Answers
Answer:
[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]
Or, their exact solutions:
[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle 2\sec^2 \theta = 4\tan \theta + 1[/tex]
For 0° ≤ θ ≤ 360°.
Recall that tan²(θ) + 1 = sec²(θ). Substitute:
[tex]\displaystyle 2\left(\tan^2 \theta + 1\right) = 4\tan \theta + 1[/tex]
Distribute:
[tex]\displaystyle 2\tan^2\theta + 2 = 4\tan\theta + 1[/tex]
Isolate:
[tex]\displaystyle 2\tan^2\theta - 4\tan\theta + 1 = 0[/tex]
This is in quadratic form. Thus, we can solve it like a quadratic. Let u = tan(θ). Hence:
[tex]\displaystyle 2u^2 - 4u + 1=0[/tex]
The equation is not factorable. Therefore, we can consider using the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]
In this case, a = 2, b = -4, and c = 1. Substitute and evaluate:
[tex]\displaytstyle \begin{aligned} u &= \frac{-(-4)\pm\sqrt{(-4)^2 - 4(2)(1)}}{2(2)} \\ \\ &= \frac{4\pm\sqrt{8}}{4} \\ \\ &= \frac{4\pm2\sqrt{2}}{4} \\ \\ &= \frac{2\pm\sqrt{2}}{2}\end{aligned}[/tex]
Therefore:
[tex]\displaystyle u = \frac{2+\sqrt{2}}{2} \approx 1.7071\text{ or } u = \frac{2-\sqrt{2}}{2}\approx 0.2929[/tex]
Back-substitute:
[tex]\displaystyle \tan\theta = \frac{2+\sqrt{2}}{2} \text{ or } \tan \theta = \frac{2-\sqrt{2}}{2}[/tex]
Take the inverse tangent of both equations. Hence:
[tex]\displaystyle \theta = \arctan\frac{2+\sqrt{2}}{2} \approx 59.6388^\circ\text{ or } \theta = \arctan\frac{2-\sqrt{2}}{2}\approx 16.3249^\circ[/tex]
The same value of tangent occurs twice in every full rotation. Hence, by reference angles, the other two solutions are:
[tex]\displaystyle \theta = 180^\circ + \arctan\frac{2+\sqrt{2}}{2} \approx 239.6388^\circ \\ \\ \theta = 180^\circ + \arctan\frac{2-\sqrt{2}}{2} \approx 196.3249^\circ[/tex]
In conclusion, the four solutions are:
[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]Or, approximately:
[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]
Related Questions
See attachment for the question
Answers
Answer:
-22
Step-by-step explanation:
f(x) = 3x^2 - 5
let x= 3
f(3) = 3*(3)^2 -5 = 3(9) -5 =27-5 =22
g(x) = -2x+5
Let x = 3
g(3) = -2(3) +5 = -6+5 = -1
f(3) *g(3) = 22(-1) = -22
Eunice buys dog bed with a listed price of $31. Eunice uses a sale that provides 30% off. What is the total
final price Eunice pays?
A. $21.70
B. $23.70
C. $25.55
D. $28.10
Answers
Answer:
21.70
Step-by-step explanation:
First find the discount
31 * 30%
31 *.30
9.3
Subtract from the original amount
31 - 9.3
21.70
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! NOT A MULTIPLE CHOICE!!!
The point (-2, 5) is reflected over an axis and the new point is located in Quadrant 3.
a. Describe the reflection that happened. What axis was the point reflected over?
b. What are the coordinates of the new point?
Answers
9514 1404 393
Answer:
x-axis(-2, -5)Step-by-step explanation:
a) The original point is in quadrant 2. Reflection into quadrant 3 is a reflection over the x-axis.
__
b) Reflection over the x-axis changes the sign of the y-coordinate. The new point is (-2, -5).
Is 1 3/4 closer to 1 or 2 ? Explain your answer
Answers
Answer:
it's closer to 2
Step-by-step explanation:
In order to get to 1 from that number, you have to subtract 3/4. In order to get to 2 from that number, you only have to add 1/4. Clearly, the jump in adding is smaller than the jump to subtracting, which means it's closer to 2.
The number is closer to 2
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Given number:
1 3/4 = 7/4
On dividing
7/4 = 1.75
Hence, the number is closer to 2.
Learn more about fraction here:
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(2x+1)(3x+4)=0
2x+1=0 3x+4=0
Solve for both equations. What are the two x-values/answers going to be? Leave your answer in a simplified fraction.
(I don’t know what to do next)
Answers
Answer:
2x+1=0.
2x=0-1.
2x=-1.
2x/2=-1/2.
x=-2.
3x+4=0
3x=0-4
3x=-4
3x/3=-4/3
[tex]x = 1 \frac{1 }{3} [/tex]
Find the midpoint between each pair of points (-1,-5) and (-5,9)
Answers
Answer:
(-3,2) is the midpoint
Step-by-step explanation:
ok
For what values of k will the equation 4x² + 8x + k = 0 have two complex solutions?
Answers
Answer:
k = -4x² - 8x
Step-by-step explanation:
Subtract 4x² from both sides of the equation.
8x + k = -4x²
Subtract 8x from both sides of the equation.
k = -4x² - 8x
Answer:
k > 4
Step-by-step explanation:
Using the discriminant to determine the nature of the solutions
• If b² - 4ac < 0 then the solutions are not real, that is they are complex
Given
4x² + 8x + k = 0
with a = 4, b = 8, c = k , then
8² - (4 × 4 × k) < 0
64 - 16k < 0 ( subtract 64 from both sides )
- 16k < - 64
Divide both sides by - 16, reversing the symbol as a result of dividing by a negative quantity.
k > 4
Any value of k greater than 4 will mean the equation has 2 complex solutions
6. (09.02 MC)
An object's velocity is defined by the vector-valued function v(t)
= (In(t –2), e^(2t-t^2))
What is the acceleration vector a(t) at t(3)? (10 points)
O
01-14
O
O
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]v_x(t)=ln(t-2)\ \Longrightarrow\ a_x(t)=\dfrac{1}{t-2} \\\\v_y(t)=e^{2t-t^2}\ \Longrightarrow\ a_y(t)=e^{2t-t^2}*(2-2t)\\\\t=3\ i\ suppose\ \\\\a_x(3)=\dfrac{1}{3-2}=1\\\\a_y(t)=e^{6-9}*(2-6)=-\dfrac{4}{e^3}[/tex]
5. (09.06 MC)
The graphs of the polar curves r = sin e-2 and r = cos(20 + 3) are shown.
Find the area of R, which is the region inside r = sin 6-2, but outside r = cos(20 + 3). (10 points)
31.416
12.566
15.708
0 25.133
Answers
Answer:
12.566
Step-by-step explanation:
A = ∫1/2(r)^2dtheta from a - b = 0 to 2π
∫1/2(sin^2theta-4sintheta+4)dtheta
[9/4theta+2costheta-1/8sin2theta] from 0 to 2π…
when you solve this you get 14.137 without taking out the cos(2theta+3)
THE STUDENTS ON THE SCHOOL NEWSPAPER ARE CONTRIBUTING MONEY FOR A GIFT FOR THEIR STAFF ADVISOR. THE COST PER STUDENT FOR THE GIFT VAIES INVERSELY AS THE NUMBER OF STUDENTS WHO CONTRIBUTE. iT WILL COST $6 PER STUDENT IF 12 STUDENTS CONTRIBUTE. HOW MUCH WILL IT COST PER PERSON IF 15 STUDENTS CONTRIBUTE
Answers
Answer:
ok
Step-by-step explanation:
-8 + 2x + 17 - x + 20
Answers
Explanation: 20+17-8=29 , 2x-x=1x=x
Given the sequence -14, -6, -2, 0, 1, ..., find the recursive formula.
Answers
Answer:
C is the answer to your question
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
Answers
Answer:
9Step-by-step explanation:
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
[tex] = 1 + 8 - 0[/tex]
= 9 (Ans)
Find the missing side, then, round to the nearest tenth.
Looking for help with this problem!
Answers
Answer:
4.6 = x the side opposite C would be 6.1
Step-by-step explanation:
you can use law of sine
you know you have a right triangle so the missing angle B = 49
4/sin41=x/sin49
The sides in each pair of figures are proportional. Find the missing length.
Answers
Answer:
41. is c.
42. is d.
Step-by-step explanation:
2ja bag has 3 red and 6 green balls. Two
balls are drawn from the bag one after the
other without replacement. What's the
probability of having a green ball drawn
both times
Answers
Answer:
5/12
Step-by-step explanation:
Probability of drawing green ball on the first time=6/9=2/3
Probability of drawing green ball on the second time=5/8
Probability of having a green ball drawn
both times=(2/3)*(5/8)=10/24=5/12
Study the figure and find the effort.
Please help...
Answers
Answer:
300
Step-by-step explanation:
I hope it will help you.
Let A = {a, b, c, d}, B = {a, c, d, e}. Let f : A → R and g : B → R such that f = {(a, 1),(b, 2),(c, 2),(d, 4)} and g = {(a, 0),(c, 4),(d, 8),(e, 0)}. State the domain and find: f/g
Answers
Answers:
Domain = {c, d}f/g = { (c, 1/2), (d, 1/2) }============================================================
Explanation:
The domain of f: {a,b,c,d} which is drawn from set A.
The domain of g: {a,c,d,e} which is drawn from set B
So far, we can see the possible inputs are: a,b,c,d,e
Let's go through each lowercase letter of the given sets
If 'a' is plugged into f/g, then we'll have 0 in the denominator due to the ordered pair (a,0) in function g. This causes a division by zero error so the input 'a' is not allowed in the domain of f/g.If we tried b, then it would work for function f, but it doesn't work for function g. If we tried to compute g(b), then the result is undefined. This is because the lowercase b input is not found in set uppercase B which is where function g selects its inputs from. So b is eliminated.The input c does work however. f(c) = 2 because of the ordered pair (c,2) in the function f. Similarly, g(c) = 4. This means f/g = 2/4 = 1/2 when the input is c. This shows that c is a valid input in the domain of f/g.The input d is pretty much the same story as input c. Moreover, the input d leads to the same output as c does. This time we have f/g = 4/8 = 1/2 when the input is d. Therefore, d is another valid input in the domain of f/g.The input e is not valid because (e,0) will lead to a division by zero error, as it's part of the g(x) function. So we must eliminate 'e' as a valid option in the domain. Even if we didn't have a division by zero error, we still have the fact that 'e' is not in the domain of the first function f. This is another reason why f/g is not defined when the input is 'e'.To summarize, only inputs c and d are valid in the domain.
The domain is the set {c, d}
Both inputs in the domain lead to the output 1/2. This means the range of f/g is {1/2}. Despite having just one element inside, we must use curly braces to indicate we have a set.
The function f/g is { (c, 1/2), (d, 1/2) }
We simply list all of the (x,y) ordered pairs to describe the function. In this case, there are only two such pairs.
What is the area of the rhombus shown below?
Answers
Answer:
54
Step-by-step explanation:
12*9/2=108/2=54mm^2
Find the area.
D
36 m
1
180 m
N
37 m
A. 1100 m
B. 1066 m
C. 555 m
D. 338 m
Answers
Answer:
Area of triangle = 1/2×base×height
= 1/2×37×30
= 555m²
The area of the triangle with the given parameters is 555 m².
Given that, NE=37 m and height=30 m.
What is the formula to find the area of a triangle?The formula to find the area of a triangle is 1/2×b×h.
Where, b=base and h=height.
Now, Area=1/2×37×30=555 m².
Therefore, the area of the given triangle is 555 m².
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how do you put 300,000+10,000+6,000+20+9
Answers
Answer:
three hundred thousand plus ten thousand plus six thousand plus twenty plus nine
Step-by-step explanation:
300,000 → three hundred thousand
10,000 → ten thousand
6,000 → six thousand
20 → twenty
9 → nine
+ → plus
Now put everything together.
Best of Luck!
Pls help will do brainliest answer
Answers
Answer:
[tex]f(x) = 15 \csc(x) + 5[/tex] (first option)
Step-by-step explanation:
[tex]f(x) = a \: \csc(x) + b[/tex]
[tex]a + b = 20[/tex]
[tex] - a + b = - 10[/tex]
••••
[tex]2b = 10[/tex]
[tex]b = 5[/tex]
[tex]a = 20 - 6 = 15[/tex]
[tex] = f(x) = 15 \csc(x) + 5[/tex]
What’s the coordinates pair
Answers
those are the points on the graph now i’m sorry if it’s not what you were looking for
Answer:
(5, 35) and (25, 20)
Step-by-step explanation:
The question is saying that x = minutes spent watching videos and y = minutes spent playing video games. Gian has 45 minutes in total to spend. The equation for Gian spending y minutes playing video games if he spent x minutes watching videos would be 45 - x, since x minutes have been taken away from Gian's 45 minutes by watching videos.
Knowing this, if he spent 5 minutes watching videos (x) on Monday, that means he spent 40 minutes playing video games. So, the first coordinate point would go to (5, 40). On Tuesday, he spent 25 minutes watching videos, which would mean he spent 20 minutes playing video games. The second coordinate point would go to (25, 20).
Classify the following polynomials. Combine like terms first. PLEASE ANSWER I'm really confused. :(
2x-x2+4x+x2
x3-5x2+3-2
x3-x3+x2-x2+3
7x-x2+x3+4x2
-6x-x3+6x-4x
Quadratic monomial
Quadratic binomial
Quadratic trinomial
Cubic monomial
Cubic binomial
Cubic trinomial
Linear monomial
Constant monomial
Answers
5−33−32+39+3
Not sure?
How do you model a decimal using a fraction?
Answers
Answer:
The only reason I can’t type it right now it’s cause I’m doing something important so I’m so sorry if I hade to type this out but I’m a bit busy right now And I’m trying to answer as much questions as possible. Thank you
Step-by-step explanation:
Hope this helps you
Write down the decimal in fractions with the denominator 1.
We multiply the denominator and numerator by 10 for every number after the decimal point.
Simplify the fraction if needed.
ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Answers
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
Write 7,08 x 10" in standard notation
Answers
Answer:
70.8
Step-by-step explanation:
7.08×10 is 70.8
...............
5x-9=2x+12
can somebody answer this and if possible, can you show work?
Answers
Answer:
X = 7
Step-by-step explanation:
5x-9=2x+12
5x-2x=12+9
3x=21
X=21/3
X=7
Plsssssssssssssssss help fast
Answers
Answer:
yes tht right pls mark me branilest
Area of a trapezium＝1/2×(upper base＋lower base)×height
Area＝1/2×(20＋25)×15＝337.5
Hope my answer helped u :)
5. Tristan wants to build a square garden in his backyard that will cover an area of 75 ft². If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
Answers
Lets find side
Area=75ft^2[tex]\\ \sf\longmapsto Area=(side)^2[/tex]
[tex]\\ \sf\longmapsto (side)^2=75[/tex]
[tex]\\ \sf\longmapsto side=8.3ft[/tex]
Perimeter
[tex]\\ \sf\longmapsto 4(side)[/tex]
[tex]\\ \sf\longmapsto 4(8.3)[/tex]
[tex]\\ \sf\longmapsto 33.2[/tex]
He has 1.2ft short material