3. Find the exact value of a. cos (tan-¹5) b. cot(sin-¹-) 4. Solve for x: a. π+3cos¹¹(x + 1) = 0 b. 2tan ¹(2) = cos ¹x c. sin¹ x = cos ¹(2x) 5. Proof a. tan x + cos x = sin x (sec x + cot x)
Answers
The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5. Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1. Then, hypotenuse = √(5² + 1²) = √26
3. a. cos (tan-¹5)
The given expression is cos(tan⁻¹ 5). Let y = tan⁻¹ 5. Then, tan y = 5
Therefore, we have a right triangle where opposite side = 5 and adjacent side = 1.
Then, hypotenuse = √(5² + 1²) = √26
Then, cos y = adjacent/hypotenuse= 1/√26
Therefore, cos (tan⁻¹ 5) = cos y = 1/√26b. cot(sin-¹-)
The given expression is cot(sin⁻¹ x).
Let y = sin⁻¹ x
Then, sin y = x
Therefore, we have a right triangle where opposite side = x and hypotenuse = 1. Then, adjacent side = √(1 - x²)
Then, cot y = adjacent/opposite = √(1 - x²)/x
Therefore, cot(sin⁻¹ x) = cot y = √(1 - x²)/x4.
a. π+3cos¹¹(x + 1) = 0
Let cos⁻¹(x + 1) = y
Then, cos y = x + 1
Therefore, we have cos⁻¹(x + 1) = y = π - 3y/3So, y = π/4
Then, cos y = x + 1 = √2/2 + 1 = (2 + √2)/2π + 3(π/4) = (7π/4) ≠ 0
There is no solution to the given equation.
b. 2tan⁻¹(2) = cos⁻¹x
Let y = tan⁻¹(2)
Then, tan y = 2
Therefore, we have a right triangle where opposite side = 2 and adjacent side = 1. Then, hypotenuse = √(1² + 2²) = √5
Therefore, sin y = 2/√5 and cos y = 1/√5
Hence, cos⁻¹x = 2tan⁻¹(2) = 2y
So, x = cos(2y) = cos[2tan⁻¹(2)] = 3/5
c. sin⁻¹ x = cos⁻¹(2x)
Let sin⁻¹ x = y
Then, sin y = x
Therefore, we have a right triangle where opposite side = x and hypotenuse = 1.
Then, adjacent side = √(1 - x²)
Then, cos⁻¹(2x) = z
So, cos z = 2x
Therefore, we have a right triangle where adjacent side = 2x and hypotenuse = 1.
Then, opposite side = √(1 - 4x²)
Then, tan y = x/√(1 - x²) and tan z = √(1 - 4x²)/2x
Hence, x/√(1 - x²) = √(1 - 4x²)/2x
Solving this, we get x = ±√2/2
Therefore, sin⁻¹ x = π/4 and cos⁻¹(2x) = π/4
Therefore, the given equation is true for x = √2/2.5.
Proof Given: tan x + cos x = sin x (sec x + cot x)
We know that sec x = 1/cos x and cot x = cos x/sin x
Therefore, the given equation can be written as tan x + cos x = sin x (1/cos x + cos x/sin x)
Multiplying both sides by sin x cos x, we get sin x cos x tan x + cos² x = sin² x + cos² x
Multiplying both sides by 1/sin x cos x, we get tan x + sec² x = 1
This is true. Hence, proved.
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Related Questions
Stan drove 3300 \text{ m}3300 m3300, start text, space, m, end text to the grocery store. The tires on his truck are 2.2 \text{ m}2.2 m2, point, 2, start text, space, m, end text in circumference.
Answers
Answer:
58,928.6 rotations
Step-by-step explanation:
2.2 in x (2.54cm/in) x (1m/100cm)= .056 m/circumference
3300m/(.056m/rotation) = 58,928.6 rotations
Drag each equation to show if it could be a correct first step to solving the equation
3(+8)=42
3
x
+
8
=
42
.
Answers
Answer:
If you are looking for 3x+8=42, then x=12.
Step-by-step explanation:
3x+8=42
Step 1:
Subtract 8 from both sides.
3x=36
Step 2:
Divide 36 by 2.
x=12.
I think this is the answer you are looking for.
What is the solution to 3x+2=x+8
Answers
Suppose X and Y are independent N(0; 1) random variables.
(a) Find P(X^2 < 1).
(b) Find P(X^2 + Y^2 < 1)
Answers
The required probability is obtained as:
(a) P(X^2 < 1) = 0.8413.
(b) P(X^2 + Y^2 < 1) = 0.7854.
(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:
P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))
Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:
P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))
Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.
(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.
We can use polar coordinates to express X and Y as:
X = Rcosθ
Y = Rsinθ
where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).
Therefore, we can find P(X^2 + Y^2 < 1) as:
P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))
Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:
P(R^2 < 1) = 0.7854
Therefore, P(X^2 + Y^2 < 1) = 0.7854.
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The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Answers
The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
According to the statement
we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.
So, for this purpose,
we know that the best method show the relationship is a slope intercept form.
So,
The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
And
Using the coordinate points on the plane (0, 6) and (10, 28)
now we Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
And then Determine the y-intercept
6 = 2.2(0) + b
b = 6
And now we have to put in the general form of the slope intercept form which is y = mx + b
Then the equation become
y = 2.2x + 6
So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
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What is the coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10?
Answers
Answer:
-1,959,552
Step-by-step explanation:
You want to know the coefficient of x^5y^5 in the expansion of (2x -3y)^10.
Binomial expansionThe k-th term of the binomial expansion of (a +b)^n, with k ∈ [0, n], is ...
C(n, k)·(a^(n-k))(b^k)
ApplicationFor n=10, k=5, the term is ...
C(10, 5)·(2x)^5(-3y)^5 = 252·32·(-243)·x^5·y^5
= -1959552x^5y^5
The coefficient is -1,959,552.
__
Additional comment
The function C(n, k) tells the number of ways k elements can be chosen from a set of n, without regard to order. The value is ...
C(n, k) = n!/(k!(n-k)!)
Many graphing and statistical calculators can compute the value for you. In this case, it is ...
(10·9·8·7·6)/(5·4·3·2·1) = 3·2·7·6 = 252
Please help! I will mark as brainliest. <3
Answers
Answer:
1: $3.30x < $95
2: x < 28.78 (78 repeating)
Step-by-step explanation:
HELP ME PLEASE
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 18 meters. The height of the figure is 12 meters. The portion from the vertex to the perpendicular height is 7 meters. The portion from a point to a vertical line created by two vertices is 5 meters.
Which of the following represents the total area of the figure?
288 m2
360 m2
416 m2
576 m2
Answers
The five-sided figure can be divided into a rectangle and a triangle. The rectangle has a base of 18 meters and a height of 12 meters, so its area is 18 x 12 = 216 square meters. The triangle has a base of 7 meters and a height of 12 meters, so its area is 0.5 x 7 x 12 = 42 square meters.
The other portion of the figure is a trapezoid. To find its area, we need to find the average of the two parallel sides (18 meters and 5 meters), which is (18 + 5) / 2 = 11.5 meters. The height of the trapezoid is 12 meters. The area of the trapezoid is 0.5 x (18 + 5) x 12 = 138 square meters.
Therefore, the total area of the composite figure is:
216 + 42 + 138 = 396 square meters
None of the answer choices are correct. The closest answer choice is 416 m2, but the actual answer is 396 m2.
The radius of a circle is (x + 9) cm. Find the area of the circle in terms of the variable x. Leave the answer in terms of .
Answers
Answer:
Area of Circle = πr²
22/7(x + 9)²
3.14 × (x²+ 81 + 18x)
SOMEBODY HELPPP PLEASEEEE. I don’t understand
Answers
Answer:
a) 18
b) 10
c) x^2 - 4x + 5
d) 4x^2 + 2
Step-by-step explanation:
f(x) = 4x - 2
g(x) = x^2 + 1
a) f(5) = 4(5) - 2 = 20 - 2 = 18.
b) g(-3) = (-3)^2 + 1 = 9 + 1 = 10.
c) g(x - 2)...
g(x - 2) = (x - 2)^2 + 1 = x^2 - 2x - 2x + 4 + 1 = x^2 - 4x + 5.
d) f(g(x)) = f(x^2 + 1) = 4(x^2 + 1) - 2 = 4x^2 + 4 - 2 = 4x^2 + 2.
Hope this helps!
student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
Answers
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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What is the area of the pentagon, rounded to the nearest tenth?
Answers
Answer:
not sure until i know the lengths
Step-by-step explanation:
I need help with geometry
Answers
Answer:
corresponding angles
the angles are equal
equation: 9x+8 = 4x+18
x=2
angle measurements: 26⁰
Step-by-step explanation:
solve your equation
9x+8 = 4x+18
subtract 4x from each side
5x + 8 = 18
subtract 8 from each side
5x = 10
divide by 5
x = 2
insert x=2 into original equations to make sure you get the same answer.
9(2) + 8 = 26
4(2) + 18 = 26
2x+1=2(x-2) solve for x
Answers
Answer:
There is no solution to this equation
Step-by-step explanation:
2x+1=2(x-2)=
2x+1=2x-4
0x = -5
Answer is no solution
this statement is false
2x+1=2(x-2)
2x+1=2x-4
cancel equal terms
1=-4
Find the distance between point P and line ℓ. Line ℓ contains points (11, −1
) and ( −3
, −11
). Point P has coordinates ( −1
, 1)
Answers
The distance between the point P and the line ℓ is 24 / √(74) units.
To find the distance between a point P and a line ℓ, we need to use the coordinates of both the point and the line. In this case, we have the coordinates of the point P, which is (−1, 1), and two points on the line ℓ, which are (11, −1) and (−3, −11).
The first step is to find the equation of the line ℓ. We can use the two points on the line to find the slope of the line, which is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line. Substituting the given coordinates, we get:
m = (-11 - (-1)) / (-3 - 11) = -10 / (-14) = 5 / 7
Now we can use the point-slope form of the equation of a line to find the equation of line ℓ:
y - y₁ = m(x - x₁)
where (x₁, y₁) is any point on the line. We can choose either of the given points, let's choose (11, −1):
y - (-1) = (5 / 7)(x - 11)
Simplifying this equation, we get:
y = (5 / 7)x - 36 / 7
So, the equation of line ℓ is y = (5 / 7)x - 36 / 7.
Now we can use the formula for the distance between a point and a line:
distance = |ax + by + c| / √(a² + b²)
where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point. In this case, the coefficients of the equation of line ℓ are a = 5 / 7, b = -1, and c = -36 / 7. Substituting the coordinates of the point P, we get:
distance = |(5 / 7)(-1) - 1 + (-36 / 7)| / √((5 / 7)² + (-1)²)
Simplifying this equation, we get:
distance = 24 / √(74)
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The measure of an angle is 2.8.what is the measure of its complementary angle
Answers
Answer:
87.2º
Step-by-step explanation:
Complimentary angles total 90º
c + 2.8 = 90
c = 90 - 2.8
c = 87.2º
Answer:
87.2°Step-by-step explanation:
When angles are complementary, it means that they both add up to 90°.
In this case, one of the angles measures 2.8°.
So, to find the other one, we subtract 2.8 from 90.
90 - 2.8 = 87.2
The measure of the complementary angle is 87.2°
I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!
What is the value of x? (giving brainliest and thanks to all!)
Answers
Answer:
x = 12
Step-by-step explanation:
Given a line parallel to a side of the triangle and it intersects the other 2 sides then it divides those sides proportionally, that is
\(\frac{x}{24}\) = \(\frac{5}{10}\) ( cross- multiply )
10x = 120 ( divide both sides by 10 )
x = 12
in order to use an expert from a movie in your history class you must pay a royalty fee. the base fee is 50 and an additional .25 cents per minute of the film. the equation for this is?
Answers
Answer:
.50=.25x x= Minutes of watching the film.
Step-by-step explanation:
ANSWER PLEASE 15 POINTS!!!!!
Point D is the center of the given circle. What is the measure of Ac?
A. 48°
48°
B. 96°
Bo
C. 84°
D. 24°
Answers
Answer:
b
Step-by-step explanation:
this is the correct answer trust
Answer:
I think its c because it's less the a 90° angle
Choose the scenario that could be represented by 4/5
A. A five-foot wooden board is cut into four equal pieces.
B. Five carrots are divided equally among four rabbits.
C. A five-hour car journey is divided into four equal parts.
D. Five people share four pastries equally.
Answers
Answer:A
Step-by-step explanation:
The correct scenario that could be represented by 4/5 is,
⇒ Five people share four pastries equally.
Option D is true.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
The scenario that could be represented by, 4/5
Now, By option D;
⇒ Five people share four pastries equally.
Hence, Every people get 4/5 part of pastries.
Thus, The correct scenario that could be represented by 4/5 is,
⇒ Five people share four pastries equally.
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Please help! THANKS!!
Answers
Answer:
6(2x - 5)
Step-by-step explanation:
Given
12x - 30 ← factor out 6 from each term
= 6(2x - 5) ← in factored form
what is 58/71= (round to the nearest HUNDREDST PLACE)
Answers
Answer:
817 10^-3
Step-by-step explanation:
58/71
0.817
817 10^-3
Answer:
0.82
Step-by-step explanation:
The question asks to change 58/71 to a decimal, then round it off to the nearest hundredst.
To change it to a decimal, divide the denominator(71) by the numerator(58)
71/58=0.81690
Then, round off to the nearest hundrest place would be to a number in which the numbers after a decimal would form a fraction with the denominator being 100 that number would be 0.81(ignore every digit after the third number after the decimal place)
if you left the answer like this, it would be wrong. You have to consider the number after the 'rounded off decimal' which is 6. If the number is 5 or higher, add 1 to the previous number.
6 is higher than 5, so we round it off as 1
hence= 0.816 ... 0.8(+1)
Hope this helps
Factorize:
a⁴-a³+2a²
Answers
\( {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} \)
Factor the expression with the common factor that is "a²".\( \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}\)
MissSpanishAnswer:
a²(a²-a+2)
Step-by-step explanation:
Solution Given:
a⁴-a³+2a²
first taking common a²
we get
a²(a²-a+2) which is a required answer.
For the sequence of positive even integers 2, 4, 6, 8, . . . find the following partial sums:
a. s2
b. s4
c. s10
d. s25
Answers
The partial sums of the sequence are;
a. s₂ = 6
b. s₄ = 20
c. s₁₀ = 110
d. s₂₅ = 650
What are the partial sum of the sequence?To find the partial sums of the given sequence of positive even integers, we need to add up the terms of the sequence up to a certain position. Let's calculate the partial sums as requested:
a. s₂ (the sum of the first 2 terms):
s₂ = 2 + 4 = 6
b. s₄ (the sum of the first 4 terms):
s₄ = 2 + 4 + 6 + 8 = 20
c. s₁₀ (the sum of the first 10 terms):
s₁₀ = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110
d. s₂₅ (the sum of the first 25 terms):
s₂₅ = 2 + 4 + 6 + 8 + ... + 48 + 50
Since it is not practical to manually add all 25 terms, we can use the formula for the sum of an arithmetic sequence to calculate it.
The formula for the sum of an arithmetic sequence is: Sn = (n/2)(a + l),
where Sn is the sum of the first n terms, a is the first term, and l is the last term.
In this case:
n = 25 = The number of terms
a = 2 = The first term
l = 50 = The last term
s₂₅ = (25/2)(2 + 50)
s₂₅ = (25/2)(52)
s₂₅ = 25 * 26
s₂₅ = 650
Therefore, the partial sum s₂₅ is equal to 650.
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1. The first four terms of a geometric progression are 3, -1, 1/3, -1/9
Find the sum to infinity.
Answers
The sum to infinity of the sequence is -2.25
How to determine the sum to infinityFrom the question, we have the following parameters that can be used in our computation:
3, -1, 1/3, -1/9
Using the above as a guide, we have the following:
First term, a -3
Common ratio, r = -1/3
The sum to infinity is then calculated as
Sum = a/1 - r
So, we have
Sum = -3/(1 + 1/3)
Evaluate
Sum = -2.25
Hence, the sum is -2.25
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Put in order from smallest to largest 1, 7/16, 0, 5/2, 2/13, 5/9
Answers
Answer:
0 < 2/13 < 7/16 < 5/9 < 1 < 5/2
Step-by-step explanation:
5/2=2.5
2/13=0.154
5/9=0.55
0, 2/13, 7/16, 5/9, 1, 2.5
PLEASE PLEASE HELP!~!!!!!!!!!!!!!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
$6.87
Step-by-step explanation:
The cost of 0.6 pounds of blueberries is ...
(0.6 lb)($3.98/lb) = $2.39
The cost of 1.8 pounds of clementines is ...
(1.8 lb)($2.49/lb) = $4.48
Then the total cost of the purchase is ...
$2.39 +$4.48 = $6.87
The combined cost is $6.87.
given that logm 3=0.903,logm4=1.139 , and logm7=1.599, find logm4/m.
Answers
The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.
Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.
Using the properties of logarithm, we have,
logm 4/m = logm 4 - logm m
=1.139 - logm m .....................................(1)
Again, using the properties of logarithm, we know that:
logm 4 = logm (2 × 2)
= logm 2 + logm 2
= 1.139 = 2logm 2 ..................................(2)
Substituting equation (2) into (1) gives:
logm 4/m = 2logm 2 - logm
m = 2logm (2/m) ..................................................(3)
Using the property of logarithm once again, we know that:
loga b = logc b / logc a ............................................(4)
Substituting equation (4) into equation (3), we have:
logm 4/m = 2 logm 2 - logm
m= logm [(2/m)² / m] .............................................(5)
Now, we are to find logm 4/m by substituting the given values.
Using equation (2), we have:
logm 2 = (1.139)/2
= 0.5695
Using equation (5), we get:
logm 4/m = logm [(2/m)² / m]
logm 4/m = logm [4/m²m]
logm 4/m = logm 4 - logm
logm 4/m = 1.139 - 2 logm m
Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.
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Help!!!please!!!!!!!
Answers
Answer:
height of the cuboid=480/(12×8)
=480/96
=5 cm
A truck is traveling at a constant speed. The diagram represents the truck's distance and time. What is the speed of the truck?
Answers
Answer:
distance divided by time
Step-by-step explanation:
distance is the speed of the moving object multiplied by the time taken to complete a certain distance therefore the speed is the distance covered divided by the time taken.