Answer:
180
Step-by-step explanation:
Plz help, and show details, will give brainliest to best answer
Solve the following trigonometric equation over the interval of [0,2π). Show your work, thank you!
[tex] \large{2sin \theta tan \theta = - 3}[/tex]
Answer:
[tex] \rm \displaystyle \theta = \{ {150}^{ \circ} , {240}^{ \circ} \}[/tex]
Step-by-step explanation:
we would like to solve the following equation:
[tex] \displaystyle 2 \sin( \theta) \tan( \theta) = - 3[/tex]
to do so we need to put the equation in term of a function of a angle therefore rewrite tanθ:
[tex] \displaystyle 2 \sin( \theta) \cdot \frac{ \sin( \theta) }{ \cos( \theta) } = - 3[/tex]
simplify multiplication:
[tex] \displaystyle \frac{ 2\sin^{2} ( \theta) }{ \cos( \theta) } = - 3[/tex]
cross multiplication:
[tex] \displaystyle 2\sin^{2} ( \theta) = - 3 \cos( \theta) [/tex]
isolate -3cosθ to left hand side and change its sign:
[tex] \displaystyle 2\sin^{2} ( \theta) + 3 \cos( \theta) = 0[/tex]
well we can rewrite sin²θ by applying Pythagorean theorem and that yields:
[tex] \rm \displaystyle 2(1 - \cos^{2} ( \theta)) + 3 \cos( \theta) = 0[/tex]
distribute:
[tex] \rm \displaystyle 2 - 2\cos^{2} ( \theta) + 3 \cos( \theta) = 0[/tex]
now notice that our equation ended up with a pattern and that is Quadratic thus by letting cosθ be x to transform the equation:
[tex] \rm \displaystyle 2 - 2 {x}^{2} + 3 x = 0[/tex]
rearrange it to standard form:
[tex] \rm \displaystyle - 2 {x}^{2} + 3 x + 2 = 0[/tex]
divide both sides by -1:
[tex] \rm \displaystyle 2 {x}^{2} - 3 x - 2 = 0[/tex]
well we can factor the quadratic to do so rewrite -3x as -4x+x:
[tex] \rm \displaystyle 2 {x}^{2} - 4 x + x - 2 = 0[/tex]
factor out 2x:
[tex] \rm \displaystyle 2x ({x}^{} - 2)+ x - 2 = 0[/tex]
factor out 1:
[tex] \rm \displaystyle 2x ({x}^{} - 2)+ 1(x - 2 ) = 0[/tex]
group:
[tex] \rm \displaystyle (2x + 1)(x - 2 ) = 0[/tex]
by Zero Product property we obtain:
[tex] \rm \displaystyle \begin{cases} 2x + 1 = 0\\ x - 2 = 0 \end{cases}[/tex]
cancel 1 from the first equation and add 2 to the e equation:
[tex] \rm \displaystyle \begin{cases} 2x = - 1\\ x = 2\end{cases}[/tex]
substitute back:
[tex] \rm \displaystyle \begin{cases} 2 \cos( \theta) = - 1\\ \cos( \theta) = 2\end{cases}[/tex]
since cosθ is only defined for the interval [1,-1] the second equation is false for any value of θ but we can still continue the first equation
[tex] \rm \displaystyle \begin{cases} 2 \cos( \theta) = - 1\\ \cos( \theta) \neq 2\end{cases}[/tex]
divide both sides by 2:
[tex] \rm \displaystyle \cos( \theta) = \frac{ - 1} {2}[/tex]
by unit circle we acquire:
[tex] \begin{cases} \rm \displaystyle \theta = {150}^{ \circ} \\ \theta = {240}^{ \circ} \end{cases}[/tex]
add period of 2nπ:
[tex] \begin{cases} \rm \displaystyle \theta = {150}^{ \circ} + 2n\pi\\ \theta = {240}^{ \circ} + 2n\pi \end{cases}[/tex]
for the interval [0,2π) θ is only defined when n is 0 Thus:
[tex] \begin{cases} \rm \displaystyle \theta = {150}^{ \circ} + 2(0)\pi\\ \theta = {240}^{ \circ} + 2(0)\pi \end{cases}[/tex]
simplify:
[tex] \begin{cases} \rm \displaystyle \theta = {150}^{ \circ} \\ \theta = {240}^{ \circ} \end{cases}[/tex]
hence,
θ is equal to 150° and 240°
Can someone help me with this, pleasee.
Answer:
i will say the first one cannot, the second one cannot and the third one can
Step-by-step explanation:
but i am not 100% sure sry
Is there any more info on this?
Step-by-step explanation:
.
Expand & simplify
(x + 10)(x + 9)
Answer:
its
[tex]x^{2} + 19x + 90[/tex]
Suppose that many large samples were taken from a population and the sample proportion centered around 0.25 which of the following is most likely the population parameter
0.25
0.45
0.35
0.15
Answer:
0.25
Step-by-step explanation:
Hope it helps, sense it’s centered around 0.25 then the parameter would be 0.25
To It’s centered around 0.25 then the parameter would be 0.25.
We have given,
Suppose that many large samples were taken from a population and the sample proportion centered around 0.25
We have to determine which of the given is most likely the population parameter.
What is the center parameter in the large sample?
A sample means from any distribution. We could have a left-skewed or a right-skewed distribution.
To It’s centered around 0.25 then the parameter would be 0.25
Therefore option A(0.25) is correct
To It’s centered around 0.25 then the parameter would be 0.25.
To learn more about the population parameter visit:
https://brainly.com/question/2292917
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Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Both A and B
Step-by-step explanation:
They both pass vertical line test
what is the value of 1 in 915,342,760
the 1 is in the 10 million place
Hi can someone help me
Answer:
D. The average time spent is 11 average.
Step-by-step explanation:
The mean is the average. The average time spent is 11 average.
if you solve this ..
u are not human being .
Answer:
I have not solved
Step-by-step explanation:
I am human being sonI didn't answer
Mark me as brainliest
Two numbers multiply to be 4 and add to be -5
Answer:
-1, -4
Step-by-step explanation:
x + y = -5
x×y = 4
=>
x = -5 - y
=> (-5 - y) × y = 4
-5y - y² = 4
y² + 5y + 4 = 0
the solution for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = 5
c = 4
x = (-5 ± sqrt(25 - 16))/2 = (-5 ± 3)/2
=> x = -2/2 = -1 or x = -8/2 = -4
=> y = 4/-1 = -4 or y = 4/-4 = -1
since the sequence in an addition and multiplication does not make any difference, the two numbers are simply -1 and -4
the diagram of g||h, with transversal f,
Type the number in standard form
4.21 x 10^4
Answer:
0.00042
Step-by-step explanation:
WILL GIVE BRAINLIEST!!
Directions: Solve using the FOIL method. Hint: Watch out for any negative signs and follow rules for signed numbers!
1. (x-2)(x+3)
2. (x+4)(x-12)
3. (x+3)(x+4)
4. (x+6)(x+7)
5. (x+8)(x+9)
6. (x-5)(x+5)
7. (x+3)(x-3)
8. (x+10)(x+10)
9. (x-2)(x+12)
10. (x + 4)(x - 3)
Need help ASAP I will give 20 points please
Answer:
Step-by-step explanation:
volume of cylinder=πr^2h
=3.14*4=2^2*6
=4=3.14*4*6
=3.14*24
=75.36
=75.4 inches ^3
=
Find the solution(s) of the system of equations.
y = –x2 + 2
y = x2 + 4x + 4
How many solutions does this equation have one, none, or infinite 12+2i-i=9i+6
Answer:
i=3/4
Step-by-step explanation:
Assuming that we are treating "i" as a variable and not the constant "i":
12+2i-i=9i+6
12+i=9i+6
12=8i+6
6=8i
8i=6
i=6/8
i=3/4
Therefore, the equation has only one real solution which is i=3/4
What is the area of the right triangle shown in the image.
Answer:
24 sq. in
Step-by-step explanation:
To find the area of a triangle, you multiply both sides by one another, then divide the product in half.
In this case it would go along the lines of:
6 x 8 = 48
48/2 = 24
And 24 is the desired answer.
Find the percent change. Round to the nearest tenth of a percent when necessary. Indicate if the percent
change is an increase or decrease.
From 50 to 94.
46.8% derease
46.8% increase
88% derease
88% increase
Answer: 88% increase
a. step one
b.step two
c. step three
d. Keisha did not make a mistake.
Answer:
d. Keisha did not make a mistake
Step-by-step explanation:
3+(-4)-7
3+(-4)+(-7) adding negatives is the same as subtracting
3+(-11) -4 and -7 do make -11
-8 3 and -11 do make -8
So she did it correctly, which means d is the right answer.
:) ur welcome
p+q/2; use p=1, and q=-1
Answer:
0
Step-by-step explanation:
Plug p and q in
1+-1/2
0/2
0
If this helps please mark as brainliest
Answer:
see below
Step-by-step explanation:
p+q/2
If
p + q/2
1 + -1/2
1/2
If (p+q)/2
(1-1)/2
0
The number of new trees planted is increasing each year. The table shows the
change in number of new trees planted from year to year. How many new
trees will there be in year 5?
Year
Population
1
30,000
2
45,000
3
67,500
88 Square centimeter in Square millimetres?
Answer:
8800 (Square Millimeters)
which function represents the sequence? A.f(n) =n+3 B.f(n)=7n-4 C.f(n)=3n+7 D.f(n)=n+7
Answer:
f( n ) = 7 n - 4
Step-by-step explanation:
Terms : 3,10 , 17, 24, 31
Means this = [tex]a_{1}[/tex] = 3
The differences:
d = 10-3=7
our term of the sequence =
f( n ) = 7 n - 4
cuanto es el p (x)-s(x)-q(x)
Answer:
sorry no answer
I apologize
The range of the data: 6,14,20,16,6,5,4,18,25,15, and 5 is
a. 4
b. 21
c. 25
d. 20
Answer:
21
Step-by-step explanation:
Range is the largest value minus the smallest value
25 is the largest value
4 is the smallest value
25-4 =21
Answer:
b. 21
Step-by-step explanation:
biggest number - smallest number
25 - 4 = 21
help asap please!!!!
Answer:
9 pi
Step-by-step explanation:
First find the circumference of the circle
C =2 * pi *r
C = 2 * pi *9
C = 18 pi
This is a semicircle which is 1/2 of a circle
Take 1/2 of the circumference
1/2 C = 1/2 ( 18 pi)
1/2 C = 9 pi
Can someone please help me figure this out. (y-6)+8 y=13
[tex]x^{2} -7x-18[/tex]
Answer:
(x - 9)(x + 2)
Step-by-step explanation:
x² - 7x - 18
x² + 2x - 9x - 18
x(x + 2) - 9(x + 2)
(x - 9)(x + 2)
Find x.
Do not round your answer.
8 cm
4 cm
X
x =
= [ ? ] cm
Answer:
x =12
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(4+x) * 4 = 8^2
Distribute
16+4x = 64
Subtract 16 from each side
4x = 48
Divide each side by 4
4x/4 = 48/4
x = 12
Answer: 12
Step-by-step explanation: 8*8 = 4(4+x), which is equal to 64 = 16 + 4x, subtract 16 from both sides, 48 = 4x, divide both sides by 4 to isolate x, 12 = x
a rectangle is 12 feet long and 5 feet wide. if the length of the rectangle is increased by 25% and the width is decreased by 20% what is the change in the area of the rectangle
Answer:
60% decrease in area
Step-by-step explanation:
12 x5 == 60 sq feet (original area)
9 x 4 == 36 sq feet (new area)
36/60 = 6/10 = 60%