Answers
The value of variable θ would be,
⇒ θ = 5π/3 and θ = 4π/3
We have to given that;
Expression is,
⇒ - 10sin θ - 8 = 5√3 - 8
Now, We can simplify as;
⇒ - 10sin θ - 8 = 5√3 - 8
⇒ - 10sin θ = 5√3
⇒ sin θ = - 5√3/10
⇒ sin θ = - √3/2
We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).
However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.
Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.
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Related Questions
What is angle CAB
Enter your answer in the box
Answers
The measure of the angle CAB in a right angled triangle ABC using given measurements is equal to 37°.
In the triangle ABC,
From the figure we have,
Measure of angle ABC = 90 degrees
Measure of angle ACB= 53 degrees
Sum of all the interior angles of a triangle is equal to 180 degrees .
⇒Measure of angle ABC + Measure of angle ACB + Measure of angle CAB = 180 degrees
⇒ 90° + 53° + Measure of angle CAB = 180°
⇒143° + Measure of angle CAB = 180°
⇒ Measure of angle CAB = 180° - 143°
⇒ Measure of angle CAB = 37°
Therefore, the measure of the angle CAB is equal to 37°.
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A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made
from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)
Answers
Answer:
499,237 ft²
Step-by-step explanation:
You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.
AreaTo find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:
A = 1/2bh
There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:
4A = 4(1/2bh) = 2bh
Slant heightThe slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)
h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet
Glass arealateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²
The surface area of the glass is about 499237 square feet.
Assignment Active
The Economic Effect of Snowsheds
With so many snowsheds along the line, annual
maintenance soared. By 1910 many of the original
wooden structures needed replacing, and heavy snows in
the winter of 1912-13 crushed others. That year the
railway hired 1,800 workers to make shed improvements
along just 8 miles of track, and the need for additional
sheds was clear....
While making repairs on the Cascade Mountain
snowsheds in 1917, the Great Northern Railway used over
35 million board feet of timber that cost triple what it had
just eight years earlier. By this time, snowsheds and
tunnels covered 6.7 of the 9 track miles between
Wellington and Scenic.
According to this passage, how did snowsheds affect
the railroad in the long term?
O They decreased delays, which lowered the railroad
costs.
They required frequent repairs, which added to the
railroad costs.
They reduced the need for bridges, which lowered
the railroad costs.
O They required many workers to operate them,
which added to the railroad costs.
Answers
In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
Answers
The percentage of pennies in the roll is A = 30 %
Given data ,
Let the percentage of pennies in the roll made before 1985 be A
Now , the total number of pennies be = 50 pennies
And , the number of pennies made before 1985 is = 15 pennies
So , the percentage is A = ( 15 / 50 ) x 100
On simplifying the equation , we get
A = 3/10 x 100
A = 30 %
Hence , the percentage is 30 %
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In a greenhouse, Brazil is grown in planters that have a base of 4 1/5 In by 1 1/3 in. If there is a 3 x 3 array of these planters with no space between them, what is the area covered by the planters
Answers
Answer:
The area of one planter is:
4 1/5 in × 1 1/3 in = (21/5) in × (4/3) in = 28/5 in²
In a 3 x 3 array, there are 3 planters in each row and 3 planters in each column, so there are a total of 9 planters.
The area covered by the planters is:
9 × (28/5) in² = 252/5 in² ≈ 50.4 in²
Therefore, the area covered by the planters is approximately 50.4 square inches.
Step-by-step explanation:
mark brainliest
What is the measure of angle b?
A
90o
B
180o
C
43o
D
47o
Answers
Answer:
b
Step-by-step explanation: makes sense
WHATS THE 2ND TO THE POWER OF THE 4TH
Answers
Answer:
16.
Step-by-step explanation:
Classifying the polynomial
Answers
Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.
The types of polynomials based on degree: zero polynomial, linear, quadratic, and cubic polynomials.
The types of polynomials based on the number of terms: monomials, binomials, trinomials, etc
find the mean of the set of data 3,5,4,4,5,7,7
Answers
Answer:
mean=5
Step-by-step explanation:
To find the mean of a set of data, we add up all the values in the set and then divide by the number of values.
Adding up the values in the set, we get:
3 + 5 + 4 + 4 + 5 + 7 + 7 = 35
There are 7 values in the set, so we divide the sum by 7 to get the mean:
mean = sum of values / number of values
mean = 35 / 7
mean = 5
plot a point to represent the approximation sqrt(20)
Answers
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
|---------------------|---------------------|
0 4.472
We have,
To plot the point representing the approximation of √(20), we need to first find the approximate value of √(20):
√(20) ≈ 4.472
This means that the point we want to plot is located approximately 4.472 units to the right of the origin on the number line.
To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.
The resulting point represents the approximation of √(20).
Thus,
A rough sketch of what the plot could look like:
|---------------------|---------------------|
0 4.472
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What function is represented in the graph?
Select one:
y = 2(.5^x)
y = 2(3^x)
y = 3(.5^x)
y = 3(2^x)
Answers
The exponential function represented by the given graph is:
y = 2(.5^x)
What function is represented by the graph?Here we have an exponential decay, the general form of these functions is:
y = A*(b)^x
Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.
Now let's look at the y-intercept, we can see that it is y = 2, then:
2 = A*(b)^0
2 = A
The function is of the form:
y = 2*(b)^x with 0 < b < 1.
The option that meets these conditions is the first one: y = 2(.5^x)
So that is the correct option.
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3
2
A ABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of
create A A'B'C'.
The center of dilation is the point (5,
(5,
-6).
What are the coordinates of vertex.
B'₂
Enter your answers, as decimals, in the boxes.
9
Answers
The coordinates of vertex B' are (76, -86).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate B, we have;
Coordinate B = (4, -4) → (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))
Coordinate B = (4, -4) → (9(9) - 5, 9(-9) - 5)
Coordinate B = (4, -4) → (81 - 5, -81 - 5)
Coordinate B' = (76, -86).
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Complete Question:
ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).
What are the coordinates of vertex B'?
(CLASSKICK) HELP ASAPPPP!
Answers
The value of the angle 3 as solved is 52 degrees.
What is the sum of the angles on a straight line?
The sum of the angles on a straight line is always 180 degrees, and this property is true for any pair of opposite angles formed by two intersecting lines.
We can see that what we have is the angles that are on a straight line
We have from the question that;
< 1= 90
<2 = 38
Thus;
<6 = 180 - (90 + 38) - Sum of angles on a straight line
<6 = 52°
Now;
<4 = 90 degrees (Vertically opposite angles)
<5 = 38 degrees (Vertically opposite angles)
Then;
<3 = 180 - (90 + 38) - Sum of angles on a straight line
<3 = 52°
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What the answer for radius huryyyyyyyyyy pleaseeee
Answers
Answer: 12.6
Step-by-step explanation:
150/360*2*pi*r=10.
divide to get r alone
El 60% de número de hombres es igual al 40% de mujeres. ¿qué tanto por ciento del total representa las mujeres?
Answers
The percentage of the total that women represent, would be 60% of the total.
How to find the percentage ?Given that 60 % of men is equal to 40 % of women, we have :
0. 6 M = 0. 4 W
Solving for women in terms of Men gives:
W = ( 0.6 x M) / 0.4
= 1.5 x M
We can then find the percentage of women to be:
= (W / Total ) x 100
= ((1.5 x M) / (2.5 x M)) x 100
= (1.5 / 2.5) x 100
= 0.6 x 100
= 60%
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What are the angles of rotation for a regular
pentagon? (Select all that apply)
a) 60
B) 72
c)90
d) 144
e) 180
f)216
g) 360
Answers
Answer:
c,,e,b,f
Step-by-step explanation:
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Answers
From the problem, we know that:
2(x + 1) + x^2 = 13
Simplifying and rearranging:
x^2 + 2x - 11 = 0
Using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(1)(-11))) / (2(1))
x = (-2 ± sqrt(48)) / 2
x = (-2 ± 4sqrt(3)) / 2
x = -1 ± 2sqrt(3)
Since the problem states that the numbers are positive, we can ignore the negative solution. Therefore, the smaller number is:
x = -1 + 2sqrt(3)
And the larger number is:
x + 1 = 2sqrt(3)
So the two numbers are -1 + 2sqrt(3) and 2sqrt(3).
Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his
friends standing? Round to the nearest foot.
Answers
tan(42) = 61 / x
tan(80) = 61 / y
Solving for y, we get:
y = 61 / tan(80)
y ≈ 12.2 feet
Therefore, Shane's friends are standing approximately 12.2 feet away from him.
This is the graph of a function in the form f(x)=a•b^x what’s the function
Answers
Answer:
Step-by-step explanation:
The function f(x) = a * b^x represents exponential growth or decay. The value of a represents the starting value or y-intercept, while the value of b represents the growth or decay factor. If b is greater than 1, the function represents exponential growth, while if b is between 0 and 1, the function represents exponential decay.
To determine the values of a and b from a graph, we need to look for specific features. The y-intercept represents the value of a, so we can read it directly from the graph. The growth or decay factor b can be found by examining the slope of the graph. If the graph is increasing, then b is greater than 1, and if it is decreasing, then b is between 0 and 1.
solve the proportion for x pls help image attached
Answers
[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]
How many permutations do I have it I select 4 things from a total of 9 with replacement? (9P4)
Answers
There are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
It is required to find the number of permutations when 4 things are selected from a total of 9 with replacement.
Use the formula for permutations with replacement, which is:
= [tex]^np_r[/tex]
Here n is the total number of items and r is the number of selections.
As per the question, n = 9 and r = 4.
So, the number of permutations is:
= ⁹p₄
= 9!/5!
= 9 x 8 x 7 x 6
= 3024
Thus, there are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
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what’s the answer? To solve the law of cosine I don’t understand this math I rly need help.
Answers
The length of u to the nearest centimeter is about 30 cm.
We are given that;'
s = 730 cm, t = 270 cm and U=125°.
Now,
The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:
c2=a2+b2−2abcosC
To find c = u. Plugging in the values, we get:
u2=7302+2702−2×730×270×cos125°
Using a calculator, we get:
u2≈912.9
Taking the square root of both sides, we get:
u≈30.21
Rounding to the nearest centimeter, we get:
u≈30cm
Therefore, by the law of cosine the answer will be 30 cm.
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The Winberg apartment complex rents out units at $200x monthly for each of their 9 units. The Hensing apartment complex has 3x more units and rents out each unit for $20 less monthly.
Which of the following equations could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out?
A. y = $(600x^2 - 180)
B. y = $(600x^2)
C. y = $(600x^2 + 1,740x - 180)
D. y = $(600x^2 + 1,860x - 180)
Answers
The equation that could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out is A. y = $(600x^2 - 180).
How to calculate the equationThe Hensing apartment complex rents out each unit for $20 less monthly than the Winberg complex, so the rent for each unit is $200x - $20 = $180x.
The equation that represents this situation is: y = $(600x^2 - 180
So the answer is (A) y = $(600x^2 - 180).
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3
Q
The diagram shows three shapes that are mathematically similar.
The heights of the shapes are in the ratio small: medium: large = 1:5:8.
Find the ratio shaded area : total unshaded area.
Give your answer in its simplest form.
NOT TO
SCALE
Answers
The ratio of the shaded area to the total unshaded area can be found to be 5 : 9.
How to find the ratio ?The three shapes are similar to each other which means that their areas must be similar as well.
The only shape that is shaded is the second largest shape and it has the value of 5 in the ratio. This means that the other two shapes are not shaded and their ratio values are 1 and 8.
This then means that the ratio of shaded area to unshaded area can be written as :
Shaded area : Unshaded area
5 x width : ( 1 x width) + ( 8 x width )
5 : 1 + 8
5 : 9
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What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
Answers
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
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help help help help help
Answers
have a good day
Can someone explain how to get the answer to…if 7p-4=8 what is the value of p?
Answers
The value of p in the equation 7p - 4 = 8 is p = 12/7
Solving for what is the value of p?From the question, we have the following parameters that can be used in our computation:
7p - 4 = 8
Add 4 to both sides
So, we have
7p = 12
Divide both sides by 7
So, we have
p = 12/7
Hence, the solution is p = 12/7
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Kevin wants to save $600 to buy a TV. He saves $17 each week. The amount, A (in dollars), that he still needs after w weeks is given by the following function.
A (w)=600-17w
Answer the following questions.
(a) If Kevin still needs $277, how many weeks has he been saving?
weeks
(b) How much money does Kevin still need after 5 weeks?
$?
Answers
Answer:
A) Kevin has been saving money for 19 weeks.
B) Kevin still needs $515.
Step-by-step explanation:
A) 277=600-17x /-600
-17=-323 /÷(-17)
x=19
B) x=600-17×5
x=600-85
x= 515
Find the area of this semi-circle with diameter, d = 20cm.
Give your answer rounded to 2 DP.
Answers
The area of the semicircle is 157. 00 cm
How to determine the area of the semi-circleTo determine the area of the semi-circle, we need to consider the formua.
the formula for calculating the area of a semi-circle is expressed with the equation;
A = 1/2π²
Such that the parameters of the formula are;
A is the area of the semi-circler is the radius of the semi-circleπ takes the constant value of 3.14It is important to note that
Formula for diameter is expressed as
Diameter = 2radius
Radius = 10cm
Substitute the values
Area = 1/2× 3.14 × 100
Multiply the values
Area = 157 cm²
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Pls help thanks!!!!!!!!!!!
Answers
Answer:
Put your calculator in degree mode.
sin(13°) = 500/x
x sin(13°) = 500
x = 500/sin(13°) = 2,222.7 miles
Using a trigonometric relation we can see that x = 2,222.7 ft
How to find the value of x?We can see a right triangle, there we can see that one of the angles has a measure of 13°.
The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.
Then we can use the relation:
sin(a) = (opp cathetus)/hypotenuse
Replacing what we know, we will get:
sin(13°) = 500/x
Solving that for x:
x = 500/sin(13°) = 2,222.7 ft
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