Use the diagram as a reference to answer the question below.
If arctan 3/3 = B find the measures of angles a and b and side lengths h, k, and r.
Answers
The trigonometric ratios for sine and tangent, where arctan(√3/3) is β, indicates that we get;
α = 60°, β = 30°, h = √3, k = 3, and r = 2·√3
What are trigonometric ratios?Trigonometric ratios expresses the relationship between an interior angle and two of the sides of a right triangle.
The details of the question are;
arctan(√3/3) = Angle β
The trigonometric ratio for tangent indicates that we get;
tan(β) = h/k
Therefore, arctan(h/k) = β
However, arctan(√3/3) = β
The comparison of the above two equations indicates that we get;
h/k = √3/3
Therefore, if h = √3, k = 3
tan(α) = k/h
Therefore, tan(α) = 3/√3 = √3
r = √(h² + k²)
r = √(3 + 9) = √(12) = 2·√3
sin(β) = h/r
Therefore, sin(β) = √3/(2·√3) = 1/2
β = arcsin(1/2) = 30°
The specified triangle is a right triangle, therefore;
α + β = 90°
α = 90° - β
α = 90° - 30° = 60°
α = 60°
Therefore, α = 60°, β = 30°, h = √3, k = 3, r = 2·√3
Learn more on trigonometric ratios here: https://brainly.com/question/25663658
#SPJ1
Related Questions
a paper company needs to ship paper to a late printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 8 cubic feet and the volume of each large box is 21 cubic feet. a total of 20 boxes of paper were shipped with a combined volume of 264 cubic feet. determine the number of small boxes shipped and the number of large boxes shipped.
Answers
If a paper company needs to ship paper to a late printing business. 12 small boxes were shipped and 8 large boxes were shipped.
How to find the number of boxes shipped?Using a system of equations to represent the problem.
Let x represent the number of small boxes shipped
Let y represent the number of large boxes shipped.
We know that:
x + y = 20 (the total number of boxes shipped)
8x + 21y = 264 (the combined volume of all boxes )
Solving the first equation for y: y = 20 - x
Substituting this expression for y into the second equation:
8x + 21(20 - x) = 264
8x + 420 - 21x = 264
-13x = -156
x = 12 (small boxes)
So,
y = 20 - x
y = 20 -12
y = 8 (Large boxes)
Therefore 12 small boxes were shipped and 8 large boxes were shipped.
Learn more about number of boxes shipped here:https://brainly.com/question/15228600
#SPJ1
The domain of y = sin x is the set of _______. all real numbers > 0 real numbers all real numbers < 0 all real numbers > x
Answers
The domain of y = sin x is the set of all real numbers.
The sine function, represented by y = sin x, is defined for all real numbers, meaning that any real number can be plugged into the function as the input (x) and will produce a valid output (y). Therefore, the domain of y = sin x is the set of all real numbers.
solve please (image attached)
Answers
Answer:
x = 1/a
Step-by-step explanation:
To solve 7ax + 8ax = 9ax + 6 for x, we can start by combining like terms on both sides of the equation:
7ax + 8ax = 9ax + 6
becomes
15ax = 9ax + 6
Next, we can subtract 9ax from both sides of the equation:
15ax - 9ax = 9ax + 6 - 9ax
becomes
6ax = 6
Finally, we can divide both sides of the equation by 6a to find the value of x:
6ax / 6a = 6 / 6a
becomes
x = 1/a
So, the solution for x is x = 1/a.
A line pae through the point (-2,-3) and (1,-9). Write it equation in lope intercept from
Answers
A line pae through the point (-2, -3) and (1, -9). Then the equation of the line is 2x + y + 7 = 0.
Determine the equation of the lineThese are the specified parameters:
Passes through the points (-2, -3) and (1, -9).
With, x₁ = -2 and y₁ = -3
x₂ = 1 and y₂ = -9
The equation of the line
[tex]\begin{aligned} \frac{y-y_1}{y_2-y_1} & = \frac{x-x_1}{x_2-x_1} \\ \frac{y-(-3)}{-9-(-3)} & = \frac{x-(-2)}{1-(-2)} \\ \frac{y+3}{-6} & = \frac{x+2}{3} \\ 3(y+3) & = -6(x+2)\\ 3y + 9 & = -6x - 12\\ 6x + 3y + 9 + 12 & = 0\\ 6x + 3y + 21& = 0\\ 2x + y + 7 & = 0\end{aligned}[/tex]
Learn more about the equation of the line here:
brainly.com/question/13763238
#SPJ4
find the domain of each function. (enter your answers in interval notation.) (a) (b) g(t) = sin(e−t) g(t) = 1 − 6t
Answers
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the given function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
learn more about Domain
https://brainly.com/question/28135761
#SPJ4
what is the measurement of Arc FQ?
Answers
The measure of arc FQ is given as follows:
155º.
How to obtain the measure of arc FQ?The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.
From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.
Applying the two secant theorem, the angle measure of arc FQ is given as follows:
(FQ - 75)/2 = 40
FQ - 75 = 80
FQ = 75 + 80
FQ = 155º.
Meaning that the last option represents the correct option in the context of this problem.
More can be learned about the two secant theorem at https://brainly.com/question/26340897
#SPJ1
consider the vectors a = (−1, −2, 3), b = (3, 0, −2), v = (2, −5, −4) and the plane p given by 2x y = z 13. 1. what should the real number y be, so that (1, y, −9) is perpendicular to v?
Answers
The value of y if (1, y, −9) is perpendicular to vector v is 38/5.
Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k
In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero
So, vector v.vector c = 0
(2i - 5j - 4k ).(i + yj - 9k) = 0
2(1) - 5(y) - 4(-9) = 0
2 - 5y + 36 = 0
5y = 38
y = 38/5
Hence, the value of y is 38/5.
To learn more about Perpendicular vectors here:
brainly.com/question/30367796
#SPJ4
If tan (theta) = 24/10, 0 < (theta) < pi/2 then
sin(theta) equals
cos(theta) equals
sec(theta) equals
Answers
To determine the cosine of an angle, use the Cos Theta Formula in mathematics.The Answer is 3.
Find the solution ?If arctan(2)=, then let the angle be.In this case, tan = 2.
We get =63.43 when we plug the value into the arctan(x) graph.
We do this by using the x=2 line and examining where it crosses the arctan graph (x).
To determine the cosine of an angle, use the Cos Theta Formula in mathematics.
The symbol for it is Cos(), and it has the following form:
adjacent/hypotenuse = cos().
f(θ) = tan(θ) = 3
Note that
tan (x+y ) = tan x +tan y/1-tan x tan y
Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
= (tanθ + tan π)/(1 -tanθ tan π)
= 3/1 = 3
Answer is 3.
To learn more about Cos Theta refer
https://brainly.com/question/4892204
#SPJ1
ms. avila got blue ribbons to give to participants at the school science fair. she ordered 120 blue ribbons from the smart start school supplier. since this was a bulk order, smart start reduced the price of each blue ribbon by $0.75. the total came to $60. which equation can you use to find the amount of money, b, smart start normally charges for a blue ribbon?
Answers
The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon
Ms. Avila ordered 120 blue ribbons from the smart start school supplier.
Smart start reduced the price of each blue ribbon by $0.75.
The total came to $60.
To express the problem in equation we have to read the question carefully and write the equation according to question.
Let the price of 1 blue ribbon = b
If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)
She buy total blue ribbons = 120
So the price of 120 blue ribbons = 120(b - 0.75)
But the total cost is $60.
So the equation is:
120(b - 0.75) = 60
To learn more about forming the equation link is here
brainly.com/question/29441246
#SPJ4
A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red. He draws out a marble at random a) what is the probability that it is either green or a blue marble? b) if the man makes two draws one of after the order from his pocket without replacement, what is the probability that; i) The first draw will be a green and the second draw, a blue marble? ii) neither is a red marble?
Answers
Answer:
Green: 5; White: 2; Blue: 3; Red: 2; Total: 12
A) 8/12
i) 5/12 and 3/11
ii) 10/12
Hope this helps!
Step-by-step explanation:
a) The probability that it is either green or a blue marble is 2/3
b) The probability that first draw will be a green and the second draw, a blue marble is 3/44
c) The probability that neither is a red marble is 15/22
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red
Now , the probability is
a)
The probability that it is either green or a blue marble is P(green or blue) = P(green) + P(blue)
P(green) + P(blue) = 5/12 + 3/12
P(green) + P(blue) = 8/12 = 2/3
Therefore , the probability is 2/3
b)
The probability that first draw will be a green and the second draw, a blue marble is P(green and blue) = P(green) x P(blue | green)
P(green) x P(blue | green) = (5/12) x (3/11)
P(green) x P(blue | green) = 15/132
c)
The probability that neither is a red marble is P(neither draw is red) = P(non-red on first draw) x P(non-red on second draw | non-red on first draw)
P ( neither red ) = ( 5/6 ) ( 9/11 )
P ( neither red ) = 15/22
Hence , the probability is solved
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ2
Help please!!!! Find the greatest common factor (GCF) y^2(2y - 1), 3(2y - 1)
Answers
The greatest common factor of y²(2y - 1) , 3(2y - 1) is 2y.
What is greatest common factor?A set's greatest common factor (GCF) is the largest factor that all of the numbers share. The greatest number that can be divided precisely into two or more numbers.A polynomial has a common factor when the same quantity, whether a number or a letter, appears in all of its terms.The terms can be expressed as follows, and their common factor can be found.Given expressions,
y²(2y - 1) , 3(2y - 1)
y²(2y - 1) = 2y³ - y
= 2 x y x y x y - y
3(2y - 1)
= 6y - 1
= 2 x 3 x y - 1
This way, you can find the elements that are shared by both terms.
2y(2y)(-y)(-3).
To learn more about greatest common factor refer to :
https://brainly.com/question/219464
#SPJ1
Can somebody translate:
2 more than the quotient of a number and 4 is equal to 5
Answers
Answer: x/4+2=5
Step-by-step explanation:
the volume of a hyper-ball is given by v equals begin display style 1 over 6 end style pi cubed r to the power of 6, where r is the radius. if the rate of change of the volume is 4 per second, find the rate of change of the radius when the radius is 2.
Answers
The rate of change of the radius when the radius is 2 is approximately 4 / (π³ * 2⁵).
Rate of Change of RadiusThe volume of a hyper-ball is given by:V = (1/6) * π³ * r⁶
Taking the derivative with respect to time, we get:dV/dt = (1/6) * π³ * 6 * r⁵ * dr/dt
We are given that the rate of change of the volume is 4 per second, so we can write:dV/dt = 4
Substituting the given value of r = 2:4 = (1/6) * π³ * 6 * 2⁵ * dr/dt
Solving for dr/dt:dr/dt = 4 / ((1/6) * π³ * 6 * 2⁵) = 4 / (π³ * 2⁵)
So the rate of change of the radius when the radius is 2 is approximately with this one: dr/dt = 4 / (π³ * 2⁵).
Learn more about Rate of Change of Radius here:
https://brainly.com/question/28891125
#SPJ4
help :')
[tex]help[/tex]
Answers
Step-by-step explanation:
What we have is...
[tex]4(-4.6+w) = 22.24[/tex]
What we'll first do is distribute the 4 into the -4.6 and w
-18.4+4w = 22.24
Next we add 18.4 to both sides to get rid of it on the right side
4W = 22.24+ 18.4
4W = 40.64
Last thing to get W alone, we will divide both sides by 4
W = 10.16
find f if f'(x) = 1/x^2
Answers
The function f(x) is 3/x³ if f'(x) is 1/x²
Given that,
f'(x) is 1/x²
To find : f(x)
Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the x.
f(x) ---> differentiation ------> f'(x)
f'(x)---> integration ------> f(x)
f(x) = ∫ f'(x)
f(x) = ∫ 1/x²
f(x) = 3/x³
Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .
To know more about integration click here:
brainly.com/question/18125359
#SPJ4
Compute (50 + 72i)^2 - (50 - 72i)^2
Answers
Answer:
[tex]14400i[/tex]
Step-by-step explanation:
(50 + 72i)^2 = 7200i - 2684
(50 - 72i)^2 = -7200i - 2684
= 7200i - 2684 - -7200i - 2684
= 7200i - 2684 + 7200i + 2684
= 14400i - 2684 + 2684
= [tex]14400i[/tex]
machine builds 300 bobble-head toys in 5 hours. The machine builds the same number of bobble-head toys each hour. Which table shows the relationship between the amount of time the machine runs and the number of bobble-head toys built?
Answers
Answer: Graph A is your answer
Step-by-step explanation:
Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.
Abigail's chemistry textbook weighs 1/2 of a pound and her geometry textbook weighs 1/4 of a pound. How much more does the chemistry textbook weigh than the geometry textbook?
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2 }[/tex] - [tex]\frac{1}{4}[/tex]
[tex]\frac{2}{4}[/tex] - [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{2}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{4}[/tex]
3. The Erie Canal runs 584 kilometers from Albany to Buffalo. Salvador travels on the canal from Albany. He
must travel 396 kilometers more before he reaches Buffalo. How many kilometers has he traveled so far?
Answers
Answer:
Salvador has traveled 584 - 396 = 188 kilometers so far.
Find the percentage error in x when it is estimated to be y and y>x
Answers
Answer:
The percentage error in x can be calculated as follows:
Percentage error = (Estimated value - Actual value) / Actual value * 100
Let x be the actual value and y be the estimated value such that y > x.
Percentage error = (y - x) / x * 100
This formula calculates the absolute error in terms of a percentage of the actual value.
four packages are delivered to four houses, one to each house. if these packages are randomly delivered, what is the probability that exactly two of them are delivered to the correct houses? express your answer as a common fraction.
Answers
The probability of exactly 2 packages being delivered to the correct houses is, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.
The total number of ways to deliver the packages to the 4 houses is 4! = 24.
To find the number of ways that exactly 2 packages are delivered to the correct houses, we first choose which 2 houses will receive the correct packages, which can be done in 4 choose 2 = 6 ways.
Then, for each of the two remaining houses, we can choose which of the two remaining packages to deliver to that house in 2 ways. So, the total number of ways to deliver exactly 2 packages to the correct houses is 6×2×2 = 24.
the probability of exactly 2 packages being delivered to the correct
houses are, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%
Therefore, the probability of exactly 2 packages being delivered to the correct houses is, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.
For more such questions on probability
https://brainly.com/question/29332657
#SPJ4
Factoring out 3x^2+2x-21=0
Answers
The factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.
How to solve quadratic equations?All related terms should be combined and moved to one side of the equation. Moving all of the components to one side of an equation while maintaining the x2 term positive is the first step in factoring an equation. The x2 terms, x terms, and constants (integer terms) must all be added to or subtracted from one another, and they must all be moved to one side of the equation so that nothing is left on the other. You may just write "0" on the other side of the equal sign if that side has no more words.
Given that the equation is 3x^2 + 2x -21 = 0
Using the method of expansion to solve the quadratic equation we have:
3x^2 + 2x -21 = 0
Multiply (a)(c) and find its prime factors:
(3)(21) = 63
Prime factors: 7, 9
Using the factors deduce the middle term:
3x^2 + 9x - 7x -21 = 0
Take the common in the first two and the last two terms:
3x(x + 3) -7(x+3) = 0
(3x - 7) (x + 3) = 0
Equate to 0:
(x + 3) = 0
x = -3
(3x - 7) = 0
x= 7/3
Hence, the factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.
Learn more about quadratic equations here:
https://brainly.com/question/30098550
#SPJ1
what would be the answer to 23 x 10^5
Answers
Answer:
2300000
Step-by-step explanation:
Please answer the question in the picture! ( the cylinder one)
Answers
The volume of the cylinder is 1413 cubic cm. Then the mass of the carbon will be 2741.22 grams.
What is density?The density is the ratio of mass to volume of any substance. Let m be the mass of the object and v be the volume of the object.
Then the density D will be
D = m / v g/cm³
The volume of the cylinder is given as,
V = (π/4) d²h
V = (π/4) x 10² x 18
V = 1413 cm³
Then the mass of the carbon is given as,
1.94 = m / 1413
m = 2741.22 grams
The mass of the carbon will be 2741.22 grams.
More about the density link is given below.
https://brainly.com/question/15164682
#SPJ1
Points K and M are points of tangency. Find the value of x.
Answers
Applying the two-tangents theorem, the value of x is: 5.
What is the Two-tangents Theorem?The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.
Since point J is formed by the two tangents, KJ and MJ, therefore:
KJ = MJ
Substitute:
4x + 7 = 7x - 8, find x
Combine like terms:
4x - 7x = -7 - 8
-3x = -15
-3x/-3 = -15/-3
x = 5
Learn more about the two-tangents theorem on:
https://brainly.com/question/9143293
#SPJ1
into which quadrant does vector $\vec{a}$ = (ax, ay), with ax = 1.5 cm and ay = –1.0 cm, point?
Answers
The vector vec{a} = (1.5, -1) points into the second quadrant.
To determine this, we look at the signs of the components of the vector. Since the x-component is positive (1.5) and the y-component is negative (-1), the vector is in the quadrant with positive x-values and negative y-values, which is the second quadrant.
The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes. Roman numerals I (where the signs of the (x; y) coordinates are I (+; +), II (-; +), III (-;-), and IV (+;-) are frequently used to identify these.
To learn more about quadrant here:
https://brainly.com/question/29298581
#SPJ4
please help me with this question.
Answers
Answer: The last option.
Step-by-step explanation:
The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;
m∠1 + m∠2 = m∠2 + m∠3
This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.
Two identical rectangular prisms and two identical cubes are joined.
Find the new solid’s surface area.
Answers
The surface area of the whole solid will be 144 square inches.
What is a surface area?The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.
The surface area will be calculated as:-
SA = SA of cuboid + SA of cube
SA = 6 x ( 11 x 2 ) + 6 x 2
SA = 132 + 12
SA = 144 square inches
Therefore, the surface area of the whole solid will be 144 square inches.
To know more about surface area follow
https://brainly.com/question/27813756
#SPJ1
Based on the scatter plot below, which is a better prediction for y when x = 5?
is it one or 6
Answers
According to the scatter plot below, when x = 5, the value of y is 1.
What is scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).
Here,
Based on the scatter plot below, when x=5 then value of y is 1.
To know more about scatter plot,
https://brainly.com/question/29231735
#SPJ1
HELP ASAP HURRY WILL MARK BRAINLIEST ID CORRECT
Answers
Answer:
a
Step-by-step explanation:
Answer:
a. a student who was not absent during unit should score about 98
