Answer:
-6
Step-by-step explanation:
f(x)=2x^2+8x
f(-1)=2(-1)^2+8(-1)
f(-1)=2(-1)(-1)-8
f(-1)=2(1)-8
f(-1)=2-8
f(-1)=-6
if z1= 3+3i and z2=7(cos(5pi/9) + i sin (5pi/9)), then z1/z2= blank
[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]
The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
What is complex number?"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".
For the given situation,
z1= 3+3i and
z2= 7(cos(5π/9) + i sin (5π/9))
To divide the complex numbers, both should be in same form.
Convert z1 in polar form.
z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]
⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]
⇒[tex]r=\sqrt{18}[/tex]
θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]
⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]
⇒[tex]tan^{-1}(1)[/tex]
⇒[tex]45[/tex]°
The polar form is of the form, z= r (cosθ + i sinθ),
⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)
The formula for dividing complex number is
z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)
⇒ z1/z2 = r(cosθ + isinθ)
where, r = r1/r2 and θ = (θ1 - θ2)
z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)
⇒ r = [tex]\sqrt{18}[/tex] / 7 and
θ = (π/4 - 5π/9 )
⇒ θ = (-11π/36)
cos(-θ) = cos θ
⇒cos( -11π/36 ) = cos ( 11π/36 )
sin(-θ) = -sin θ
⇒ sin ( -11π/36 ) = -sin ( 11π/36 )
Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))
Hence we can conclude that the value of z1/z2 is
√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).
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Evaluate. 5.8 – 3.63 = ________
Select all that apply.
Zack is taking a test in which he answers questions at a rate of question per minute. If Q represents questions and
M represents minutes, which of the following equations describe this rate relationship?
M= 20 x Q
Q = 2 x M
M=1/2 x Q
Q=1/2 x M
The equation Q = 2 x M represents the relationship between question and time.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Zack takes a test, in which he answers at rate of 2 question per minute.
Also, Q represents questions
And M represents minutes.
According to given condition,
In 1 minute, Zack answers 2 question,
In M minutes, Zack answers 2 x M question,
Total questions presented by Q,
Q = 2 x M.
The required relationship for M and Q is Q = 2 x M.
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On the 1st January 2014 Carol invested some money in a bank account.
The account pays 2.5% compound interest per year.
On 1st January 2015 Carol withdrew £1000 from the account.
On 1st January 2016 she had £23517.60 in the account.
Work out how much Carol originally invested in the account.
Answer:
didn't know how to workout iam only 3rd standard
Answer:
Step-by-step explanation:
bubble gum
What percent of 80 is 60
Answer:
80% of 75 is 60
Step-by-step explanation:
0.80x=60
x=60/0.80
x=75
-2 2/3 divided by 1 5/6 + 2
NO MIXED NUMBERS
Answer:
14/15
Step-by-step explanation:
Answer:
6/11
Step-by-step explanation:
-2 2/3 divided by 1 5/6 = -16/11 and when you add two to that you get 6/11.
the line passes through the point (4,7) and has a slope that is reciprocal of the slope of the line y=1/3x+2
point slope form and slope intercept form pls
first you have to change 1/3 to -3
y=-3x+2
then you have to replace 2 with 'b' because you don't know the y intercept yet
y=-3x+b
then you substitute the point (4,7) into the equation
7= -3(4) + b
7= -12 + b
19 = b
y = -3x + 19 is the equation in slope intercept form
for point slope form:
-3x is still the slope and you replace x and y with the point 4,7
y- 7= -3 (x-4)
a Find the total surface area of a cuboid with dimensions 4cm × 3cm × 2cm.
B)If the length of the cube, 4cm, is doubled, what is the new surface area of the cuboid?
Answer:
24 millimeters B) Area of one side= 4*4
=16
Total number of faces= 6
Then total area= area of one side* number of sides
=16*6
=96 square cm
Step-by-step explanation:
A nationwide survey claimed that at least 65% of parents with young children condone spanking their child as a regular form of punishment. In a random sample of 100 parents with young children, how many would need to say that they condone spanking as a form of punishment in order to refute the claim at α = 0.5?
Answer:
here p=0.65 and n=100 hence standard error =(p*(1-.
Step-by-step explanation:
Find the digits in the tens place, in the hundredths place, and in the thousandths place for the following number 748.6291
Answer:
8 for tens, 9 for hundredths and thousandths is 1
Step-by-step explanation:
you can find the number by looking at the place of the numbers if it is tens look at the tens place which is the number eight as tens are 2 digit numbers
If <11 = <8, then which lines are parallel?
Answer:
lines c and p
Step-by-step explanation:
Is the relationship between x and y proportional? Explain.
x y
5 25
6 30
7 35
8 40
Answer:
yes
Step-by-step explanation:
because
5/25=1/5
6/30=1/5
7/35=1/5
8/40=1/5
plz tag in brainlist...
P(x)=x-3
g(x) = 2x-5
Find the following.
(p °q) (5)= and (q °p) (5)=
Part 1) Computing (p °q) (5)
[tex]p(x) = x-3\\\\p(q(x)) = q(x)-3\\\\(p \circ q)(x) = 2x-5-3\\\\(p \circ q)(x) = 2x-8\\\\(p \circ q)(5) = 2(5)-8\\\\(p \circ q)(5) = 2\\\\[/tex]
Answer: 2===========================================================
Part 2) Computing (q °p) (5)
[tex]q(x) = 2x-5\\\\q(p(x)) = 2(p(x))-5\\\\q(p(x)) = 2(x-3)-5\\\\(q \circ p)(x) = 2x-6-5\\\\(q \circ p)(x) = 2x-11\\\\(q \circ p)(5) = 2(5)-11\\\\(q \circ p)(5) = -1\\\\[/tex]
Answer: -1Find the equation of the line passing through the point (−5,−9) and parallel to the line y=3x+2 .
Answer:
Root:(-⅗,0)
vertical intercept:(0,5)
Step-by-step explanation:
Solve 3 - x= -9.
O A. x= 6
O B. x= 12
O c. x= -6
O D. x=-12
Answer:
x=12
Step-by-step explanation:
you need the x alone so you substract 3 from both sides.
Then you have, -x= -12
You need the x positive so you change the sign for it but as it is an equation you need to do the same thing on the other side, making both sides positive.
x=12
find the discriminant of -2x^2+8=x^2-28
show work please
Answer:
432
Step-by-step explanation:
Use the values of A, B, C to find the discriminant
Apply distributive 15+22
Answer:37
Step-by-step explanation:
log x √x + log √c c² = ?
[tex] log_{x}\sqrt{x} + log_{ \sqrt{c} } {c}^{2} = \\ [/tex]
please help me!!!!?;
Given that
log √x (x) + log c² (c)
⇛ log x^1/2 (x) + log c² (c)
We know that
log a^m (b^n) = m/n log a (b)
⇛ 1/2 log x (x) + 2 log c (c)
We know that
log a ( a) = 1
⇛ (1/2)(1) + 2(1)
⇛ (1/2)+2
⇛ (1+4)/2
⇛ 5/2
Answer:- log √x (x) + log c² (c) = 5/2
[(x) ,(c) , (a) represents the bases ]
Additional comment:
(a+b)(a-b) = a²-b²log a^m (b^n) = m/n log a (b)log a ( a) = 1also read similar questions: if log^2(x)=log^2(a)+log^2(b)-log^2(c) then x is....
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simplify the following expression. log(x2) - log(x) A. log(x^2+x) B. log(x^3) C. log(x^2-x) D. log(x)....
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what the area of a triangle whose base is 23 inches and whose height is 28. write your answer in decimal
Answer:
322
Step-by-step explanation:
Triangle area = base*height)2Here, area = 23*28/2=322
Answer:
322 [tex]in^{2}[/tex]
Step-by-step explanation:
Hope this helped!
Integrate:Cos 7x/(1+sin**2(7x))
Answer:
7x/1+7sin(2)x
Step-by-step explanation:
Line f is parallel to line g.which statements about line f and g is true
Answer:
Step-by-step explanation:
They have different y intercepts.
They have the same slope.
Here are 2 examples
y = 3x + 5
y = 3x + 19
The slopes are both three. The y intercepts are 5 for the top equation and 19 for the bottom equation.
They are both lines. That means their domain is -infinity <x < + infinity
Their range is - infinity <y < + infinity.
We are excluding examples like x = 3 and x = 5 and y = 1 and y = 3.
It is true that they both are parallel in both cases, but the discussion for each pair is a little different.
A retailer needs to purchase 11 printers. The first printer costs $58, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 11 printers?
$381.99
$500.19
$606.10
$609.00
Answer:
$500.19 is the answer
Step-by-step explanation:
pls vote branliest
The total cost of 11 printers is $500.19.
Given that,
A retailer needs to purchase 11 printers.
The first printer costs $58, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers.
We have to determine,
What is the total cost of 11 printers?
According to the question,
The first printer costs $58.
Each additional printer costs 5% less than the price of the previous printer, up to 15 printers.
The cost of a second printer is,
= 0.95 × 58 = $55.1
The cost of a third printer is,
= 0.95 × 55.1 = $52.345
The cost of a fourth printer is,
= 0.95 × 52.345 = $49.727
The cost of a fifth printer is,
= 0.95 × 49.727 = $47.241
The cost of a sixth printer is,
= 0.95 × 47.241 = $44.879
The cost of a seventh printer is,
= 0.95 × 44.879 = $42.635
The cost of an eight printer is,
= 0.95 × 42.635 = $40.50
The cost of a nineth printer is,
= 0.95 × 40.50 = $38.478
The cost of tenth printer is,
= 0.95 × 38.478 = $36.554
The cost of the eleventh printer is,
= 0.95 × 36.554 = $34.726
Therefore,
The total cost of 11 printers is,
= $58 + $55.1 + $52.345 + $49.727 + $47.241 + $44.879 + $42.635 + $40.50 + $38.478 + $36.554 + $34.726 = $500.19.
Hence, The total cost of 11 printers is $500.19.
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A bus traveling at a constant rate of 50 miles per hour. At this rate, how far will the bus travel 3 1/4 hours?
First, let's do the easy part! Multiplying 50 by 3 will give us how far the bus would travel in 3 hours. 50 x 3 = 150.
Now let's do the quarter. 50 / 4 = 12.5. Simply add these two together now!
The bus will travel 162.5 miles!
Hope this helps :)
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many
of them were adults?
A. 29 adults
B. 16 adults
C. 24 adults
D.10 adults
Answer:
C.24
Step-by-step explanation:
First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40
What is the percent of decrease from 80 to 68?
Answer:
-15%.
Step-by-step explanation:
Subtract 68 by 80 to get -12.
Divide -12 by the absolute value of 80 to get -0.15.
Multiply 100 to -0.15 to get -15.
A box is filled with five green card six green card and three blue cars. A card is chosen at random from the box. What is the Probability that it is a green or blue card
Answer:
so there is 14 cards in total so out of those 14 14 cards are either blue or green so 100%
Hope This Helps!!!
Evaluate the expression 5xy+ -2xy+y^2 when x=4 and y=-5
Answer:
-35
Step-by-step explanation:
5(4)(-5) + -2(4)(-5) + (-5)²
= -100 + 40 + 25
= -35
Answer: -35
Step-by-step explanation:
5(4)(-5)+(-2)(4)(-5)+(-5)^2
-100+40+25
-35
an expression that is equivalent to 10x - 8 +0.5(2x - 3)?
-
Answer:
......................
I need to know the area of this triangle and I would like to have an explanation because I dont know how to do it I know the formula just not how to get the height
Answer:
18 square units
Step-by-step explanation:
When one side is vertical or horizontal, it is convenient to find the height from the opposite vertex to that side. It is generally an integer number of grid squares.
Here, the height is 4 -(-2) = 6. The base length is 1 -(-5) = 6. That means the area is ...
A = 1/2bh
A = 1/2(6)(6) = 18 . . . . square units
_____
Alternate solution
If you want to go at this the hard way, you can find the length of LK and the distance of J to that line.
The length of LK is ...
d = √((x2 -x1)^2 +(y2 -y1)^2) = √((4 -(-2))^2 +(3 -(-5))^2) = √(36 +64) = 10
The distance to line LK can be found by writing the equation of the line LK in general form:
4x -3y -7 = 0
Then the distance formula for point (x, y) is ...
d = |4x -3y -7|/√(4^2 +3^2)
d = |4(-2) -3(1) -7|/5 = |-8 -3 -7|/5 = 3.6
Using the area formula with these dimensions gives ...
A = 1/2bh = 1/2(10)(3.6) = 18 . . . . square units
Answer:
18 square units
Step-by-step explanation:
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If angle CAB= x+40, angle ACB=3x+10, angle CBD= 6x, what is angle CAB