If cosec ∅ = √2, find the value of 1+sin²∅+cos²∅/1+sec²∅-tan²∅.
Answers
Given: \(cosec\) \(A\) \(=\sqrt{2}\)
∴ \(A=\frac{\pi }{4} =45^{0}\)
\(sin\) \(A\) \(=sin\) \(45^{0}\) = \(\frac{1}\sqrt{2}\)
\(cot\) \(A\) \(=cot\) \(45^{0}\) \(=1,\)
\(tan\) \(A\) \(=\) \(tan\) \(45^{0}\) \(=1\)
\(cos\) \(A\) \(=\) \(cot\) \(45^{0}\) \(=\frac{1}{\sqrt{2} }\)
∴ \(=2\)
\(\large\underline{\sf{Solution-}}\)
METHOD 1: Using Trigonometric values.
We have given that,
\(\sf\cosec\theta=\sqrt2\)
So,
\(\sf\theta=45^{\circ}\)
We need to find:
\(\sf\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}\)
So,
\(\sf\longmapsto\dfrac{1+\sin^2(45^{\circ})+\cos^2(45^{\circ})}{1+\sec^2(45^{\circ})-\tan^2(45^{\circ})}\)
\(\sf\longmapsto\dfrac{1+\left(\frac{1}{\sqrt2}\right)^2+\left(\frac{1}{\sqrt2}\right)^2}{1+(\sqrt2)^2-(1)^2}\)
\(\sf\longmapsto\dfrac{1+\frac{1}{2}+\frac{1}{2}}{1+2-1}\)
\(\sf\longmapsto\dfrac{1+1}{2}\)
\(\sf\longmapsto\dfrac{2}{2}\)
\(\sf\longmapsto\bf1\)
METHOD 2: Using Trigonometric Identities
We need to find:
\(\implies\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}\)
But, we know that,
\(\sf\red⇛ \sin^2\phi+\cos^2\phi=1\)
And,
\(\sf\red⇛ \sec^2\phi-\tan^2\phi=1\)
So,
\(\sf\longmapsto\dfrac{1+(\sin^2\theta+\cos^2\theta)}{1+(\sec^2\theta-\tan^2\theta)}\)
\(\sf\longmapsto\dfrac{1+1}{1+1}\)
\(\sf\longmapsto\dfrac{2}{2}\)
\(\sf\longmapsto\bf1\)
Therefore, by both methods the answer is 1.
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Prove that:
\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...
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Identify the domain of the function shown in the graph.
Answers
answer:
c
because all of them is the real number
What is the difference of (- 2x + 9) and (3x - 4)
Answers
Answer:
\(-5x+13\)
Step-by-step explanation:
\((-2x+9)-(3x-4)\\=-2x+9-3x+4\\=-5x+13\)
Select all the equations where a = 8 is a solution.
Choose 3 answers:
A 2 + 11 = 15
6 l = 8 + 0
©
15
a = 23
0 42 = 7a
Answers
Answer: B, C and E
Step-by-step explanation:
Pls help show work plsss
Answers
The transformation that takes the graph of \(f(x) = 7^{x}\) to the graph of \(g(x) = 7^{x+8}-2\) include the following:
A. The graph is translated down 2 units.
B. The graph is translated to the left 8 units.
What is a translation?In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent a function.Based on the information provided above, a function that represents g(x) is given by:
g(x) = f(x + N) - N
\(g(x) = 7^{x+8}-2\)
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A retailer sold an electric item to a customer at a loss of 10 percent the customer purchase it for rs 25425 including 13, percent VAT calculate the cost price of the electric item to the retailer
Answers
Answer: Rs 25,000
Step-by-step explanation:
Given
Retailer sold an electric iron to a customer at a loss of 10%
Suppose the Cost price of iron is \(x\)
So, selling price is \(0.9x\)
This price must be equal to \(25425\)+ VAT
\(\Rightarrow 0.9x=25425-0.13(0.9x)\\\Rightarrow 0.9x+0.117x=25425\\\Rightarrow 1.017x=25425\\\Rightarrow x=\text{Rs }25,000\)
Thus, the cost price is \(Rs.25,000\)
In a basketball game Elena scored twice as many points as Tyler Tyler scores four points fewer than Noah and Noah scores three points as Mai of Mai scores 5 points how many points did Elena score
Answers
Full question:
In a basketball game, Elena scores twice as many points as Tyler. Tyler scores four points fewer than Noah, and Noah scores three times as many points as Mai. If Mai scores 5 points, how many points did Elena score? Explain your reasoning
Answer and explanation:
We start from known to unknown. We know that Mai scored 5 points and so we work from here.
Since Mai scored 5 points and Noah scored three times as many points then Noah's score = 3×5= 15 points
Since Tyler scored four points less than Noah, Noah's score= 15-4= 11 points
Finally Elena's score is twice that of Tyler hence Elena's score =2×11= 22 points
if you answer i will give you brainliest
Answers
Answer:
OK hiiiiiiiiiiiiiiiii.
Part) J
What is the relationship between circle A and circle B?
Answers
Answer:
See the answer below.
Step-by-step explanation:
These two circles are similar objects.
The ratio of a corresponding part is a: b.
The area ratio is a²: b² and the volume ratio is a³ : b³
Therefore if AE : CD which is 2:3
The area ratio 4 :9
The volume ratio is 8: 27
The relation between both circles is the area of circles in ratio to the radius and both circles are similar circles.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circle objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Given two circle
Circle 1 = radius 2
Circle 2 = radius 3
All circles are similar objects so their area ratio is radius ratio.
(Area of circle 1)/(Area of circle 2) = (radius 1)/(radius 2)
(Area of circle 1)/(Area of circle 2) = 4/9 = 2/3
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Lucía pagó $539.50 por una playera que costaba $650. ¿Qué porcentaje le hicieron de descuento?
Answers
Answer:
17%
Step-by-step explanation:
Lucía pagó 539.5 en lugar de 650 (el original) Entonces el descuento fue 650-539.5=110.5
Ahora, nosotros necesitamos buscar qué porcentaje de el original fue el descuento:
(porcentaje)% de 650 = 110.5
(porcentaje)/100 * 650 = 110.5
(porcentaje) = 110.5*100/650 = 11050/650 = 1105/65 = 17
El descuento fue: 17%
Max and jake file mfj. max received $15,424 and jake received $27,452 in social security benefits. jake also received taxable income of $22,148 from his pension and $2,378 in interest. using the social security benefits worksheet - line 6a and 6b, determine their combined taxable social security benefits
Answers
According to the income, the combined taxable social security benefits is $67,402
Here we have given that Max and Jake file mfg. max received $15,424 and Jake received $27,452 in social security benefits
Here we also know that Jake also received taxable income of $22,148 from his pension and $2,378 in interest.
While we looking into the given question, we have identified that
Jake Social security benefit = $27,452
Max Social security benefit = $15,424
Jake income has been divided into two part s that is pension and interest.
Pension = $22,148
Interest = $2,378
Then the total income is calculated as,
=> 22148 + 2378
=> 24,526
Therefore, the combined taxable benefit is written as,
=> 27452 + 15424 + 24526
=> 67402
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Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find the intervals of convergence for f '. find the intervals of convergence for f ''
Answers
Best guess for the function is
\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)
By the ratio test, the series converges for
\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)
When \(x=1\), \(f(x)\) is a convergent \(p\)-series.
When \(x=-1\), \(f(x)\) is a convergent alternating series.
So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).
The derivative of \(f\) is the series
\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)
which also converges for \(|x|<1\) by the ratio test:
\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)
When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.
When \(x=-1\), \(f'(x)\) is a convergent alternating series.
The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).
Differentiating \(f\) once more gives the series
\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)
The first series is geometric and converges for \(|x|<1\), endpoints not included.
The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).
Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).
What is the slope-intercept equation of this line
Answers
Answer:
y = -3x + 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope = y2 - y1/x2 - x1
-2 - 4/2-0 = slope
slope = -6/2 or -3
Equation:
y = -3x + 4
Answer:
\(y = 4x-3\)
Step-by-step explanation:
y-intercept = b = 4 (because x becomes zero here)
Now, Finding the slope:
Slope = m = \(\frac{rise}{run}\)
Slope = \(\frac{-2-4}{2-0}\)
Slope = \(\frac{-6}{2}\)
Slope = -3
Now putting m and b in the slope intercept equation to get the required form:
=> \(y = mx+b\)
=> \(y = 4x-3\)
The population, in millions, of arctic flounder in the Atlantic Ocean is modeled by the function P(t), where t is measured in ye 7t + 5 P(t) 0.2t2 + 1 (a) Determine the initial flounder population (in millions). million flounder (b) Determine P'(10) (in millions of flounder per year). (Round your answer to four decimal places.) P'(10) - million flounder/yr
Answers
The initial flounder population in millions is 1 million. The derivative of the population function at t = 10 is 1.4000 million flounder per year.
(a) To find the initial flounder population, we substitute t = 0 into the population function P(t). Given that t is measured in years, we have:
P(0) = 7(0) + 5 - 0.2(0^2) + 1 = 0 + 5 - 0 + 1 = 6 million flounder.
Therefore, the initial flounder population is 6 million.
(b) To determine P'(10), we need to find the derivative of the population function P(t) and evaluate it at t = 10. Taking the derivative of P(t) with respect to t, we have:
P'(t) = 7 + 0.4t.
Now, substituting t = 10 into the derivative equation:
P'(10) = 7 + 0.4(10) = 7 + 4 = 11 million flounder per year.
Rounded to four decimal places, P'(10) is approximately 11.0000 million flounder per year.
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which statement is correct?
Answers
The length of a rectangle is a centimeters, and the width of this rectangle is b centimeters. Write an expression for the area of the rectangle. "a" and "b" are variables.
Answers
Answer:
Area = ab
Step-by-step explanation:
Area is length × width, so fill in a for the length and b for the width. Multiply a and b together.
A = a×b
A = ab
Use algebra tiles to solve
–5x=-30
Answers
Compare the probability that a student will pass the test in the morning with
the probability that a student will pass the test in the afternoon. Draw a
conclusion based on your results.
A. P(pass morning) = 0.24
P(pass afternoon) = 0.41
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon
O B. P(pass morning) = 0.24
P(pass | afternoon) = 0.41
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
O c. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
D. P(pass morning) = 0.48
P(pass afternoon) = 0.82
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon.
Answers
Answer: C
Step-by-step explanation:
just took the quiz
The conclusion based on the statement would be option C. Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We need to Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon.
The conclusion based on the statement would be;
C. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
Therefore, the correct option is C.
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a family on a trip budgets $800 for sit-down restaurant meals and fast food. if the price of a fast food meal for the family is $20, how many such meals can the family buy if they do not eat at restaurants? group of answer choices 8 15 20 40 160
Answers
Answer:
If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.
Step-by-step explanation:
yw;)
Answer:
40
Step-by-step explanation:
No. Of Meal=Budget/price of Meal
=800/ 20
=40
use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.
Answers
The counterclockwise circulation around c is 12 and the outward flux through c is zero.
Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.
In this case,
we have a field f=(7x−4y)i+(9y−4x)j and
a square curve c bounded by x=0, x=4, y=0, y=4.
To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.
The curl of f is given by (0,0,3), so the line integral evaluates to 12.
To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.
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2 The following functions are equivalent.
Sketch a graph and label the points.
f (2) = 3 (x + 4) (x – 4)
f (x) = 3x2 - 48
Answers
The team is 52 yards away from a touchdown. Steve ran the football 26 yards toward the end zone, but on the next play Keith was pushed back 8 yards. How many yards until they get a touchdown
Answers
Answer:
34 yards
Step-by-step explanation:
52 - 26 + 8
26 + 8
34
i need help please: if
Answers
Answer:
If what??? can you please finish the question in the reply?
PLEASE HELP!!!!! PLEASE
Answers
Answer: d. (if a polygon has congruent angles, then it is regular)
Step-by-step explanation:
Converses follow the format of "if q, then p" (while the original conditional is "if p, then q")
Just because there are clouds does not mean its raining (cloudy days)
just because it has four equal sides does not make it a square (rhombi have four equal sides but are not squares)
just because you cannot see the sun does not mean it is not daytime (solar eclipses)
if a polygon is regular, it must have congruent angles
Please Help:The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. The function is quadratic.Rainfall (in.)Population (millions)0019216321424525624Enter your answers in the boxes.The x-intercept represents that after in. of rain there are mosquitoes.
Answers
To answer this question, we need to remember that, for any function, the x-intercept happens when the value of the function is zero.
In this case we have the function:
\(P(x)\)where P(x) represents the population (in millions) of mosquitoes and x is the amount of rainfall in inches.
From the table we notice that the function is zero when x=0. This means that the x-intercept of the function is x=0. Now, if we remember what our function and independent variable mean we conclude that:
The x-intercept represents that after 0 in. of rain there are 0 mosquitoes.
Simplify 1/3 (1-1/4)2
Answers
Answer:
3/16
Step-by-step explanation:
1 - ¼ = ¾
(¾)² = 9/16
1/3 × 9/16 = 3/16
A backyard is 40.5 feet long and 25 feet wide. In order to install a pool, the yard needs to be reduced by a scale of One-third. What is the area of the reduced yard?
Answers
Answer:
112.5 feet
Step-by-step explanation
Length = (40.5 ft) x (1/3) = 13.5 ft
Width = (25 ft)(1/3) = 25/3 ft
Area of the yard = (13.5 ft)(25/3) = 112.5 ft²
the final area of the yard is equal to 112.5 ft².
Show that w is in the subspace of R4 spanned by V1, V2, and V3, where these vectors are defined as follows. 1 -4 -9 -4 6 3 5 W= -2 - 1 - 1 -2 4 11 -8 - 15 To show that w is in the subspace, express was a linear combination of V1, V2, and V3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. O A. The vector w is in the subspace spanned by V1, V2, and V3. It is given by the formula w= (v1+ 2+ 3. (Simplify your answers. Type integers or fractions.) B. The vector w is not in the subspace spanned by V1, V2, and V3.
Answers
To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:
w = c1V1 + c2V2 + c3V3
We can write this as a matrix equation:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
We can solve this system of equations using row reduction:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
R2 = R2 - 6R1
R3 = R3 - 2R1
R4 = R4 + 15R1
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 -23 67 -59 | | -32 |
R4 = R4 + 23R2
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 0 174 -294 | | 225 |
R3 = R3 - (12/27)R2
R4 = (1/174)R4
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 0 -1 22/3 | | c3 | | -13/3 |
| 0 0 1 -98/87 | | 25/58 |
R1 = R1 + 4R3
R2 = R2 - 59R3
R4 = R4 + (98/87)R3
| 1 0 -13 -10/3 | | c1 | | 21/29 |
| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |
| 0 0 1 -98/87 | | c3 | | 25/58 |
| 0 0 0 1390/2391 | | 1009/2391 |
R1 = R1 + (13/1390)R4
R2 = (1/27)R2
R3 = R3 + (98/1390)R4
| 1
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You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity?______m/s.
Don't forget to include a negative sign if the answer is negative!
Ex: 10 m/s or -10 m/s. DO NOT USE DECIMALS.
Answers
Velocity is 5m/s.
In the given statement is :
You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity? ______m/s.
Firstly, Let's know the:
What is Velocity?
Velocity refers to the rate of change in displacement with respect to time.
Furthermore, distance and displacement are the key points of the velocity.
Now, Calculate the velocity, by using formula of Velocity
Velocity = Displacement/ time
And, Velocity = 45/9 = 5m/s.
Therefore Velocity is 5m/s
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DONT SEND A LINK TO DOWNLOAD A PIC IN THIS
Is the relation shown a function? Explain.
Answers
Answer:
no because there are more than 1 X inputs.
Step-by-step explanation:
Answer:
Nope
Step-by-step explanation:
The relation isn't a function because a function is a relation where each x-value has only one corresponding y-value. Try to put a vertical line through that shape made by the graph to test if it's a function. If it passes through multiple points, it's not a function. For example, if you put the vertical line x=3 in that same graph, it will intersect with the relation at points (3, -3) and (3, 4), and therefore is not a function.
hope this helps, please lmk if im wrong!!!
3
To find the height of a tower standing on a small hill,
Maria made some measurements (see diagram).
From a point B, the angle of elevation of C is 20°, the angle of
elevation of A is 50° and the distance BC is 25 m.
a Calculate these angles.
i ABC
ii BAC
b Using the sine rule and triangle ABC, calculate the height
h of the tower.
B
50⁰
20⁰
25 m
C
Answers
Using the sine rule and triangle ABC, the height is 14.43375ft. BAC=40° and ABC=30°
if C is 20° and A is 50°
ABC=50°-20°=30°
BCA=20°+90°=110°
ABC+BCA+BAC=180°
30°+110°+BAC=180°
BAC=180°-140°=40°
Using the sine rule and triangle ABC,
opposite=x
adjacent =25 m.
tanθ =x/25
Multiplying both sides by 25 gives
x=25* tan 30° =25* 0.57735.=14.43375
To put it another way, there is only one plane that contains all of the triangles. All triangles are enclosed in a single plane on the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless otherwise specified, this article deals with triangles in Euclidean geometry, specifically the Euclidean plane.
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