If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta
Answers
Step-by-step explanation:
Need to FinD :We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.[tex] \red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}[/tex]
Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.
Where,
PQ = Opposite sideQR = Adjacent sideRP = Hypotenuse ∠Q = 90°∠C = θAs we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,
[tex] \rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}} [/tex]
Since, we know that,
cosθ = 5/13QR (Adjacent side) = 5RP (Hypotenuse) = 13So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.
Therefore,
[tex] \red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}} [/tex]
[tex]\rule{200}{3}[/tex]
[tex] \sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}} [/tex]
∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.
[tex] \rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}} [/tex]
Where,
Opposite side = 12Hypotenuse = 13Therefore,
[tex] \sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}} [/tex]
Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.
[tex] \rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}} [/tex]
By substituting the values, we get,[tex]\rule{200}{3}[/tex]
[tex] \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}} [/tex]
∴ Hence, the required answer is 17/7.
Related Questions
Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons?
Answers
Answer:
6 liters
Step-by-step explanation:
The ratio of lemons to water is 4:3. When the amount of lemons is 8, that menas the ratio is doubled, so then it is 8:6. The answer is 6 litres.
Steve says,
“There are more prime numbers between 20 and 30 than there are between 10 and 20" Is Steve right?
Answers
Answer:
prime numbers between 20-30 are 23,29
prime numbers between 10-20 are 11,13,17,19
No,Steve is not right
Reason-there are two prime numbers between 20 to 30.Whereas there are 4 prime numbers between 10 to 20.
(03.06 MC)
Choose the equation below that represents the line passing through the point (-2, -3) with a slope of -6.(1
point)
O y=-6x - 15
O y = -6x - 20
y=-6x + 15
Oy=-6x + 20
What’s the answer
Answers
Answer:
y= -6x - 15
Step-by-step explanation:
First you need to plug in the x and y coordinates into the equation y = -6x and you should get (-3) = -6(-2). Then you do -6 x -2 which is 12 then subtract 12 from -3 and get -15.
Just took the exam and the answer is c :)
NEED HELP, WOULD REALLY APPRECIATE IT, Thanks!
Which would most likely be graphed using a continuous graph? Check all that apply.
1-total cost, c, of buying b cans of beans
2-total cost, c, of buying g pounds of broccoli
3-speed of a car, s, as it accelerates over time, t
4-number of stamps, s, needed to mail p postcards
5-total distance, d, that has been driven over time, t
6-decrease in outside temperature, F, one evening over time, t
Answers
Answer:
3, 4, and 5, i think
Step-by-step explanation:
because its continious and the other ones arent
Answer:
2,3,5, and 6
Step-by-step explanation:
use the distributive property to simply 3[ n-5) =
Answers
Answer:
3n - 15
Step-by-step explanation:
3 multiplied by n which is 3n
Then 3 multiplied by 5 which is 15
So your answer is 3n - 15
Hope I helped :)
Please consider Brainliest
PLEASE HELP ME!!!!!
If m
Answers
Answer:
could you add more details? you only put ¨ if M¨
Step-by-step explanation:
Answer:
[tex]if \: m \: then \: m \: can \: be \: any \: variable.[/tex]
Solve inequality -4x+5<-5
please hurry
Answers
Answer: x > [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
-4x + 5 < -5
Subtract 5 from both sides
-4x < - 10
Divde each side by -4
x < -10 / -4
Dividing each side by a negative number flips the inequality
x > - 10 / -4
- 10 / -4 = 10 / 4 = 5/2
x > 5/2
Answer:
-4x+5<-5
-4x<-5-10
-4x<-15
-4x/-4>-15/-4
x>15/4
Need this for my homework! Please help! Image attached!
Answers
The relationship between the variables x, y and z is an illustration of similar triangles
The values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]
How to determine the values of x, y and zRight triangles are triangles with an angle measure of 90 degrees, and we have the following equivalent ratio from the triangle
[tex]x : 9 = 4 : x[/tex]
Express as fraction
[tex]\frac x9 = \frac 4x[/tex]
Cross multiply
[tex]x^2 = 36[/tex]
Take the square root of both sides
[tex]x = 6[/tex]
The value of y is then calculated using the following Pythagoras theorem
[tex]y = \sqrt{9^2 + x^2[/tex]
This gives
[tex]y = \sqrt{9^2 + 6^2[/tex]
[tex]y = \sqrt{117[/tex]
The value of z is then calculated using the following Pythagoras theorem
[tex]z = \sqrt{4^2 + x^2[/tex]
This gives
[tex]z = \sqrt{4^2 + 6^2[/tex]
[tex]z = \sqrt{52[/tex]
Hence, the values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]
Read more about triangles at:
https://brainly.com/question/17972372
3 (x + 4) + 2 (2x - 3)
Answers
Answer: 7x + 6
Step-by-step explanation:
Use distribution property
(3x + 12)+(4x - 6)
Combine like terms
7x + 6
Answer:
7x + 6
Step-by-step explanation:
Apply the distributed property, so it now looks like this: (3x + 12) + (4x - 6)Combine like terms: 7x + 6I hope this helps!
Divide x4-3x3-5X2-7x-9 by x + 1.
Answers
The division of x4-3x3-5X2-7x-9 by x + 1. yields; x²-4x²-x-6 with a remainder of -3.
Division of polynomialsFrom the task content;
It follows that the division can be carried out using the long division method.The division of the polynomial x⁴-3x³-5x²-7x-9 by (x+1) therefore yields; x²-4x²-x-6 with a remainder of -3.
Read more on polynomial division;
https://brainly.com/question/24662212
Mrs. Harper asked the class to find the area of an isosceles trapezoid.
Suzy decomposed the trapezoid and rearranged the parts to form
a rectangle of equal area as shown.
Which pair of expressions represents the area
of the trapezoid and rectangle?
12(5 X 4) and (8 – 3)(4)
12(2 + 8)(4) and (2 + 3)(4)
8 X 5 and 2(5)(4)
2(8 + 4) and (8 – 2)(4)
Answers
1/2(2 + 8)(4) and (2 + 3)(4)
area of trapezoid:
[tex]\sf \dfrac{1}{2} (a + b) *h[/tex]
Here:
height: 4 unita, side 1: 2 unitb, side: 8 unitslant height: 5 unitSo area of this trapezium:
[tex]\sf \dfrac{1}{2} (2 + 8) *4[/tex]
[tex]\sf 20 \ units[/tex]
area of rectangle:
length * width
5 * 4
20 units²
Area of trapezoid:-
1/2(Sum of parallel sides)(Height)Put the values
1/2(2+8)(4)2(10)20units²What is the answer to the equation
g(x) = 1/5 × (1/3)^x
X = 3
Answers
Step-by-step explanation:
since x=3
1. substitute into the equation
g(3) = 1/5 x (1/3)^3
2. solve
g(3) = 1/5 x (1³/3³)
= 1/5 x (1/27)
= 1/5 x 1/27
= 1/135 (0.00740740741)
Can someone help with this question please
Answers
Answer:
[x - 5]² + [y + 7]² = 6²
Step-by-step explanation:
It should be noted:
Equation of circle: (x - h)² + (y - k)² = r²"h" represents the x coordinate of the center point, "k" represents the y coordinate of the center point, and "r" represents the radius of the circle.
⇒ h = 5; k = -7; r = 6When the values are substituted:
[x - 5]² + [y - (-7)]² = 6²
⇒ [x - 5]² + [y + 7]² = 6² = 36
PLEASE HELP OVERDUE ASSIGNMENT WORTH 24 POINTS!!
The pizzeria sold 85 pizzas yesterday. Suppose the number of pizzas sold today
was 60. Determine the percent increase or decrease in the pizzas sold, rounded to
the nearest hundredth. (Show your work)
Answers
Answer:
App. percent decrease of 29.41%
Step-by-step explanation:
60-85/85=0.2941- 29.41%
please help with this im really confused and please explain abit with words. please and thanks!
Answers
Step-by-step explanation:
just add all the given angles and equate it with 540° and then find x
x/2 + x/2 + x - 25 + 100 + x - 15 = 540°
3x + 60 = 540°
3x = 540 - 60
x = 480/3
x = 160°
on checking, the given shape values of x-25 and x - 15 are both still obtuse angles thus the answer is correct.
What is 17/100 + 6/10 = ?
thx if you helped
Answers
Answer:
0.77
Step-by-step explanation:
correct me if im wrong this is just what i got
Please someone help me with nine through 16 I’m not understanding it and I really need some help! The instructions are in bold.
Answers
Answer:
Hey there!
9) Answer: D. :---- (x +8)(x-8)
10) Answer: P. :------(x-2y)^2
11) Answer: D. :-----(2a+3b)*(2a-3b)
12) Answer: P. :-----(a+4b)^2
13) Answer: P. :-----(x-3)^2
14) Answer:. D. :----(5xy+9z)*(5xy-9z)
15) Answer: P. :-----(2a+1)^2
16)Answer: D. :---(4ab+5)*(4ab-5)
Solve for x. Round to the nearest tenth, if necessary.
Answers
ANSWER
14.3
EXPLANATION
angle = 21⁰
opposite side = 5.5
adjacent side = x
Knowing this, we must use tangent (opposite / adjacent)
tan (21⁰) = 5.5 / x
x = 5.5 / tan (21⁰) (use calculator)
x= 14.3
Are the following fractions
equivalent? Explain what
strategy you used to find
your answer 4/9 and 8/18
Answers
Answer:
they are
Step-by-step explanation:
the simplest form 8/18 is 4/9
In a class of 28 students, 15 earned an A on the final exam, 10 earned an A for the entire course, and 7 earned an A for both final exam and the entire course. What is the probability that a randomly selected student in this class did not earn an A on the final exam and did not earn an A for the entire course?
Answers
Using it's concept, it is found that there is a 0.3482 = 34.82% probability that a randomly selected student in this class did not earn an A on the final exam and did not earn an A for the entire course.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 13 out of 28 students did not earn an A on the final course, and 21 out of 28 students did not earn an A for the entire course, hence:
[tex]p = \frac{13}{28} \times \frac{21}{28} = 0.3482[/tex]
0.3482 = 34.82% probability that a randomly selected student in this class did not earn an A on the final exam and did not earn an A for the entire course.
More can be learned about probabilities at https://brainly.com/question/14398287
Tell whether (2, 5) is a solution of the equation y = 2x + 1. Show your work. I’LL PUT YOU AS BRAINLIEST
Answers
Answer:
The solution of (2,5) indeed equals the solution of the equation y=2x+1
Step-by-step explanation:
to solve just plug in the values.
y=2(2)+1 which gives us the y value of y=5
to solve for x, plug in y. 5=2x+1.
subtract 1 from both sides, and you get 4=2x
then divide 2 on both sides to get x, which is 2. therefore this is true.
please rate and mark as brainlest.
write 0.216 as a rational number in lowest terms
Answers
Answer:
[tex]=\frac{27}{125}[/tex]
Step-by-step explanation:
[tex]0.216[/tex]
[tex]\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}[/tex]
[tex]\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000[/tex]
[tex]=\frac{0.216\cdot \:1000}{1000}[/tex]
[tex]=\frac{216}{1000}[/tex]
[tex]216,\:1000[/tex]
[tex]\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}[/tex]
[tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]
[tex]=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3[/tex]
[tex]2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]
[tex]=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5[/tex]
[tex]\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}[/tex]
[tex]=2\cdot \:2\cdot \:2[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8[/tex]
[tex]=8[/tex]
[tex]=\frac{8\cdot \:27}{8\cdot \:125}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:8[/tex]
[tex]=\frac{27}{125}[/tex]
Hence, the correct answer is [tex]=\frac{27}{125}[/tex]
Miranda wants to give her 14-year-old daughter $20,000 when she turns 18. How much does she need to put in the bank now if the interest rate is 10 percent per year? A. $12,418. 43 B. $13,660. 27 C. $15,026. 30.
Answers
Answer:
B $13,660.27
Step-by-step explanation:
Find the surface area of a square pyramid with side length 3 km and slant height 4 km.
Answers
Answer:
The pyramid consists of 4 triangles having bases of 3 km and height of 4 km (measured along the face)
A = 4 * 3 / 2 * 4 = 24 km^2
Each triangle has an area of 1/2 * bottom length * height
3 cannot refer to the length of one of the isosceles triangles because a slant height of 4 km is given and is less than one such side
The surface area of the square pyramid is 24 km².
What is the surface area of a square pyramid with a slant height?The surface area of a square pyramid with a slant height can be determined by the product of the base perimeter with the slant height divided by two.
Mathematically, it can be expressed as:
Surface Area S.A = P × l/2
where;
Side length (a) = 3Base perimeter (P) = 4a = 4(3) = 12kmSlant length (l) = 4 kmSurface Area (S.A) = 12 × (4/2)
Surface Area (S.A) = 24 km²
Learn about calculating the surface area of a square pyramid here:
https://brainly.com/question/22744289
#SPJ6
what is −2.9, −2 3/5, −2.4 in least to greatest
Answers
Answer:
-2.9, -2 3/5, -2.4
Step-by-step explanation:
Convert 3/5 in -2 2/5 to a decimal (3/5x2=6/10=0.6)
Sort it from least to greatest (-2.9, -2 3/5, 2.4)
If UV=p+13 and RT=p–1, what is the value of p?
Answers
Answer: 15
Step-by-step explanation:
true or false: A triangle can be made by segments that are 15.9 cm, 10 cm and 25.9 cm.
Answers
Answer:
false
Step-by-step explanation:25.9cm is too big to connect to 15.9cm and 10 cm
HELP ASAP ILL GIVE BRAINIEST!
What is the median of the data set represented by the dot plot?
Answers
Answer:
the median is 36
Step-by-step explanation:
31, 34 , 34 , 35 37, 38 ,38 39
1. 2. 3. 4. 5. 6. 7. 8
(i put the numbers below because i like umm doing this weird technique where i count it)
since theres no median there then you have to add 35 and 37 then divide by 2
A fish population that started at 250 has begun to decrease by 12 percent each week. Which equation below could be used to model this situation?
P=250(0.12)x
B
P=250(0.88)x
C
P=12(250)x
D
P=−250(0.12)x
Answers
250 - 250 * 12% = 250 * (1 - 12%) = 250 * 0,88
with x = fish number
=> P = 250 * 0,88 * x
Answer: A. P=250(0.12)x
Step-by-step explanation:
12%= 0.12
250 x 0.12 = the amount decreased by each week
please answer quickly