[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]
Answers
Answer:
\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}
\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}
Step-by-step explanation:
![[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/DA8qrAO0kFjoIkqGIwXz1StIwJ0NHFbq.png)
Related Questions
3a + 2 = 20
5(b+1) = 10
3 (2y - 3) - 2y = y-3
2+ (2+4p) =6p
Please answer these questions with steps please!
Answers
3a=18
a=6
2. b+1=2
b=2-1
b=1
3. 6y-9-2y=y-3
4y-9=y-3
4y-y=-3+9
3y=6
y=2
4. 2+2+4p=6p
4+4p=6p
4p-6p=-4
-2p=-4
p=2
If LM = 9x + 27 and RS = 135, find x.
Answers
Answer:
x=12
Step-by-step explanation:
LM = RS
9x+27 = 135
Subtract 27 from each side
9x+27-27 =135-27
9x=108
Divide each side by 9
9x/9 = 108/9
x = 12
the boxes are equivalent so the one with a single dash is equal to the other with a single dash.
the one with 2 dashes is equal to the other with 2 dashes so on and so forth
SR=LM
LM=9x+27
RS=135
9x+27=135
so I solve it in my own weird way but you can solve it differently. 135-27=108
108/9=12
so your answer is 12
If a line has a midpoint at (2,5), and the endpoints are (0,0) and (4,y), what is the value of y? Please explain each step for a better understanding:)
Answers
Answer:
y = 10
Step-by-step explanation:
To find the y coordinate of the midpoint, take the y coordinates of the endpoints and average
(0+y)/2 = 5
Multiply each die by 2
0+y = 10
y = 10
What is the smallest 3-digit palindrome that is divisible by both 3 and 4?
Answers
Answer:
252
Step-by-step explanation:
To be divisible by 3, it's digits have to add to a number that is a multiple of 3.
To be divisible by 4 its last 2 digits have to be divisible by 3.
So let's start with 1x1 which won't work because 1x1 is odd. so let's go to 2x2 and see what happens.
212 that's divisible by 4 but not 3
222 divisible by 3 but not 4
232 divisible by 4 but not 3
242 not divisible by either one.
252 I think this might be your answer
The digits add up to 9 which is a multiple of 3 and the last 2 digits are divisible by 4
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answers
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
A natural number is a positive whole number.
A whole number is a positive number with no fractions or decimals.
A interger is a whole number negative or positive.
A rational number is a number that terminates or continue with repeating digits.
A irrational number is a number that doesn't terminate or continue with repeating digits.
1. Rational Number
2. Natural,Whole,Interger,Rational
3. Whole,Rational,Interger
4. Rational
5.Irrational
6.Rational
7.Natural,Whole,Interger,Rational
8.Interger,Rational
9.Irrational
Which value of x makes this equation true?-9x+15=3(2-x)
Answers
Step-by-step explanation:
-9x+15=3(2-x)
expand the bracket by the right hand side6-6x
2. collect like terms
-9x+15= 6-6x
15-6 = 6x+9x
11= 15x
3. divide both sides by the coefficient of X which is 15
x= 11/15
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answers
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
Lilian is building a swimming pool in the shape of a right rectangular prism. The area of the base of the swimming pool is 72 square meters. The depth of the swimming pool is 3 meters. What is the volume of the swimming pool?
Answers
Answer:
216
Step-by-step explanation:
Volume of a rectangular prism = area of base * depth
Area of base: 72
Depth: 3
Volume = 72 * 3 = 216
help help help help
Answers
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
−30=5(x+1)
what is x?
Answers
[tex]\\ \rm\Rrightarrow -30=5(x+1)[/tex]
[tex]\\ \rm\Rrightarrow -30=5x+5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-30-5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-35[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-35}{-5}[/tex]
[tex]\\ \rm\Rrightarrow x=7[/tex]
Answer:
x = -7
Step-by-step explanation:
-30 = 5 (x -1 )
5 ( x + 1 ) =-30
5 (x + 1 ) = - 30
5 5
x + 1 = -6
x + 1 -1 = -6 -1
x = - 7
Write the equation of the sinusoidal function shown?
A) y = cos x + 2
B) y = cos(3x) + 2
C) y = sin x + 2
D) y = sin(3x) + 2
Answers
Answer:
günah(3x) + 2
Step-by-step explanation:
Gösterilen sinüzoidal fonksiyonun denklemini yazınız? A) y = cos x + 2 B) y = cos(3x) + 2 C) y = günah x + 2 D) y =
Answer:
y = sin(3x) + 2
Find the value of the sum 219+226+233+⋯+2018.
Assume that the terms of the sum form an arithmetic series.
Give the exact value as your answer, do not round.
Answers
Answer:
228573
Step-by-step explanation:
a = 219 (first term)
an = 2018 (last term)
Sn->Sum of n terms
Sn=n/2(a + an) [Where n is no. of terms] -> eq 1
To find number of terms,
an = a + (n-1)d [d->Common Difference] -> eq 2
d= 226-219 = 7
=> d=7
Substituting in eq 2,
2018 = 219 + (n-1)(7)
1799 = (n-1)(7)
1799 = 7n-7
1799 = 7(n-1)
1799/7 = n-1
257 = n-1
n=258
Substituting values in eq 1,
Sn = 258/2(219+2018)
= 129(2237)
= 228573
2. Determine the measure of the angles indicated by letters. Justify your answers with the
properties or theorems you used.
Answers
Answer:
a = 50°
b = 130°
c = 50°
d = 50°
e = 130°
f = 130°
g = 50°
Answered by GAUTHMATH
Where did term “infinity” come from
Answers
how many inches is 775 centimeters
Answers
Answer:
305.11
Step-by-step explanation:
Just use a calculator. A centimeter is 2.5 inches. Divide 775 by that.
3,125 subtracted by what can give me 514
Answers
Answer:
2611
Step-by-step explanation:
3125-2611= 514
for more answers check my bio
Determine three consecutive odd integers whose sum is 2097.
Answers
Answer:
first odd integer=x
second odd integer=x+2
third odd integer=x+4
x+x+2+x+4=2097
x+x+x+2+4=2097
3x+6=2097
3x=2097-6
3x=2091
3x/3=2091/3
x=697
therefore, x=697
x+2=697+2=699
x+4=697+4=701
Given 12 consecutive integers, how many ways can three of these integers be selected to give a sum which divides by 4.
Disclaimer: A lot of points to be given, Full explanation required. Not only answer. Remember the sum of the number must be divisible by 4. I think modular arithmetic is the way to solve it, but who knows???
Answers
Answer:
55 waysStep-by-step explanation:
Out of 12 consecutive integers:
3 - divide by 4, so the remainder is 0 3- give remainder of 1 3- give remainder of 2 3 - give remainder of 3Sum of 3 integers will be divisible by 4 if the remainders are:
0 - 0 - 0 ⇒ 1 combination 0 - 1 - 3 ⇒ 3*3 = 9 combinations 0 - 3 - 1 ⇒ 3*3 = 9 combinations 1 - 1 - 2 ⇒ 2*3 = 6 combinations 1 - 2 - 1 ⇒ 2*3 = 6 combinations 2 - 1 - 1 ⇒ 2*3 = 6 combinations 3 - 0 - 1 ⇒ 3*3 = 9 combinations 3 - 1 - 0 ⇒ 3*3 = 9 combinationsSo total number of combinations is:
1 + 9*4 + 6*3 = 55ax^2-y^2-x-y factorize
Answers
Answer:
x(ax-1)-y(y+1)
Step-by-step explanation:
you have to group the like terms
ax^2-x-y^2-y
x(ax-1)-y(y+1)
I hope this helps
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answers
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
What is the area of a rectangle with vertices at (7,3) (12,3) (12,11) (7,11)
Answers
Answer:
Area = 5 × 8
= 40 square units
Answer:
40^2
Step by Step Solution:
I counted the difference between the length and the width, which was 5 and 8, then using the formula for area, lw=a^2, I did 5(8)=40^2. Some people leave out the squared part of the area, but 40^2 would be the most correct option if they do not square any of the answers, just put 40 that'll probably be accepted too.
F is on the bisector of angle BCD. Find the length of FD (with lines over FD)
Answers
Answer:
8n-2 = 6n+9
2n-2 = 9
2n = 11
n = 5.5
So C is correct
Let me know if this helps!
help me pls??????? :)
Answers
Answer:4 in each bad 2 left over
Step-by-step explanation:
Answer:
4 in each bag and 2 left over
Step-by-step explanation:
divide 14 by 3
3 goes into 14, 4 times
14 - 12 = 2
4 in each bag and then 2 left over
result of 5 and 75 with dividid by 3
Answers
Answer:
your answer is 30
Step-by-step explanation:
I hope this help
PLS HELP ME ON THIS QUESTION I WILL MRK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following measures is a measure of spread?
A. median
B. range
C. mode
D. mean
Answers
Answer:
range
Step-by-step explanation:
Answer:
B. range.
Step-by-step explanation:
others are:
» Standard variation.
» Interquatile range.
» Quatiles, deciles and percentiles.
» variance.
[tex]{ \underline{ \blue{ \sf{christ \: † \: alone}}}}[/tex]
Please help I’ll mark as brainlist
Answers
Answer:
Ekta and Preyal
Step-by-step explanation:
Originally the cubes have a perimeter of 15, both Ekta and Preyal have a perimeter of 17 which is exactly a 2 unit increase
Hi, Which option is correct??
Answers
Answer:
B
Step-by-step explanation:
option B is not similar.
the ratio of each side isn't same
What is an example in your house of a point ?
Answers
Answer:
Step-by-step explanation:
Nothing. A point is dimensionless. Ugh what an awful LOL.
How about the tip of a candle that has never been lit?
Two observers are 300 ft apart on opposite sides of a flagpole. The angles of
elevation from the observers to the top of the pole are 20°
and 15°. Find the
height of the flagpole.
