4 sin(x) + 9 cos(x) = 0
4 sin(x) = -9 cos(x)
tan(x) = -9/4
x = arctan(-9/4) + nπ … … … (in radians)
or
x = arctan(-9/4) + 180n ° … … … (in degrees)
where n is any integer.
I'm guessing you're solving for x over some domain, probably 0° ≤ x < 360°. In that case, you would have two solutions for n = 1 and n = 2 of
x ≈ 113.96° and x ≈ 293.96°
3. Find the product, using suitable properties :
a) 26 x (-48) + (-48) x (-36)
b) 625 x (-35) + (-625) x 65
please answer fast 10 marks
a) 26 x (-48) + (-48) x (-36) = ( –1248) + ( + 1728) = – 1248+ 1728 = 480
b) 625 x (-35) + (-625) x 65 = ( –21875) + ( –40625) = – 21875 –40625 = –62500
I hope I helped you^_^
4.
Find the inverse of A if it has one, or state that the inverse does not exist.
Answer:
Hello,
[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]
Step-by-step explanation:
See jointed file
The inverse of the matrix A is
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]
The matrix A is a square matrix and its determinant is not zero.
So the inverse exist.
The inverse of matrix A.
We will change the rows into columns and columns into rows.
So,
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
Thus,
The inverse of the matrix A is given above.
Learn more about matrix here:
https://brainly.com/question/28180105
#SPJ2
if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me
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?
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
A factory inspector found flaws in 3 out of 18 wooden boxes. What is the experimental probability that the next wooden box will be flawed?
Write your answer as a fraction or whole number.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{1}{6}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Box Probability}}\\\\\rightarrow \frac{\text{# of boxed flawed}}{\text{# of boxes checked}} \\\\\rightarrow \frac{3}{18}\\\\\rightarrow \frac{3/3}{18/3}\\\\\rightarrow\boxed{\frac{1}{6}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Helpppp pleaseeee !!!!!!
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9
Answer:
(-3)
Step-by-step explanation:
follow me if you want
Explain why they substituted cos(60) with 1/2 ?
(Look at image)
9514 1404 393
Answer:
equals can be substituted anytime anywhere
Step-by-step explanation:
cos(60°) = 1/2, so wherever one appears, the other can be substituted. This is allowed by the substitution property of equality.
__
If you don't substitute at some point, you find the answer to be ...
x = 10/cos(60°)
Most of us are interested in a numerical value for x, so we prefer that cos(60°) be replaced by a numerical value.
pls help me ASAP !!!!!!!!!
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
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
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.
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]
ax^2-y^2-x-y factorize
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
help lol i forgot everything of the summer time
fill in the table using this function rule
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
Which function represents g(x), a refection of f(x)=1/2(3)^x across the y-axis
Answer: g(x) = (1/2)3^-x reflection over y axis yields (-x,y)
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
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
The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?
Answer:
9 years older
Step-by-step explanation:
The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )
In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so
[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides
40x + 150 = 30x + 180 ( subtract 30x from both sides )
10x + 150 = 180 ( subtract 150 from both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Then
Michell is 8x = 8 × 3 = 24 years old
Connor is 5x = 5 × 3 = 15 years old
Mitchell is 24 - 15 = 9 years older than Connor
PLS HELP ME ON THIS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU KNOW TGE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
LOL
Answer:
D. The over 30s have a larger range and interquartile range than the under 30s
Step-by-step explanation:
In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.
Independent Practice
Which model is most appropriate for the set of points?
(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)
A.
exponential
B.
linear
C.
quadratic
Please help me find x
Need help fast!!
Answer:
x = 100°
Step-by-step explanation:
p and q are parallel lines. Construct line 'l' parallel to p and q
a = 30° {p// l when parallel lines are intersected by transversal alternate interior angles are congruent}
c +110 = 180 {linear pair}
c = 180 - 110
c = 70°
b= c {q // l when parallel lines are intersected by transversal alternate interior angles are congruent}
b = 70°
x = a + b
x = 30° + 70°
x = 100°
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
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]
I NEEDDD HELPPP ITSSSSSS URGENTTTTT!!!
Basically count/add up the total amount of degrees that are include in the angle <FHD.
-- (central angles)
So, 35 + 65 = 100 degrees
F is on the bisector of angle BCD. Find the length of FD (with lines over FD)
Answer:
8n-2 = 6n+9
2n-2 = 9
2n = 11
n = 5.5
So C is correct
Let me know if this helps!
find the missing side. Round it the nearest tenth.
Answer: x= 11√3= 19.0525 = 19.1
Step-by-step explanation:
Let the reference angle be 30
so
cos 30 = b/h
√3/2 = x/22
or, 22√3 = 2x
or. x = (22√3)/2
so, x = 11√3
Answer:
x = 19.1 cm
Step-by-step explanation:
→ Find the name of the side you are not given
Opposite
→ Find a formula without opposite in it
Cos = Adjacent ÷ Hypotenuse
→ Rearrange to make adjacent the subject
Adjacent = Cos × Hypotenuse
→ Substitute in the values
Adjacent = Cos ( 30 ) × 22
→ Simplify
Adjacent = 19.1
What is the smallest 3-digit palindrome that is divisible by both 3 and 4?
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
7t + 6 + 3v + 6v
Hey can someone help ne
Answer:
7t + 6 + 9v
Step-by-step explanation:
7t + 6 + 3v + 6v (since 3v and 6v are like terms you will add them both.)
7t + 6 + 9v
Hope this helps, thank you :) !!
Answer:
7t+6+9v
Step-by-step explanation:
7t+6+3v+6v
7t has no opponent it is =7t
6 is on it own =6
3v+6v=9v,reason is 3v has an opponent which is 6v so addition of 3v and 6v is =9v
so ur ans. is =7t+6+9v
Help me! thank you so much
Answer:
Step-by-step explanation:
[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]
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:)
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
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.
What would it be tho 300 doesn’t show up in my options my options are
1/49 -1/49 -49 and 49
Answer ASAP please!
………
Answer:
47.746, answer choice C
Step-by-step explanation:
47.746
