Answer: sin2y =240/289 where 0<y <π/2
Step-by-step explanation:
Given sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2.
We now that
[tex]cosy = \frac{1}{secy} =\frac{15}{17} \\and\\\text{using identity } sin^2y+cos^2y=1\\\text{we have}\\siny=\sqrt{1-cos^2y}=\sqrt{1-(\frac{15}{17} )^2}=\sqrt{1-\frac{225}{289} }=\sqrt{\frac{64}{289} }=\frac{8}{17} \\\Rightarrow\ siny=\frac{8}{17} \\\text{Now we are using identity sin2A=2sinAcosA we have}\\sin2y=2\cdot\ siny\cdot\ cosy=2\cdot\ \frac{8}{17} \cdot\ \frac{15}{17} =\frac{240}{289}[/tex]
To solve the question, we firstly find cos(y) from 'sec(y) = 17/15' because secant is the reciprocal of cosine. Then, we use the Pythagorean identity to find sin(y). Finally, we substitute these values into the double angle identity 'sin(2y) = 2sin(y)cos(y)' to find the final answer.
Explanation:In this high school level mathematics problem, 'sin(x) = 1/3' and 'sec(y) = 17/15' are given. From 'sec(y) = 17/15', we can calculate cos(y) because secant is the reciprocal of cosine. Hence, 'cos(y) = 15/17'. The question asks for the evaluation of the expression 'sin(2y)'. Here, we can use a trigonometric identity for double angles, which states 'sin(2y) = 2sin(y)cos(y)'.
However, we are only given secant of y, not sine. To find sin(y), we can use the Pythagorean identity. According to this identity, 'sin^2(y) = 1 - cos^2(y)'. So, 'sin(y) = sqrt[1 - (15/17)^2]'.
So, the final answer becomes 'sin(2y) = 2 * √[1 - (15/17)²] * 15/17'. It's useful to note that you should always check that your angle lies within the given range when using a square root in trigonometry, to ensure your answer is correct.
Learn more about Trigonometry here:https://brainly.com/question/11016599
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Which of the following is the equation of a line in slope intercept form for a line with slope = 2/3 and y-intercept at (0,-2)
*(The Answer)*= [tex]y = \frac{2}{3} x-2[/tex]
*(Equation)*= The equation for slope-intercept form is [tex]y=mx+b[/tex]
*(Additional Information)*= m = slope, and b = y-intercept
Hope this helps
Person who answered: BangtanBoyScouts
Answer: The correct option is
(C) [tex]y=\dfrac{2}{3}x-2.[/tex]
Step-by-step explanation: We are given to select the equation of a line in slope-intercept form with slope [tex]\dfrac{2}{3}[/tex] and y-intercept at (0, -2).
We know that
the slope-intercept form of the equation of a line with slope m and y -intercept at the point (0, c) is given by
[tex]y=mx+c.[/tex]
For the given line, we have
[tex]\textup{slope, }m=\dfrac{2}{3},\\\\\\\textup{y-intercept},~(0,c)=(0,-2)\\\\\Rightarrow c=-2.[/tex]
Therefore, the equation of the line in slope-intercept form is
[tex]y=mx+c\\\\\Rightarrow y=\dfrac{2}{3}x+(-2)\\\\\\\Rightarrow y=\dfrac{2}{3}x-2.[/tex]
Thus, the required equation of the line in slope-intercept form is [tex]y=\dfrac{2}{3}x-2.[/tex]
Option (C) is CORRECT.
Can someone help me with this math question pls?
Solution is attached below
Complete the square to transform the quadratic equation into the equation form (x – p)2 = q. x2 + 14x + 34 = 5
(x + 7)² = 20
subtract 34 from both sides
x² + 14x = - 29
add (half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = - 29 + 49
(x + 7)² = 20
The graph models the function f(x) = 2(1/2)x. What is the domain and range of the function?
A-Domain: x < 0; Range: y > 0
B-Domain: x > 0; Range: all real numbers
C-Domain: all real numbers; Range: y > 0
D-Domain: all real numbers; Range: y ≥ 0
Please explain with the answer !!
Hello!
Given the function, [tex]f(x) = 2(\frac{1}{2})^{x}[/tex], notice that the function f(x) is an exponential function.
All exponential functions have a horizontal asymptote at y = 0, and this means that the graph never goes over the line y = 0. Therefore, the range is less than zero, but never equal to zero.
Also, this means that the domain of the function f(x) is all real numbers because as we substitute positive x-values into the function, the graph goes closer to zero, but never across zero. But, if we substitute negative x-values into the equation, it goes to infinity.
Therefore, the answer is choice C. The domain of f(x) is all real numbers, and the range is y > 0.
We want to find the domain and range of the given equation.
We will see that the correct option is C:
Domain: all real numbers;
Range: y > 0
First, we need to define what these are.
For a given function y = f(x), the domain is the set of all the possible x-values we can input on the function, and the range is the set of the possible outcomes.
We have the exponential equation:
f(x) = 2*(1/2)^x
To get the domain we start by assuming that the domain is the set of all real numbers, and then we see if the equation has a problem for a given value of x, then we remove that from the domain.
But here we have x on the exponent, so there are no value of x that causes problems, thus the domain is the set of all real numbers.
To get the range we can look at the graph, we can see that the range goes from near 0 to infinity, so we can say that:
range = y > 0.
(note that the function tends asymptotically to zero, meaning that it never becomes equal to zero).
Then the correct option is C:
Domain: all real numbers;
Range: y > 0
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Rhino can run at speed about 28 miles per hour what is the speed in feet per second to the nearst whole number
(28 mph) x (5,280 ft/mi) / (60 min/hr) / (60 sec/min) = 41 feet per second
What is the volume of a cube with edge 5cm
The cost of a tyre has increased by 20% to £78. Work out the original price. Please reply ASAP, thank you.
Given the following perfect square trinomial, fill in the missing term.
x2 − 16x + ____
Answer:
[tex]x^{2}-16x+64[/tex]
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following perfect square trinomial given in the problem:
[tex]x^{2}-16+[/tex]
2. To fill the missing term, you must divide the coefficient -16 by 2 and then you must square it, as following:
[tex](\frac{-16}{2})^{2}=(-8)^{2}=64[/tex]
A triangle has side lengths of 8 inches,12 inches,and 16 inches. Determine whether this is a right triangle and why.
Answer:
the answer is no
Step-by-step explanation:
8²+12²≠16²
Taxi A charges $0.20 per mile and an initial fee of $4. Taxi B charges $0.40 per mile and an initial fee of $2. Write an inequality that can determine when the cost of Taxi B will be greater than Taxi A. A) 0.20x + 4 > 0.40x + 2 B) 0.20x + 4 < 0.40x + 2 C) 0.20x + 0.40x > 4 + 2 D) 0.20x + 0.40x < 4 + 2
The expression for the cost of Taxi B is 0.40x + 2. The expression for the cost of Taxi A is 0.20x + 4. The inequality asks for when the cost of Taxi B will be greater than Taxi A, so you write it as 0.40x + 2 > 0.20x + 4, or 0.20x + 4 < 0.40x + 2.
The answer is B) 0.20x + 4 < 0.40x + 2.
Answer: B. [tex]0.20x+4<0.40x+2[/tex]
Step-by-step explanation:
let x denotes the number of mile taxi runs.
Given : Taxi A charges $0.20 per mile and an initial fee of $4.
i.e. the expression to show total charge by Taxi A will be :[tex]0.20x+4[/tex]
Taxi B charges $0.40 per mile and an initial fee of $2.
i.e. the expression to show total charge by Taxi B will be :[tex]0.40x+2[/tex]
Now, the inequality that can determine when the cost of Taxi B will be greater than Taxi A will be :-
[tex]0.20x+4<0.40x+2[/tex]
Hence, B is the correct answer.
Math, Not sure how to do this one help me out please?
You need to know the 30-60-90 triangles rules for lengths. (b, b√3, 2b)
the given side length of corresponds to the 30° angle. So, b = 8
side y corresponds to the 60° angle so it is b√3. Since we determined that b = 8, then b√3 is 8√3.
side x corresponds to the 90° angle so it is 2b. Since we determined that b = 8, then 2b = 2(8) = 16
Answer: x = 16, y = 8√3
A rectangular field is three times as long as it is wide. If the perimeter of the field is 600 feet, what are the dimensions of the field?
Final answer:
To find the dimensions of the field with a perimeter of 600 feet where the length is three times the width, solve the equation derived from the perimeter formula. The width comes out to be 75 feet and the length 225 feet.
Explanation:
The question is about finding the dimensions of a rectangular field that is three times as long as it is wide, with a total perimeter of 600 feet. First, let's denote the width of the field as W and the length as 3W since the length is three times the width. The formula for the perimeter of a rectangle is 2(length + width), which in this case is 2(3W + W) = 8W. Given that the perimeter is 600 feet, we can set up the equation 8W = 600. Solving this for W gives us W = 75 feet. Therefore, the length, being three times the width, is 225 feet.
So, the dimensions of the field are 75 feet in width and 225 feet in length.
plzzz help - i will mark brainest
1.-Write the recursive rule of the sequence 9, 3, 3, 9,... −− .
________________________________________
2.-A line has an x-intercept of (4, 0) and a y-intercept of (0, 12). Find the slope of the line.
________________________________________
3.-A horizontal line includes the points (0, -5 ) and ( 2, -5 ) Find the slope of the line.
Answer:
1. You divide by 3 then multiply by 1 and multiply by 3 again
2. Slope of -3
3. Slope of 0
Step-by-step explanation:
Joseph completed the two-way table on the left about the social networking habits of his classmates as follows:
Step 1: 85 – 30 = 55
Step 2: 80 – 55 = 25
Step 3: 140 – 80 = 60
Step 4: 60 – 30 = 30
Step 5: 25 + 30 = 55
Choose ONE OPTION from BELOW
The student made...
A) and error in step 1
B) and error in step 2
C) an error in step 3
D) an error in step 4
E) an error in step 5
F) no error
Joseph made no error.
The answer is F) no error
Answer:
Option: F is the correct answer.
F) No error.
Step-by-step explanation:
We are given the steps that Joseph used while solving as:
Step 1: 85 – 30 = 55
Step 2: 80 – 55 = 25
Step 3: 140 – 80 = 60
Step 4: 60 – 30 = 30
Step 5: 25 + 30 = 55
Clearly the steps involves simple addition as well as subtraction of the mathematical numbers.
Hence all his steps are correct as he has not committed any wrong operation.He evaluated the expressions in the right manner.
Hence, the answer is:
Option: F
A parts distributor's customers always order spark plugs in groups of 4, 6, or 8. Which is the smallest quantity the supplier has that could accommodate every order?
Answer:
24 spark plugs
Step-by-step explanation:
To find smallest quantity that could accommodate every order we will find LCM of 4,6 and 8.
Multiples of 4 are: 4,8,12,16,20, 24,28,..
Multiples of 6 are: 6,12,18,24,30,36,42,..
Multiples of 8 are: 8,16,24,32,40,..
We can see that LCM of 4, 6 and 8 is 24. Therefore, order of 24 spark plugs will accommodate every order.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Solve the equation.
x^2 + 10x + 24 = 0
A) -12 and 2
B) 12 and -2
C) -4 and -6
D) 4 and 6
[tex]x^2 + 10x + 24 = 0\\\\x^2+2x+12x+24=0\\\\x(x+2)+12(x+2)=0\\\\(x+12)(x+2)=0\\\\x=-12 \vee x=-2\Rightarrow \text{A}[/tex]
What are the first four terms of the sequence shown below?
an = 5n ‒ 1
A.
‒1, 4, 9, 14
B.
4, 9, 14, 19
C.
5, 6, 7, 8
D.
6, 11, 16, 21
[tex]a_n=5n-1\\\\a_1=5(1)-1=5-1=4\\\\a_2=5(2)-1=10-1=9\\\\a_3=5(3)-1=15-1=14\\\\a_4=5(4)-1=20-1=19\\\\Answer:\ B.\ \{4,\ 9,\ 14,\ 19\}[/tex]
Which of the following are ordered pairs for the equation y = -4x + 5?
(0,5) (1,1) (-1,9)
(0,5) (-1,-1) (-1,-9)
(0,5) (1,-1) (-1,9)
(0,5) (-1,1) (-1,-9)
(0, 5), (1, 1 ), ( - 1, 9 )
to test the points substitute the x-coordinate into the equation and if the value is equal to the y- coordinate then it is an ordered pair
(0, 5 ) → y = 0 + 5 = 5 ← ordered pair
(1, 1 ) → y = - 4 + 5 = 1 ← ordered pair
(- 1, 9 ) → y = 4 + 5 = 9 ← ordered pair
( - 1, - 1 ) → y = 4 + 5 = 9 ← not an ordered pair
( - 1, - 9 ) → y = 4 + 5 = 9 ← not an ordered pair
(1, - 1 ) → y = - 4 + 5 = 1 ← not an ordered pair
(- 1, 1 ) → y = 4 + 5 = 9 ← not an ordered pair
A company sells lab equipment. The daily revenue and costs are modeled by the functions below where x is the number of units sold.
Pleeeeaaasssseeeee help! <3 I'm just trying to graduate.thanks.
Subtract the cost from the revenue:
(-0.32x^2+270x) - (70x+52)
270x - 70x = 200x
The answer would be -0.32x^2 + 200x + - 52
Answer:
P(x) = -0.32x² + 200x + (-52)
Step-by-step explanation:
A company sells lab equipment. Daily revenue and costs are modeled by the function as given in the question.
Revenue: R(x) = -0.32x² + 270x
Cost : C(x) = 70x + 52
Here x = Number of units sold.
Now we have to determine the function P(x) for daily profit.
Since Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = (-0.32x² + 270x) - (70x + 52)
= -0.32x² + 270x - 70x - 52
P(x) = -0.32x² + 200x - 52
Therefore, answer will be P(x) = -0.32x² + 200x + (-52)
please help asap 30 pts
[tex]14-4y\geq38\qquad|\text{subtract 14 from both sides}\\\\-4y\geq24\qquad|\text{change the signs}\\\\4y\leq-24\qquad|\text{divide both sides by 4}\\\\y\leq-6\\\\Answer:\ \boxed{d.\ y\leq-6}[/tex]
What is the area of the shaded region in the diagram? Use the value `pi` = 3.14, and round your answer to two decimal places.
Answer:
Can you attach a picture of the diagram?
Step-by-step explanation:
Answer:
9.42 Square Units
How:
You need to use the sector area formula.
Sector Area = Measure of Arc / 360° × π r²
So then you just plug in the numbers:
Sector Area = 45° / 360° × π 5²
Sector Area = 1/8 × 25π
Sector Area = 9.817477
Sector Area = 45° / 360° × π 7²
Sector Area = 1/8 × 49π
Sector Area = 19.242255
Then all you have to do is subtract them both to find the area.
19.242255 - 9.817477 = 9.42 Square Units
I Hope this helped!
The skeeters baseball team charges $7. Per ticket plus $3. Processing fee for each order. Is the cost of an order proportional to the number of tickets ordered? Explain how you know.
True or false? The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
The statement is true.
Step-by-step explanation:
Given the statement we have to tell the statement is true or false.
The statement is
"The circumcenter of a triangle is the center of the only circle that can be circumscribed about it"
The circumcenter of triangle is the point in the triangle where the perpendicular bisectors of sides intersect.
The center of the circumscribed circle is the the point where the perpendicular bisectors of the sides meet.
Hence,
The circumcenter is also center of the triangle's circumcircle - the circle that pass through all three of the triangle's vertices.
Therefore, the given statement is true.
Answer:
True
Step-by-step explanation:
Circumcircle: A circle drawn outside a circle is called circumcircle and its center is called circum-center.
Circum-center of triangle:It is the point where the perpendicular bisectors of a triangle intersect.
The circumcenter of triangle is also the center of triangle's circumcircle.
The circumcenter is equidistant from each vertex of the triangle.
The circumcenter of right triangle falls on the side opposite the right triangle.
Hence, the circumcenter of a triangle is the center of the only circle that can be circumscribed about it.
Answer :True
Kayla has budgeted $400 for day trips during the summer. She needs at least $100 available at the end of summer to buy scrapbooks to memorialize her travels. If Kayla spends $60 for each day trip, what is the greatest number of trips that she can take without exceeding her budget?
A) 3
B) 4
C) 5
D) 7
400-100=300
300÷60=5
5 trips
Answer:- C) is the right answer. She can take 5 trips without exceeding her budget .
Explanation:-
Given: Budget for trips = $400
Amount needed by Kayla at the end of the trip= $100
Thus the exact amount she spends on trips= $400-$100= $300
Amount spend for each day trip = $ 60
Then The number of trips she can take[tex]=\frac{\text{Amount spend on trips }}{\text{Amount for each trip}}=\frac{300}{60}=5[/tex]
Thus she can take 5 trips without exceeding her budget .
2 3 of the children at a school are scared of snakes, 1 3 are scared of spiders, and 1 6 are scared of snakes and spiders. What fraction of those who are scared of spiders are also scared of snakes?
The fraction of those who are scared of spiders and also scared of snakes is 1/2.
What are Fraction?A fraction is a way of representing a part of a whole or a division of quantities. It consists of two components: a numerator and a denominator, separated by a horizontal line called a fraction bar.
We have,
1/3 of the children are scared of spiders and 1/6 of both snakes and spiders, we can find the fraction of those who are scared of spiders and snakes by dividing the overlap by the total number scared of spiders.
Fraction scared of spiders and snakes
= (Overlap) / (Total scared of spiders)
Overlap = 1/6
Total scared of spiders = 1/3
Fraction scared of spiders and snakes = (1/6) / (1/3) = (1/6) * (3/1) = 1/2
Therefore, the fraction of those who are scared of spiders and also scared of snakes is 1/2.
Learn more about Fraction here:
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Final answer:
Half of the children who are scared of spiders are also scared of snakes, calculated by dividing the fraction of children scared of both by those scared of spiders.
Explanation:
To find the fraction of those who are scared of spiders that are also scared of snakes, we start with the information that 2/3 of the children are scared of snakes, 1/3 are scared of spiders, and 1/6 are scared of both snakes and spiders. Since we want to find out the fraction of those scared of spiders (1/3 of the total) who are also scared of snakes, we focus on the 1/6 portion that represents children scared of both. This fraction is relative to the whole group. To express it as a fraction of just those scared of spiders, we divide the fraction of both phobias (1/6) by the fraction scared of spiders (1/3).
Calculation: (1/6) ÷ (1/3) = (1/6) * (3/1) = 1/2.
Therefore, 1/2 of those who are scared of spiders are also scared of snakes.
4x + 8 = 2x + 7 + 2x - 20.
PLEASE SHOW WORK!!!
How to get answer:
[tex]\mathrm{Group\:like\:terms}\\4x+8=2x+2x+7-20\\\mathrm{Add\:similar\:elements:}\:2x+2x=4x\\4x+8=4x+7-20\\\mathrm{Add/Subtract\:the\:numbers:}\:7-20=-13\\4x+8=4x-13\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\4x+8-8=4x-13-8\\\mathrm{Simplify}\\4x=4x-21\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\4x-4x=4x-21-4x\\Simplify\\0=-21\\The\:sides\:are\:not\:equal\\[/tex]
Steps:
4x + 8 = 2x + 7 + 2x - 20
Group like terms:
4x + 8 = 2x + 2x + 7 - 20
Add similar elements: 2x + 2x = 4x
4x + 8 =4x + 7 - 20
Add/Subtract the numbers: 7 - 20 = -13
4x + 8 = 4x - 13
Subtract 8 from both sides
4x + 8 - 8 = 4x - 13 - 8
Simplify:
4x = 4x - 21
Subtract 4x from both sides:
4x - 4x = 4x - 21 - 4x
Simplify
0 = -21
Hope this helps! :) and Happy Halloween! ~Zane
Express the number in scientific notation.
0.00341 x 104
A) 3.41 x 10-3
B) 3.41 x 10-1
C) 3.41 x 101
D) 3.41 x 104
Answer:
It's 3.14x10^1
Step-by-step explanation:
What is bigger 400 pints or 100 gallons
A car travels 65km in 45minutes. What is the average speed of the car in km/h
65X60/45=260/3km/hr=86.66km/hr
If 45 Cookies will serve 15 student do you live students,how many cookies are needed for 30 students?
90
divide 45 cookies by 15 to obtain cookies per student then multiply this amount by 30 to obtain cookies for 30 students
15 students → 45 cookies
30 students → 45 × [tex]\frac{30}{15}[/tex] = 90 cookies