Answers
The above prompts are related to the concepts of Degrees, Radians, Sines and Cosines. See the solutions below.
What are the solutions to the above prompts?
1)
(a) Cos 150 degrees
To convert 150 degrees to radians, we multiply by π/180:
150 degrees = (150π/180) radians = (5π/6) radians
We can use the unit circle and reference angle of π/6 to find the cosine of 5π/6:
cos(5π/6) = -cos(π/6) = -(√3/2) = -√3/2
Therefore, cos 150 degrees = -√3/2.
(b) Sin 240 degrees
To convert 240 degrees to radians, we multiply by π/180:
240 degrees = (240π/180) radians = (4π/3) radians
We can use the unit circle and reference angle of π/3 to find the sine of 4π/3:
sin(4π/3) = -sin(π/3) = -(√3/2) = -√3/2
Therefore, sin 240 degrees = -√3/2.
2)
To use the law of cosines, we need either a side and the two angles opposite that side, or two sides and the angle between them. In this case, we have two angles and the side opposite one of them, so we can use the law of sines to find the other side and then use the law of cosines to find the remaining side or angle.
Using the law of sines, we have:
sin A / AB = sin B / AC
where AC is the side opposite angle B. Substituting the given values, we get:
sin 52 / 26.7 = sin 70 / AC
Solving for AC, we get:
AC = sin 70 / sin 52 * 26.7 = 30.4
Now we can use the law of cosines to find the remaining side, x:
x^2 = AB^2 + AC^2 - 2ABACcos A
Substituting the given values, we get:
x^2 = 26.7^2 + 30.4^2 - 226.730.4*cos 52
Solving for x, we get:
x ≈ 22.1
Therefore, the missing side is approximately 22.1.
To find the area of the triangle, we can use the formula:
Area = (1/2) * a * b * sin C
where a and b are the lengths of the two sides, and C is the included angle. Substituting the given values, we get:
Area = (1/2) * 7 * 9 * sin 30
Using the fact that sin 30 = 1/2, we can simplify this to:
Area = (1/2) * 7 * 9 * (1/2) = 15.75
Therefore, the area of the triangle is 15.75 square units.
From the law of sines, we have:
sin A / a = sin B / b
Substituting the given values, we get:
sin 45° / (7√2) = sin B / 7
Solving for sin B, we get:
sin B = (7/7√2) * sin 45° = √2/2
Therefore, B = 45° or 135°. We can use the fact that the angles of a triangle sum to 180° to find C:
C = 180° - A - B = 90° or 0°
If C = 0°, then the triangle is degenerate and the sides a and b lie on top of each other. Therefore, we must have C = 90°.
Now we can use the Pythagorean theorem to find the remaining side:
c^2 = a^2 + b^2 - 2ab*cos C
Substituting the given values, we get:
c^2 = (7√2)^2 + 7^2 - 2(7√2)(7)*cos 90°
Solving for c, we get:
c = √(98 + 49) = √147 = 7√3
Therefore, the sides of the triangle are:
a = 7√2
b = 7
c = 7√3
Using the law of cosines to find x:
In triangle ABC with side lengths AB = 18, AC = 15, and angle A = 108 degrees, we want to find the length of side BC (denoted by x). Using the law of cosines:
x^2 = 18^2 + 15^2 - 2(18)(15)cos(108 degrees)
We can evaluate the cosine of 108 degrees using the identity cos(180 - 108) = -cos(108):
cos(108 degrees) = -cos(180 - 108 degrees) = -cos(72 degrees)
Substituting this into the equation above, we get:
x^2 = 18^2 + 15^2 - 2(18)(15)(-cos(72 degrees))
Simplifying:
x^2 = 729
Taking the square root of both sides:
x = ±27
Since x represents a length, we take the positive root:
x = 27
Therefore, the length of BC is 27 units.
Using the law of cosines to find theta:
In triangle ABC with side lengths AB = 20, BC = 12, and AC = 10, we want to find the measure of angle B (denoted by theta). Using the law of cosines:
cos(B) = (12^2 + 10^2 - 20^2) / (2(12)(10)) = -1/2
Since -1/2 is the cosine of an angle in the second quadrant, we have:
B = 180 degrees - arccos(-1/2)
Using a calculator, we find:
B ≈ 150.5 degrees
Therefore, the measure of angle B is approximately 150.5 degrees (or theta = 150.5 degrees).
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Related Questions
how much is the scale factor if you dilate it until its area is 36?
Answers
Answer:
1/32xp
Step-by-step explanation:
but not sure was there a picture to go with this
The graph shows the number of miles you and a friend run each week while training for a race. Your friend runs______ more miles than you each week.
Answers
Answer:
42
Step-by-step explanation:42
Answer:
4
Step-by-step explanation:
Determine which translations would map Figure
W onto Figure X
Answers
The sequence of steps that translates figure W to figure X are -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.To solve more questions on translations, visit the link-
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change 123/8 to a mixed number
Answers
The normal fraction given which is 123/8 can be written as the mixed number 15 3/8.
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. The whole number part of the result will become the whole number part of the mixed number, and the remainder will become the numerator of the fraction part.
In this case, we have 123/8. To divide 123 by 8, we can use long division method.
So, the whole number part is 15, and the remainder is 3. Therefore, we can write:
123/8 = 15 3/8
This means that 123/8 is equal to 15 and 3/8. The whole number part, 15, represents the number of whole units that can be formed using 8 parts each. The fraction part, 3/8, represents the remaining amount that cannot form a whole unit of 8 parts.
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Use the GCF to factor 12 + 60
Answers
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
12 is the GCF
O
Tom wants to pour 84.99 grams of salt into a container. So far, he has poured. 17.4 grams. How much more salt should Tom pour?
grams
Explanation
Check
X
G
Eple Charter
Answers
The remaining amount of salt that Tom needed to pour was 67.59 grams.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
As per the given,
The total amount that Tom needs to pour = 84.99 grams
Amount poured = 17.4 grams
Remaining = 84.99 grams - 17.4 grams = 7.59 grams
Hence "The remaining amount of salt that Tom needed to pour was 67.59 grams".
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find two vectors each of norm 1 that I perpendicular to vector A={3,2}
Answers
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13) are two vectors of norm 1 that are perpendicular to A = (3 , 2) .
What is perpendicular vectors ?In Cartesian coordinates, the given vector can be represented by the line y = -2x/3. The vector is the line segment that connects (0,0) and (3,-2).y = 3x/2 can be used to represent the normal.
If the vector is represented by a line connecting (0,0) to a point (p,q), then,p2 + q2 = 1 because the normal is one length, and q = 3p/2.
As a result,p² + 9p²/4 = 1, 13p²/4 = 1, p = ±√(4/13) = ±2/√13, q = ±3/√13.
After rationalization, one normal vector is (2√13/13 , 3√13/13) and the other is (-2√13/13 , -3√13/13).The two vectors of norm 1 perpendicular to A = (3 , 2) is :
(2√13/13 , 3√13/13) and (-2√13/13 , -3√13/13).
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I need help with this please I will give brainlist
Answers
Answer:
It should be 49
Step-by-step explanation:
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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Someone help me please!
Answers
Answer:
ACD
Step-by-step explanation:
PLZZ mark brainliest!!
Answer:
D i think i havent done this in a while
Step-by-step explanation:
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages
Answers
Answer:
Brian is 6 years old, John is 9 years old
Step-by-step explanation:
i.
J = 3 + B
J x B = 54
ii.
(3 + B) x B = 54
B² + 3B = 54
iii.
(B + 9)(B - 6) = 0
B = -9 or 6 -- -9 is irrational as one cannot be negative years old
Brian = 6 years old; therefore, John = 9 years old
Plz I need help plz plz plz
Answers
Answer:
we can write
42/7 as 30/7
and
21/5 as 11/5
now
\( \frac{30}{7} \times \frac{11}{5} \\ = \frac{6}{7} \times 11 \\ = \frac{66}{7} \)
we can write 66/7 as 93/7
hence,
option D is correct.
hope this answer helps you dear....take care!
See whether you're understanding the subject and skills.
Answers
If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training
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However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.
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.
Question is in the picture, please explain your answer with steps.
Answers
Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.
How to find the costs?Let's define the variables:
x = cost of the washer.
y = cost of the dryer.
We know that the cost combined is $1000, then:
x + y = 1000
And the washer cost 3 times the cost of the dryer, then we will get:
x = 3y
So we have a system of equations, we can replace the second equation into the first one, so we will get:
3y + y = 1000
4y = 1000
y = 1000/4
y = 250
The cost of the washer is:
x = 3*250 = 750
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I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
An adult ticket to the show costs $2 more than a student ticket. The total cost of 3 student tickets and 2 adult tickets is $39.
How much does an adult ticket cost?
Answers
Answer:
An adults ticket costs $9
Step-by-step explanation:
Kids:
$7
Adults:
$9
So if you add 7+7+7= 21 (kids)
then do 9+9=18(adults)
Then add them together you get 39$
the density of the copper is 9.86g/cm\(x^{3}\)
![the density of the copper is 9.86g/cm[tex]x^{3}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/kBdJoEKedYKgyZmbWgXrufRB5h52H33f.png)
Answers
The mass of the cubic cuboid is 1.479 kilograms.
What is the mass of a copper cuboid?
Dimensionally speaking, density (ρ), in kilograms per cubic meter, is mass (m), in kilograms, per unit volume (V), in cubic meters. By the assumption of uniform density within the copper cuboid, the mass of the solid is equal to:
m = ρ · V
Where V is the volume of cuboid, in cubic meters.
And the volume of cuboid is:
V = w · h · l
Where:
w - Width, in meters. h - Height, in meters.l - Length, in meters.Please notice that a kilogram equals 1000 grams and a meter equals 100 centimeters.
First, calculate the volume of the cuboid:
V = (0.05 m) · (0.03 m) · (0.10 m)
V = 1.5 × 10⁻⁴ m³
Second, determine the mass of the cuboid:
m = (9.86 g / cm³) · (1 kg / 1000 g) · (1000000 cm³ / m³) · (1.5 × 10⁻⁴ m³)
m = 1.479 kg
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What multiples and adds up to -1/2
Answers
1 and -1/2 can be multiplied to get -1/2
2 and -2 can be multiplied to get -4, and then dividing by 8 gives -1/2
-3 and 1 can be multiplied to get -3, and then dividing by 6 gives -1/2
And so on. In general, if you have two numbers x and y, then their product is xy and their sum is x + y. If you want these to equal -1/2, you can solve the equation xy + x + y = -1/2 for one variable in terms of the other, and then substitute that expression into the other equation. This will give you a quadratic equation that you can solve for one of the variables, and then use that value to find the other variable.
S={(3,p),(3,0),(4,q),(1,4)}
Answers
Answer:
S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:
(3,p): The first element is 3 and the second element is p.
(3,0): The first element is 3 and the second element is 0.
(4,q): The first element is 4 and the second element is q.
(1,4): The first element is 1 and the second element is 4.
If you have 54/4 how does it equal 13.5
Answers
54 * 4 = 13.5
Multiply 54 * 4
216 = 13.5
Solving
216 = 13.5
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
Answer:
I don't like mathematics
A bank wants to estimate the difference in the proportion of its "big" customers who have a second account with a different bank and the proportion of its "small" customers who also have an account with another bank. Of the 200 “big” customers who were randomly selected, 160 claimed to also bank with other banks. Of the 300 “small” customers who were randomly selected, 120 claimed to also bank with other banks.
Based on the 99% confidence interval (0.297, 0.503), is there convincing evidence of a difference in the proportion of “big” bank customers who bank with more than one bank as compared with the “small” customers who bank with more than one bank?
Because
contained in the interval, there is
to believe there
a difference in the proportion of “big” bank customers who bank with more than one bank as compared to the “small” customers who bank with more than one bank.
Answers
Yes, based on the 99% confidence interval (0.297, 0.503), there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.
The confidence interval (0.297, 0.503) represents the range of values within which the true difference in proportions between the two customer groups is likely to fall with 99% confidence. Since the interval does not include zero (0), we can conclude that there is a statistically significant difference between the proportions.
To further explain, the confidence interval was constructed using the sample proportions and the standard error. The sample proportion for the "big" customers who bank with other banks is 160/200 = 0.8, and for the "small" customers, it is 120/300 = 0.4. The standard error takes into account the sample sizes and proportions, and it measures the uncertainty in the estimation.
Since the confidence interval does not include zero, it indicates that the true difference in proportions is unlikely to be zero. In other words, there is strong evidence that the proportion of "big" bank customers who bank with more than one bank is higher than the proportion of "small" customers who do the same.
Therefore, based on the provided data and the confidence interval, we can conclude that there is convincing evidence of a difference in the proportion of "big" bank customers who bank with more than one bank compared to the "small" customers who bank with more than one bank.
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A stone is dropped from the upper observation deck of a tower, 950 m above the ground. (Assume g = 9.8 m/s2.)
(a) Find the distance (in meters) of the stone above ground level at time t.
h(t) = 13.92
(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)
s
(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)
m/s
(d) If the stone is thrown downward with a speed of 6 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)
s
Answers
a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.
b) It takes approximately 13.93 seconds for the stone to reach the ground.
c) The stone strikes the ground with a velocity of approximately 136.04 m/s.
d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.
When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.
First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:
h(t) = h0 + vt + 0.5at²
where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.
Using the given values, we can plug in the numbers and simplify:
h(t) = 950 + 0t + 0.5(9.8)t²
h(t) = 950 + 4.9t²
To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:
0 = 950 + 4.9t^2
t^2 = 193.88
t ≈ 13.93 seconds
To find the velocity at which the stone strikes the ground, we can use the formula:
v = v₀ + at
where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:
v = 0 + 9.8(13.93)
v ≈ 136.04 m/s
Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:
h(t) = 950 - 6t + 0.5(9.8)t²
0 = 950 - 6t + 4.9t²
t² - 1.22t - 193.88 = 0
t ≈ 16.75 seconds
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What is the image of (1, -1) after a dilation by a scale factor of 4 centered at the origin?
Answers
Answer:
5, 3
Step-by-step explanation:
1,-1 enlarged by 4
New coordinates = 4 + 1 = 5
-1 + 4 = 3
The required scaled image of (1, -1) after dilation by scale factor 4 is (5,3).
As per the question, determine the image of (1, -1) after dilation by a scale factor of 4 centered at the origin.
What is the scale factor?The scale factor is defined as the ratio of modified change in length to
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
The dilation of the coordinate by a scale factor of 4 can be given as,
x = 1 + 4 = 5
y = -1 + 4 = 3
Thus, the required scaled image of (1, -1) after dilation by scale factor 4 is (5,3).
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in a class of students the following data table summarizes how many students play an instrument or Sports what is probability that a student chosen randomly from the class plays neither a sport Nor an instrument?
Answers
Answer: 3 out of 27 chance
Step-by-step explanation:
14. And 16. Find the value of the trigonometric ratio. And the degree of the angle. Show work!
Answers
14. The value of tan A from the given diagram is 21/20
16. The value of tan X from the given diagram is 3/4
How do i determine tan ratio?Tan ratio is given by the following formula:
Tan θ = Opposite / Adjacent
With the above formula, we can determine tan A and tan X. This is is illustrated below:
14. For tan A:
Opposite = 21Adjacent = 20Tan A =?Tan θ = Opposite / Adjacent
Tan A = 21 / 20
Thus, we can conclude that the value of tan A is 21/20
16. For tan X:
Opposite = 30Adjacent = 40Tan X =?Tan θ = Opposite / Adjacent
Tan X = 30 / 40
Tan X = 3 / 4
Thus, we can conclude that the value of tan X is 3/4
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Help! Quick! Find the area of the composite figure
Answers
Answer:
60m
Step-by-step explanation:
To find the area of the triangle you multiply the base by height and divide by two, but we don’t know the base of the triangle!
Luckily, the bottom of the triangle is a rectangle. Rectangles are symmetrical, and the other side of the rectangle is 8.
So, the base of the triangle is 8.
Now let’s find the area of the triangle:
8 x 5 = 40
40/2 = 20
20 is the area of the triangle
Now, we must find the area of the rectangle!
The formula for rectangle area is just width x length:
8 x 5 = 40
Add them together:
40 + 20 = 60
Therefore, the area is 60m.
A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-
Answers
Answer:c
Step-by-step explanation:
c
Answer:b
Step-by-step explanation:
Write the equation of the line that passes through (6, 2) with a slope of 4.
Answers
Answer:
y=mx-22
Step-by-step explanation:
Take standard line equation y=mx+c and substitute the given values of m=4, x=6, y=2 to find out the value of c
Answer choices please help
240
200
240
280
Answers
Question 14 of 25
Which situation is most likely to have a constant rate of change?
• A. The number of dimes you have with you compared with the day of
the month
• B. The cost for
a group of friends to see a movie compared with the
number of friends
C. The number of downloads of a hit a song compared with the
number of days since its release
D. The temperature of the sand on a beach compared with the time
of day
SUBMIT
l