Answer:
[tex]\sec \theta + \csc \theta = \frac{2\cdot \sqrt{3}+6}{3}[/tex]
Step-by-step explanation:
We proceed to simplify the given trigonometric expression into a form with a single trigonometric function:
1) [tex]7\cdot \sin^{2}\theta + 3\cdot \cos^{2}\theta = 4[/tex] Given.
2) [tex]4\cdot \sin^{2}\theta + 3\cdot (\sin^{2}\theta + \cos^{2}\theta) = 4[/tex] Definition of addition/Associative and distributive properties.
3) [tex]4\cdot \sin^{2} \theta +3 = 4[/tex] [tex]\sin^{2}\theta + \cos^{2}\theta = 1[/tex]/Modulative property
4) [tex]4\cdot \sin^{2}\theta = 1[/tex] Compatibility with addition/Existence of additive inverse/Modulative property
5) [tex]\sin \theta = \frac{1}{2}[/tex] Compatibility with multiplication/Existence of multiplicative inverse/Modulative property/Definition of division
6) [tex]\theta = \sin^{-1} \frac{1}{2}[/tex] Inverse trigonometric inverse.
7) [tex]\theta = 30^{\circ}[/tex] Result.
By Trigonometry, we know that secant and cosecant functions have the following identities:
[tex]\sec \theta = \frac{1}{\cos \theta}[/tex], [tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (1, 2)
In addition, we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the sum of the two trigonometric function abovementioned is:
[tex]\sec \theta + \csc \theta = \frac{1}{\cos \theta} + \frac{1}{\sin \theta}[/tex]
[tex]\frac{2}{\sqrt{3}} + 2 = \frac{2\cdot \sqrt{3}}{3} + 2[/tex]
[tex]\sec \theta + \csc \theta = \frac{2\cdot \sqrt{3}+6}{3}[/tex]
HI PLEASE ANSWER EACH OF THESE QUESTIONS (if you can) IM GIVING OUT 50 POINTS AND BRAINLIEST TO THE BEST ANSWER !! D:
Answer:
4/55
90
90
Step-by-step explanation:
P= 4/55
mean = 90
median = 90
---------------------
Answer:
1) 4/55
2) 90
3) 90
4) 1046.67 cubic feet
Step-by-step explanation:
What numbers multiply to make -384 and add to make 8?
Answer:
-16 and 24
Step-by-step explanation:
-16 x 24 = -384
-16 + 24 = 8
Please help me with 1,2,3,4 please I need help
Answer:
1. 9.43
2. 13
3. 5
4. 10.77
Step-by-step explanation:
solve for -3x ≤ -9
I need it for math so be correct
Divide each term by −3-3 and simplify.
Inequality Form:
x≥3
Answer:
x≥3
Step-by-step explanation:
Divide both sides by -3.
−3x/ −3 ≤ −9/ −3
x≥3
7. Which relation is a function?
CC8F.1
A. {(0,0). (1.1), (2.2), (0,3)}
B. {(0,0). (0,1),(0,2), (0,3)}
C. {(0,0), (0.1), (1.0), (0.2)}
D. {(0,0), (2.0), (4.0), (6,-2)}
Answer:
D. relation is a function
hope this helps :-))
The bear was chosen _____ more times than the elephant as the favorite animal.
11
10
9
8
Find the volume of the cylinder. Either enter an exact answer in terms of pi or use 3.14 for pi . units3
Answer:
Step-by-step explanation:
Tienes que multiplicar el seis y el cuatro lo que te multiplicarlo por 3,14y después dividirlo por dos
If the area of AABC is D, give the expressions that complete the equation for the measure of ZB?
m
m=
n =
Given:
The figure of triangle ABC.
The area of the triangle ABC is D.
[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex]
To find:
The value of m and n in the given expression.
Solution:
Let h be the height of the triangle ABC.
Area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times h[/tex]
Where, b is the base and h is the height of the triangle.
[tex]Area=\dfrac{1}{2}\times a\times h[/tex]
The area of the triangle ABC is D.
[tex]D=\dfrac{1}{2}\times a\times h[/tex]
[tex]2D=ah[/tex]
[tex]\dfrac{2D}{a}=h[/tex] ...(i)
In a right angle triangle,
[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin B =\dfrac{h}{c}[/tex]
[tex]\sin B =\dfrac{1}{c}\times \dfrac{2D}{a}[/tex] [Using (i)]
[tex]\sin B =\dfrac{2D}{ac}[/tex]
[tex]m\angle B =\sin ^{-1}\dfrac{2D}{ac}[/tex] ...(ii)
We have,
[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex] ...(iii)
On comparing (ii) and (iii), we get
[tex]m=2D[/tex]
[tex]n=ac[/tex]
Therefore, the required values are [tex]m=2D, n=ac[/tex].
Neeeddddd HELP LOOKONG FOR ANSWERS!!
Answer:
a.) 13 students
b.) 53 members
Step-by-step explanation:
a.) In the given equation of y=4x+13, "x" represents how many years have gone by since the club had started. The number "13" in this equation represents the y-intercept, or the value of "y" when x = 0. Therefore, when "x" is 0 years, there were 13 students in the clubs, meaning that the original group that started the club contained 13 students.
b.) Since the question asks how many members that the club will have after their tenth year and you already know that "x" in the equation y=4x+13 represents the number of years since the club started, all you have to do is plug 10 in for "x" in the equation; so, the equation will now look like this: y=4(10)+13. Keeping PEMDAS in mind, you first multiply 4 and 10 to get 40, and then you add 13 to get an answer of 53 members after year 10.
In the number 344,589, how many times greater is the value of the 4 in the ten thousands place than the value of the 4 in the thousands place?
Answer:
10 times
Step-by-step explanation:
9 = units
8 = tens
5 = hundred
4 = thousand
4 = ten thousand
3 = 100 thousand
Number of times 4 in the ten thousands place than the value of the 4 in the thousands = 10,000 / 1000 = 10 times
comparison of the value of 6 to 3
10,000 / 1000 = 10 times
Which length is equal to 4 yards 3 feet?
Answer:
12
Step-by-step explanation:
Find the length of diagonal of square land having side of length 50m
Answer:
70.7
Step-by-step explanation:
a2 +b2 = c2
50^2 + 50^2 = c2
c2 = 2500+2500
c = [tex]\sqrt{5000}[/tex] = 70.7
I hope im right!
(repost) Can anyone answer these?
questions:
1. Alexa knocked down 70 bowling pins in 10 frames. In each frame, Alexa knocked down the same number of pins. How many Pins did Alexa knock down in each frame?
2. Equation: 28 ÷ 4 = 7. Write a related multiplication sentence.
3. Bonnie had 6 bags of 6 gel pens. she wanted to give the same number of gel pens to 9 friends. How many gel pens did each friend get?
4. Show two ways to solve this problem: 4 × 3 × 2
5. Round each number to the nearest 100, Then Subtract. 187 - 69 is about?
(gosh im tired it took me forever to write this XD)
Answer:
1.) 7 pins
2.)56 ÷ 8 = 7
3.)Each friend gets 4 pens
4.)(4x3)x2 and 4x(3x2)
5.) 100
Step-by-step explanation:
1.) 70 ÷10= 7
2.)28x 2 = 56
4 x 2= 8
3.)6 x 6 = 36
36 ÷ 9= 4
4.)(4 x 3 )x 2 or 4 x (3 x 2)
5.)187-69 =118
The graph shows how many miles Barrett traveled over a 5 hour time frame. The point (1,50) is on the graph what is the unit rate for the first hour?
Answer:
Step-by-step explanation:
The answer is B 50
The diameter of a circle is 8 feet. What is the angle measure of an arc a feet long?
Give the exact answer in simplest form.
20 points
Answer:
Given: circle
diameter = 10 cm => radius (R) = 5 cm
Find: measure of angle bounding sector = 11 π sq. cm.
Plan: determine what part of the circle’s total area equals the sector’s area.
Total Area of Circle A = π R^2 = π 5^2 = 25 π sq. cm.
Therefore: Sector Area = 11 π cm^2/25 π cm^2 = 11/25
Since the sector is 11/25 th of the circles area, the sector angle will measure 11/25 th of the circle’s circumference. They are proportional.
C = 2 π R = 2 π (5) = 10 π cm
Sector Arc = measure of sector angle = 11/25 (10 π) =
22π/5 radians
Answer: Sector Arc = 22π/5 Radians
PLEASEEE HELPPP I REALLY NEED IT IM TAKING A TESTTT
Answer:
Coping is very bad habit.... sorry I will not answer your question because ur coping...
Answer:
A. Quadrilateral
B. 360° = 2(82°) + 2( 3x - 1 )°
C. f(x) = ( 3x - 1 )
Step-by-step explanation:
360° = 164° + (6x - 2)°
360° - 164° + 2 = 6x
196° = 6x
x = 196°/6
x = Rationalize(32.33333333333)
in a given classroom the number of girls is 10 greater than number of boys if the ratio of the number of girls to the number of boys is 7:5 then find a) the number of girls b) the number of boys c) the total number of students
Answer:
a) 35, b) 25, c) 60
Step-by-step explanation:
The number of girls is 10 more than the number of boys, so it's a good thing to choose a variable to represent the number of boys.
Number of boys: b
Number of girls: b + 10
Ratio of girls:boys is 7:5, so
[tex]\frac{b+10}{b}=\frac{7}{5}[/tex]
"Cross multiply" to get
[tex]7b=5(b+10)\\7b=5b+50\\2b=50\\b=25[/tex]
There are 25 boys. There are 10 more girls, so the number of girls is 35, and the total number of students is 60.
That's a packed classroom!
Plz solve ASAP plz plz
Answer:
1,243.88 units² I think
Step-by-step explanation:
22 x 22 = 484
A = (3.14 x 11²)2 = 759.88
759.88 + 484 = 1,243.88 units²
andy bought a cellphone for $120. After six months, he sold the cell phone for $78. What percent did he decrease the price of the cellphone?
Answer:
45%
Step-by-step explanation:
$78 is 65% of $120, therefore, the price was decreased by 45%. To prove 78 is 65% of 120, multiply 120x0.65 and you'll get 78. The reason you use 0.65 is because 65% is 0.65 in it's decimal form.
Questions 7,11,12,14,15and 16 please thanks
7) 20y-8=52
20y=60
y=3
11)2x+17=5x-4
21=7x
x=3
12)2x+7=16-4x
6x=9
x=9/6
x=3/2
x=1.5
14)8y+4=24-2y
10y=20
y=2
15)7-3x=2x+2
5=5x
x=1
16)
[tex] \frac{x - 3}{2} = 5 \\ x - 3 = 10 \\ x = 13[/tex]
Broderick needs to solve the formula below for r. Which correctly describes the first step he should take?
The first step to solve for r is (J) He should divide both sides of the equation by π.
How to solve the formula for r?The equation is given as:
A= πr^2
Divide both sides of the equation by π.
So, we have:
r^2 = A/π
Hence, the first step to solve for r is (J) He should divide both sides of the equation by π.
Read more about subject of formulas at:
https://brainly.com/question/11154728
A) p= 12h -2
B) p= 2h -12
C) p= 12 - 2h
D) p= 2 -12h
write an absolute value equation that has the solutions x=2 and x=14
Answer:
|2| and |14|
Step-by-step explanation:
Answer:
if I am not mistaken I think my answer 56
Which fraction is equivalent to 1/3?
Answer:2\6 or 4\12 etc.
Step-by-step explanation:
Answer please it will make my day
Pls help ASAP will mark Brainlyest!!
Find the area of the following figure.
1. 312 cm2
2. 400 cm2
3. 252 cm2
4. 300 cm2
Answer:
312cm2
Step-by-step explanation:
Area of the triangles:
A =1/2bh
A=1/2(10*12) = 1/2*120=60.
There are two triangles. 60*2=120. 120 is the area of both triangles.
Area of the rectangle:
16*12=192.
120+192=312cm2
A circle with a radius of 6 feet has a central angle of 120° in terms of π what is the area of the sector?
if the radius of the circle is 8 units find the area of the hexagon
The sum of interior angle of the given regular hexagon is 720 degree. The area of the hexagon with side of 8 units is 96√3 square units
Area of a hexagonThe sum of interior angle of the given regular hexagon is 720 degrees
The measure of one of the angles is 120 degrees
<ABO = 120/2 = 60 degrees
Since all the angles of triangle ABO are the same, hence AB = 8 units
Determine the area of the hexagon
A = 3√3/2 a²
Substitute a = 8 units
A = 3√3/2 (8)²
A = 3√3/2 * 64
A = 3√3 * 32
A = 96√3 square units
Hence the area of the hexagon with side of 8 units is 96√3 square units
Learn more on area of hexagon here: https://brainly.com/question/2919364
#SPJ2
Write the next three terms in each sequence. Describe the pattern rule.
a) 1, 7, 13, 19, 25 …
b) 2, 3, 6, 18…
c) 1, 5, 21, 85, …
please do it separated so i understand it
Justin and Ari go on a 30 km run. They usually run together at a speed of 10 km/h. If they start together but Justin runs at 12 his usual speed and Ari runs at 112 times her usual speed, how many hours after Ari finishes will Justin finish?
Answer:
4 hours
Step-by-step explanation:
Distance covered = 30 km
Usual Speed of both = 10km/hr
Justin's speed = 1/2 * 10 = 5km/hr
Ari's speed = 3/2 * 10 = 15 km/hr
Time taken = distance / speed
Justin's time = 30 / 5 = 6 hours
Ari's time = 30 / 15 = 2 hours
Time difference = (6 - 2) = 4 hours