Given that z = 10 cis 30° and w = 5 cis 10°, find z/w. Leave your answer in polar form
Giving almost 100 pts!!
Answer:
2cis(20°)
Step-by-step explanation:
we are given that
[tex] \displaystyle \rm z = 10cis ({30}^{ \circ} )[/tex]
[tex] \displaystyle \rm w = 5cis ({10}^{ \circ} )[/tex]
We want to find z/w . To do so, divide 10cis(30°) by w = 5cis(10°) which yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )}[/tex]
recall that,
[tex] \displaystyle \rm \frac{ r_{1} cis ({ { \theta}_{1}} )}{ r_{2}cis( { \theta}_{2})} = \frac{ r_{1} }{ r_{2} } cis({ \theta}_{1} - { \theta}_{2})[/tex]
consider,
[tex]{ r}_{1} \implies 10[/tex][tex]{ r}_{2} \implies 5[/tex][tex]{ \theta}_{1} \implies {30}^{ \circ} [/tex][tex]{ \theta}_{2} \implies {10}^{ \circ} [/tex]Therefore, utilizing the formula yields:
[tex] \displaystyle \rm \frac{ z}{w} = \frac{10cis ({30}^{ \circ} )}{5cis( {10}^{ \circ} )} \\ \implies \rm\frac{ z}{w} = \dfrac{10}{5} cis( {30}^{ \circ} - {10}^{ \circ} ) \\ \implies \rm \dfrac{z}{w} = \boxed{ \rm2cis( {20}^{ \circ} )}[/tex]
and we're done!
NB: cis(x) is also known as cos(x)+i×sin(x)
i need help with question 16 and 17
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?
find the slope of the line that passes through the points (-6, - 18) and (-7, -17)
Answer:
-1
Step-by-step explanation:
The slope is the change in the Y value divided by the change in the X value. Therefore, the slope of this line is:
(-17-[-18])/(-7-[-6) = (-17+18)/(-7+6) = (1)/(-1) = -1
What is the minimum value for the function shown in the graph?
Enter your answer in the box.
Check the picture below.
What is the value of x2(7−x)+2 when x=5?
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
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
the answer is 82 million
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.
Please HELP! I will mark BRAINLIEST. YOU ALSO GET 20 POINTS FOR HELPING ME! THANK YOU!
y=x-50
[tex]\huge\mathfrak\colorbox{white}{}[/tex][tex]\huge\mathfrak\colorbox{white}{}[/tex]
Graph the line to complete the chart
Answer:
Slope : 1, Intercept- 3, equation: y = 1x + 3
Step-by-step explanation:
slope is the change of rate and it can be observed that the rate of change from each square is 1
y intercept is the spot where the line intersects with the y axis
equation format: y = mx + b where mx is slope and b is the y intercept
help me3 i dont really understand it I try so many times but I didn't get it right
What two-dimensional shape iS formed by the cross section
shown below?
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.
The population of a small village has fallen by 6% to 658. What was the population of the village before the decrease?
Answer: answer below
Step-by-step explanation:
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
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
(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.
650$ was the amount of money that was taken away
Step-by-step explanation:
What is the area of the square shown below?
A. 16 ft2
B. 32ft
C. 32ft2
D. 64ft2
Answer:
64 feet squared
Step-by-step explanation:
Since it's a square, all sides have a length of 8 ft. Area is length x width, so simply multiply 8 by itself. 64 feet squared is therefore the answer.
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?
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.
Learn more about maxima and minima of a function here:
https://brainly.com/question/13333267
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If you flipped a fair coin 18 times, about how many times would you expect heads to appear? please ansewr i need help
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
If AB is perpendicular to radius CP at P, then is tangent to C.
Given: QRn
Prove: n is tangent to Q at R.
A. Scalene
B.Right
C.Equilateral
Answer: Right triangle
Step-by-step explanation:
QR is perpendicular to line n, so the indicated angle is a right angle. Thus, QRS is a right triangle because a triangle with a right angle is a right triangle.
Solve the following system of equations and show all work.
y = x^2 + 3
y = x + 5
please help me! i know that i have to do substitution or something like that but i got really confused halfway through it and i also need to show all of the work!
Consider the diagram below. where h represents height and l represents length. Which of the following represents the approximate area of both figures?
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
HELP I REALLY NEED HELPPPPP
Answer:
100 degrees
Step-by-step explanation:
What is the slope of the compass needle (the bottom red line)?
Answer:
176/317
Step-by-step explanation:
The formula for slope is [tex]\frac{y2 - y1}{x2 - x1}[/tex], which means you have to subtract the second point's y coordinate (286) minus the first point's y coordinate (110).
Now you have [tex]\frac{286-110}{x2 - x1}[/tex] or [tex]\frac{176}{x2 - x1}[/tex].
Now you have to do the same for x.
446 - 129 = 317, which gives you the final answer of
[tex]\frac{176}{317}[/tex], or about 0.555.
Hope this helps :)
jp524
I need help asap please
Answer:
B = 21.4°
Step-by-step explanation:
Using the Law of Sines.
[tex]sin(42)/22=sin(B)/12[/tex]
Cross Multiply
[tex]12*sin(42)=22sin(B)[/tex]
Get Sin(B) by itself.
sin(B)= 12*sin(42°) / 22
B° = sin^-1((12*sin(42°))/22)
B = 21.4°
Write .00003088 in scientific notation
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.
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
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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anyone know the answer i really need help?
Answer:
8
Step-by-step explanation:
HOPE THIS HELPS! PLS GIVE ME BRAINILIEST PLSSSSSSSSSSSSSSSSSSS!
The ratio of the number of oranges in a fruit salad to people served is 9/40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
180
Step-by-step explanation:
9:40
?:800
9×20=180
40×20=800
it is a ratio. 9 oranges to 40 people. 40 times 20 is 800 so you do the same to 9 (which gives you 180)
Answer:
180/800
Step-by-step explanation:
if you multiply the numbers by 20 you can get your answer
Move a symbol to each box to compare the fractions.
5/6 10/12
12/100 10/12
<>=
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 < 10/12Sam ran 2 5/4 miles last weekend. This weekend he ran 3 5/1 miles. How many miles did he run in all?
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