPPPPP
Answers
Answer:
100 degrees
Step-by-step explanation:
please help me find the answe asap
Answers
Answer:
B
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
this year's mean = [tex]\frac{7+3.3+2}{3}[/tex] = [tex]\frac{12.3}{3}[/tex] = 4.1
last year's mean = [tex]\frac{5.3+1.6+2.4}{3}[/tex] = [tex]\frac{9.3}{3}[/tex] = 3.1
difference = 4.1 - 3.1 = 1
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
∆The lateral surface area of cylinder =417.62 mm²
Step-by-step explanation:
Diameter = 7
Radius = 7/2
Lateral Surface Area of cylinder = 2πrh
=> 2× π × 7/2 × 19
=> 38 × 7/2 × π
=> 133 × π { taking π as 3.14}
=> 133× 3.14
=> 417.62 mm²
If you flipped a fair coin 18 times, about how many times would you expect heads to appear? please ansewr i need help
Answers
Answer:
1/2, or around 9 times
Step-by-step explanation:
since a fair coin has 2 sides, that makes you have 2 possible outcomes. Heads and tails, 2 sides, makes it 50-50 so you would expect to get around 9 heads because 50% or 1/2 of 18 is 9. Hope this helps
(lengthy question, pls help will def give brainliest asap)
Cecilia decided to start a savings plan. On January 1, she opened a bank account and made a depositZ she then made monthly deposits without ever taking money out of the account. At the end of each month, she recorded the total amount in her savings account the table below shows her data for the first five months of the year.
What is the initial value, in dollars, for the function that represents Cecilia’s total savings? Explain your answer.
Answers
650$ was the amount of money that was taken away
Step-by-step explanation:
How can i find the circumference of a circle if I already know it's area?
Answers
Answer:
With the area you can find the radius and then substitute the radius in the circumference formula
What is an equation of the line that passes through the points (−3,−4) and (-4, -6)
Answers
Answer:
[tex]\Large\boxed{\sf{y=2x+2}}[/tex]Step-by-step explanation:
Use the slope formula.
SLOPE FORMULA:
[tex]\Rightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]:\Longrightarrow \sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}}[/tex]
Solve.
[tex]\sf{\dfrac{-6-\left(-4\right)}{-4-\left(-3\right)}=\dfrac{-6+4}{-4+3}=\dfrac{-2}{-1}=2}[/tex]
The slope is 2.
Use the slope-intercept form.
SLOPE-INTERCEPT FORM:
[tex]\sf{y=mx+b}[/tex]
X=slopeB=y-intercept.The y-intercept is 2.y=2x+2
Therefore, the final answer is y=2x+2.I hope this helps, let me know if you have any questions.
[tex]\text{Given that,}\\\\(x_1,y_1) =(-3,-4)~~ \text{and}~~ (x_2,y_2) = (-4,-6)\\\\\text{Slope,}~m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{-6+4}{-4+3} = \dfrac{-2}{-1} =2\\ \\\text{Equation of line,}\\\\~~~~~y-y_1 = m(x-x_1)\\\\\implies y+4=2(x+3)\\\\\implies y =2x+6-4\\ \\\implies y= 2x+2[/tex]
i need help with question 16 and 17
Answers
Answer:
16 is definitely a
17 is c
Step-by-step explanation:
an app that I use that helps a lot is desmos u should try it out
hope this helps :)
can i get brainliest?
What is the volume of a sphere with a radius of 9.1 ft, rounded to the nearest tenth of a cubic foot?
Answers
The volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.
We have given that, the radius of the sphere is 9.1ft.
We have to determine the volume of the sphere
What is the formula for the volume of the sphere?The volume of the sphere is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]
r is the radius of the sphere
V- is the volume of the sphere
So use the given value in the formula so that,
[tex]V=\frac{4}{3}\pi (9.1)^3[/tex]
[tex]V=3156.55082 ft^3[/tex]
Therefore the volume of the sphere with a radius of 9.1ft is 3256.55cubic feet.
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Answer:3156.6
Step-by-step explanation:
write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
28:7
Answers
Answer:
[tex] \frac{4}{1} [/tex]
Step-by-step explanation:
[tex]writing \: as \: a \: fraction \: the \\ numerator = 28 \\ denominator = 7 \\ as \: a \: fraction \: it \: is \: \: \frac{28}{7} \\ dividing \: numerator \: and \: denominator \: by \: four \\ = \frac{4}{1} \\ hope \: this \: helps \\ please \: rate \: and \: mark \: brainliest[/tex]
Write .00003088 in scientific notation
Answers
Answer:
Step-by-step explanation:
3.088 x [tex]10^{-5}[/tex]
scientific notation requires one number before the decimal, moving the decimal place to the right requires counting down.
A fair die is rolled 5 times. What is the probability of having no 1 and no 4 among the rolls? Round your answer to three decimal places.
Answers
Answer:
0.132
Step-by-step explanation:
Rolling a die is an independent event.
Chance of not rolling a 1 or 4 is 4/6 or 2/3
[tex]\frac{2}{3} ^5 = \frac{32}{243} = 0.13168[/tex]