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iren2701 [21]
3 years ago
11

The complex number -5i has the complex trigonometric form of 5(cos 270° + isin 270)

Mathematics
1 answer:
Verizon [17]3 years ago
5 0

Answer:

True ,   -5i =  5*(0 - i) =  5*( cos 3π/2  + i*sin 3π/2)  = 5*(cos 270 + i*sin 270)

Step-by-step explanation:

5*( cos 3π/2 radians  + i*sin 3π/2 radians)  = 5*(cos 270 degrees + i*sin 270 degrees)

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 ft.
Vedmedyk [2.9K]

Answer:

it 12

i litterally just got it right so...

3 0
3 years ago
PLEASE HELP ME WITH THIS MATH!!!!!!!!!. pLeAsE i ReAlLy NeEd SoMe HeLp
KonstantinChe [14]
Part 1) we know that
m∠5=44°    m∠11=86°
m∠2=m∠5------> by vertical angles
m∠2=44°
m∠13=m∠11------> by vertical angles
m∠13=86°
m∠12+m∠13=180°-----> supplementary angles
m∠12=180-86-----> m∠12=94°
m∠14=m∠12----> by vertical angles
m∠14=94°
m∠1=m∠11----> by corresponding angles
m∠1=86°
m∠4=m∠1----> by vertical angles
m∠4=86°
m∠2+m∠1+m∠6=180
m∠6=180-(86+44)----> 50°
m∠6=50°
m∠3=m∠6----> by vertical angles
m∠3=50°
m∠8=m∠3----> by corresponding angles
m∠8=50°
m∠8+m∠7=180°-----> supplementary angles
m∠7=180-50----> 130°
m∠7=130°
m∠10=m∠6----> by corresponding angles
m∠10=50°
m∠10+m∠9=180°-----> supplementary angles
m∠9=180-50-----> 130°
m∠9=130°

the answers Part 1) are
m∠1=86°
m∠2=44°
m∠3=50°
m∠4=86°
m∠5=44° 
m∠6=50°
m∠7=130°
m∠8=50°
m∠9=130°
m∠10=50°
m∠11=86°
m∠12=94°
m∠13=86°
m∠14=94°

Part 2) 
a) what is m∠TPR?
in the right triangle PTR 
m∠PTR+m∠TPR+m∠TRP=180° ( the sum of internal angles of triangle is equal to 180 degrees)
m∠PTR=30°
m∠TRP=90°
so
m∠TPR=180-(90+30)----> 60°

the answer Part 2a) is 
m∠TPR=60°

b) what is the length in inches of segment PR?
in the right triangle PTR 
sin 30=PR/TP-----> PR=TP*sin 30-----> PR=14*(1/2)----> 7 in

the answer Part 2b) is
PR=7 in

c)  what is the length in inches of segment TR?
in the right triangle PTR 
cos 30=TR/PT-----> TR=PT*cos 30-----> TR=14*(√3/2)---> TR=7√3 in

the answer Part 2c) is
TR=7√3 in

d)  what is the length in inches of segment PQ?
in the right triangle PQR
PR=7 in
RQ=PR-----> by angle 45°
so
RQ=7 in
applying the Pythagoras Theorem
PQ²=RQ²+PR²-----> 7²+7²-----> PQ²=98-----> PQ=√98 in---> PQ=7√2 in

the answer Part 2d) is
PQ=7√2 in

Part 3) Patrice buys a block of wax in the shape of a right rectangular prism. The dimensions of the block are 20 cm by 9 cm by 8 cm.
  <span><span>(a)   </span>What is the volume of the block?

volume of the prism=20*9*8-----> 1440 cm³

the answer Part 3 a) is
the volume of the block is 1440 cm³
<span>
Patrice melts the wax and creates a candle in the shape of a circular cylinder that has a diameter of 10 cm and a height of 15 cm.<span>(b)   </span>To the nearest centimeter, what is the volume of the candle?
</span></span>volume of a cylinder=pi*r²*h
diameter=10 cm
radius r=10/2----> 5 cm
h=15 cm
volume of a cylinder=pi*5²*15----> 1177.5 cm³-----> 1178 cm³

the answer Part 3b) is
the volume of the candle is 1178 cm³

<span>Patrice decides to use the remaining wax to create a candle in the shape of a cube.<span>(c)   </span>To the nearest centimeter, what is the length of the side of the cube?
</span>
the remaining wax=volume of the prism-volume of a cylinder
=1440-1178-----> 262 cm³

volume of a cube=b³
where b is the length side of the cube
262=b³-------b=∛262-----> b=6.40 cm-----> b=6 cm

the answer Part 3c) is
the length of the side of the cube is 6 cm
5 0
3 years ago
Tracy is filling the box with unit cubes that are 1 inch on each side. She will fill the box with cubes without any gaps or over
balu736 [363]

Answer:

Volume = 48in^3

Step-by-step explanation:

Given

See attachment for box

Required

The volume of the box

The number of boxes in each direction represents the length of that dimension.

So, from the attachment

Width = 4in

Length = 3in

Height = 4in

The volume is:

Volume = Length * Width * Height

Volume = 4in * 3in * 4in

Volume = 48in^3

5 0
3 years ago
-
inysia [295]

Answer:

D. The graph of function g is the graph of function f shifted 4 units to the left.

Step-by-step explanation:

the function g is composite function between f and x + 4, then you can re-write g as:

g(x) = 10^{x+4}

The transformation happened in the input, then you have an horizontal shifted and how it's adding 4 units then you go "faster" and move to left the graph.

In the image you can see what's mean sum a constant in the x of a function.

8 0
2 years ago
The average score of students in Mr. Blake's science class was 73 with a standard deviation of 11, while the average score of st
Pani-rosa [81]

Answer:

Mr Blake's science class

Step-by-step explanation:

The standard deviation is a measure of variation.

It tells us how far each of the data set in the distribution are far from the mean of the distribution.

The average score of students in Mr. Blake's science class was 73 with a standard deviation of 11, while the average score of students in Mrs. Arnold's class was 75 with a standard deviation of 10.

Since 11>10, Mr Blake's science class is more variable than Mrs. Arnold's class.

3 0
3 years ago
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