The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.
How to solve a trigonometric equation
In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.
First, write the complete expression:
2 · tan² θ - 7 · sec θ + 8 = 0
Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:
2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0
2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0
2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0
6 · cos² θ - 7 · cos θ + 2 = 0
Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:
6 · u² - 7 · u + 2 = 0
u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]
u = - 7 / 12 ± (1 / 12) · 1
u = - 7 / 12 ± 1 / 12
There are two possibilities:
u₁ = - 2 / 3, u₂ = - 1 / 2
Fourth, find the angles associated to roots by inverse trigonometric functions:
u₁ = - 2 / 3
θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°
u₂ = - 1 / 2
θ₂₁ ≈ 120°, θ₂₂ ≈ 240°
To learn more on trigonometric equations: https://brainly.com/question/22624805
#SPJ1
PLS HELP !!!!!!!!!!!!
Answer:
y-intercept is -9
Step-by-step explanation:
g(0) = -3(0)² - 5(0) - 9
g(0) = 0 - 9
g(0) = -9
does the parabola open up or down -5(x-4)^2-3
pls helpp i'll give u brainliest
Answer:
(-5, -1)
Step-by-step explanation:
Equation Form:
x = -5
y = -1
Answer:
Solve the System of Equations
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(−5,−1)
Equation Form:
x= −5, y= −1
Which side lengths form a right triangle?
Answer:
(a) and (c)
Step-by-step explanation:
if you use the pythagorean theorem, 'a' and 'c' work out
a) 3² + [tex]\sqrt{27}[/tex]² = 36 True
b) 8² + 15² ≠ 17² False
c) 5² + 5² = 50 True
Encircle the correct formula in getting the area of the shaded region
Answer:
1. A=bh/2
2. I don’t know, I‘m sorry :(((( but if I had to guess I’d pick A = s x s
3. A = πr² (might be wrong, i’m so sorry)
Step-by-step explanation:
1. The formula for area of a triangle is A = bh/2
2. The formula for area of a square is s x s.
3. The formula for area of a circe is A = πr².
The formula used in getting the area of the shaded region is (1/2)bh, s * s and πr²
What is an area?
An area is the amount of space occupied by a two dimensional shape or object.
1) The area of a triangle = (1/2) * base (b) * height (h) = (1/2)bh
2) Area of square = side (s) * side(s) = s * s
3) Area of circle = π * radius (r)²= πr²
The formula used in getting the area of the shaded region is (1/2)bh, s * s and πr²
Find out more on area at: https://brainly.com/question/25292087
Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.
The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes
How to determine the time taken for 21,000 spectators to vacate the stadium?
A variation is a relation between a set of values of one variable and a set of values of other variables
Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively
We can write the variation as:
T α N/E
T = kN/E (where k is constant of proportionality)
when N = 25,000, E = 25, T = 20:
T = kN/E
k = TE/N
k = (20×25)/25000 = 0.02
when N = 21,000 and E = 15:
T = kN/E
T = (0.02×21,000)/15 = 28 minutes
Learn more about variation on:
brainly.com/question/2375770
#SPJ1
[tex]25^{a+3}* 5^{3a}[/tex]
Please explain how you got your answer.
will give brainliest please
Answer:
Step-by-step explanation:
a. we konw triangle have 180°
b. A straight line have 180°， so
∠abc=180-5x-12=168-5x,
∠bca=180-10x+37=217-10x
∠cab=180-9x-1=179-9x
then add them all 564 - 24x = 180
c.384=24x, x=16
d.so ∠bca=217-10·16=57.
Answer:
m∠BCA = 57°-------------------------------------------
Sum of exterior angles is 360°:
9x + 1 + 5x + 12 + 10x - 37 = 36024x - 24 = 36024x = 384x = 384/24x = 16The exterior angle at vertex C is:
10x - 37 = 10*16 - 37 = 160 - 37 = 123The ∠BCA is the linear pair with 123°:
m∠BCA = 180° - 123° = 57°Please help me! Find the circumference of the circle
Answer:
convert to cmthen write the perimeter of the circle and solveThere are 250 bricks used to build a wall 20 feet high.How many bricks will be used to buld a wall that is 30 fet high
Answer: 375
Step-by-step explanation:
Since we are given the information that there are 250 bricks used to build a wall 20 feet high, the number of brick used per feet will be:
= 250/20
= 12.5 bricks per feet.
Therefore, the number of bricks that will be used to buld a wall that is 30 fet high will be:
= 12.5 × 30
= 375 bricks.
Therefore, 375 bricks would be used.
What literary device did Oscar Wilde use?
Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
Who is Oscar Wilde?Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.
He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.
The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.
Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.
Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
Know more about Oscar Wilde here:
https://brainly.com/question/21636339
#SPJ4
PLEASE HELP ASAP!!! will mark
Answer:
Vertex (2, 3)
Axis of Symmetry: x = 2
Step-by-step explanation:
You can look at the labeling from my last answer, the parabola is just upside down but it is still the same label.
Hope it makes sense :)
Answer:
Axis of Symmetry: x = 2
Vertex: (2, 3)
Step-by-step explanation:
find axis of symmetry: x = -b/2a
x = -8 ÷ 2(-2)
x = 2
find vertex by substituting 2 for 'x':
y = -2(2²) + 8(2) - 5
y = -8 + 16 - 5
y = 8 - 5
y = 3
Vertex: (2, 3)
what is an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]
Find the volume and round to the nearest hundredths place when necessary.
Answer:
477
Step-by-step explanation:
Answer:
half of 8 is 4
4^4 = 16
16 x 3.14 = 50.24 (area of a circle)
Now we multiply it by the height:
50.24 x 19 = 954.56 rounded to the nearest hundredths place is:
954.56 yd3 is your answer.
At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes
Answer:
165 students or the sophomore class of 220 are not athletic.
Step-by-step explanation:
60/240 = .25 This means that 25% of the class is athletic. That would mean and .75 or 75% are not athletic.
220 x .75 = 165
Question 1 of 10
How many lines of symmetry are there in the object pictured below?
A. O
B. 1
C. 3
D. 2
Answer:
B. 1
Because of the shape you can have only one line of symmetry
A horse walks 4224 feet in 12 minutes at this rate how many yards does a horse walk in twelve minutes.
Answer:
1408 yards
Step-by-step explanation:
A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:
4224 feet / 3 feet/yard = 1408 yards
So a horse walks 1408 yards in 12 minutes.
Plz help. Describe the impact drought had on west Africa.
find x using the trig ratios please
Answer:
12.9
Step-by-step explanation:
cos 72 = 4/x
x = 4/cos72
x = 12.9
Suppose m = 2 + 6i, and║m + n║ = 3√10, where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.
Answer:
the modulus of a complex number z = a + bi is:
Izl= √(a²+b²)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nl = 3√10
√(a² + b²+ 2²+ 6²)= 3√10
√(a^2 + b^2 + 40) = 3√10
squaring both side
a²+b²+40 = 3^2*10 = 9*10 =90
a²+b²= 90 - 40
a²+b²=50
So,
|n|=√(a^2 + b^2) = √50
The modulus of n must be equal to the square root of 50.
now
values a and b such
a^2 + b^2 = 50.
for example, a = 5 and b = 5
5²+5²=25+25= 50
Then a possible value for n is:
n = 5+5i
make a the subject
2a+9b=4c
Answer:
This equation involves three variables: a, b, and c. Each variable is multiplied by a coefficient and then added together to equal a constant. To solve the equation, we must first determine what the value of the three variables are. To do this, we must use the coefficients to isolate each variable. We can start by isolating c. Divide both sides of the equation by 4 to get 2a + 9b = c. Now we can isolate b by subtracting 2a from both sides to get 9b = c - 2a. Divide both sides by 9 to get b = (c - 2a)/9. Finally, we can isolate a by subtracting 9b from both sides to get 2a = 4c - 9b. Divide both sides by 2 to get a = (4c - 9b)/2. Once we have the values of the three variables, we can substitute them into the original equation to check our work.
Step-by-step explanation:
Answer:
a=\frac{4c-9b}{2}
The probability distribution for a random variable x is given in the table.
Find the probability that
-2
Step-by-step explanation:
[tex]P( - 2 \leqslant x \leqslant 2) = 0.33 + 0.16 + 0.11 \\ = 0.6[/tex]
I don't get this. Please help and I'll mark brainiest
Answer:
A. 10 points
Step-by-step explanation:
The average test score for studying 3 hours is 75, while the average test score for studying 4 hours is 85. Therefore the average rate of increase of test scores between 3 and 4 hours studied is 10 points, since 85-75=10.
Find the number of real number solutions for the equation.
x2 − 6 = 0
1
2
0
Answer:
2
Step-by-step explanation:
am i this right?? this is graded and no links!!!!!!
Answer:
Your right
Step-by-step explanation:
How do you find the missing side of a right triangle without a calculator?
The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .
that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex] ;
let the missing side of the right triangle be the hypotnuse ;
So , missing side can written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .
For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10
The length of side "base" is unknown.
So , to find length of side b, we put the known values into theorem:
[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;
[tex]base^{2} = 100 - 36[/tex] ;
So , the missing side "base" = 8 ;
Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .
The given question is incomplete , the complete question is
How do you find the missing side of a right triangle without a calculator when the other two sides are given ?
Learn more about Right Triangle here
https://brainly.com/question/30104289
#SPJ4
You were planning to buy a new smartphone for
$1,100. You only paid $900 for it because it was on sale.
Find the percent of decrease in the cost.
Answer:
22% decrease
Step-by-step explanation:
(1100-900)/900 = .22
Fill in the missing number. % of 70 = 63
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 11 minutes to fill the swimming pool with 99 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
Answer:
[tex]11 \: minutes = 99 \: gallons \\ 1 \: minute = (\frac{1 \times 99}{11} ) \: gallons \\ = 9 \: gallos \: per \: minute[/tex]
The question is in the picture
Answer:
For the first line its distributive property
The 2nd is combining like terms
4th is simplifying it
Im not sure about the last one since its just the answer of the problem
Step-by-step explanation: