Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.
What is a trigonometry?Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).
Here,
Let's first use trigonometric identities to separately simplify each term:
=> cos(x - 90°) equals sin(x)
=> cos(x - 180°) = -cos(x)
=> tan(x) = cos(x) / sin(x)(x)
=> x(cos(-)) = x(x)
=> (180° + x) sin = -sin(x)
When we replace the equation with these simplifications, we get:
=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))
=> sin(180° plus x) * sin(-cos2(x))
=> -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))
Using the identity sin2(x) +cos2(x) = 1, we get = -1.
Consequently, -1 is the simplified formula.
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How many face edges and verties in cube
Using the order of operations, which operation should you perform last to evaluate this expression? 8 + {[( 14 divided by 2 x ( 3 - 1)} - 1} * 1 point A. Addition B. Division C. Multiplication D. Subtraction
Answer:
A addition
Step-by-step explanation:
You would simply everything in the parentheses first and then multiply that by 1. Lastly, you would add 8.
Helping in the name of Jesus.
What is the value of x? Enter your answer in the box.
Answer: 54°
Step-by-step explanation: As the sum of all angles in a Pentagon is 540°
so value of X is 540° - 456 = 54°
A soccer player is going to kick a soccer ball from one corner of a field to the opposite corner. If the field is 80 yards long and 60 yards wide, how far will the soccer player have to kick the ball?
Answer: Assuming the field is rectangular, the distance between the two corners diagonally can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the length and width of the field form the two sides of the right triangle, and the diagonal is the hypotenuse.
So, using the Pythagorean theorem:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 80^2 + 60^2
Diagonal^2 = 6400 + 3600
Diagonal^2 = 10000
Diagonal = √10000
Diagonal = 100 yards
Therefore, the soccer player will have to kick the ball 100 yards to reach the opposite corner of the field.
Step-by-step explanation:
5p+10q = 10; 2p-q= 1
Answer:
Step-by-step explanation:
5p+10 equals big 5
Answer:
p = 0.8; q = 0,6
Step-by-step explanation:
5p + 10q = 10
2p - q = 1
5p + 10q = 10
q = 2p - 1
5p + 10 ( 2p - 1 ) = 10
5p + 20p - 10 = 10
25p = 20
p = 0,8
q = 2 x 0,8 - 1
q = 0,6
A triangle has side lengths 1 units, 1 units, and x units. Determine the range in which x must lie in order for a triangle to exist.
Responses
A -1 < x < 2-1 < x < 2
B 1 < x < 21 < x < 2
C 0 < x < 20 < x < 2
D 0 < x < 1
The range in which x must lie in order for a triangle to exist is: 0 < x < 2.
The correct option is (D). 0 < x < 1.
A triangle has side lengths of 1 units, 1 units, and x units.
Determine the range in which x must lie in order for a triangle to exist.
Triangle is the type of polygon that is formed when three line segments join.
A triangle can be formed when and only when the sum of any two sides is greater than the third side.
Using the triangle inequality theorem we know that,1 + 1 > x1 + x > 11 + x > 1x > 0
Now combining both results:
x > 0
Therefore, the range in which x must lie in order for a triangle to exist is: 0 < x < 2.The correct option is (D). 0 < x < 1.
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prove that
cos x =
√csc²x-1
---------------------------
csc²x
By answering the presented question, we may conclude that Therefore, trigonometry the given identity is true.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
= 1/sin x
= √(1/sin²x - 1) / (1/sin²x)
= √(1 - sin²x) / sin x
= √(cos²x) / sin x
= √(1 - sin²x) / cos x
= √(csc²x - 1) / cos x
cos x = √(csc²x - 1) / cos x
cos²x = csc²x - 1
cos²x + sin²x = csc²x
1 = csc²x
Therefore, the given identity is true.
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The frequency of grades earned on a Spanish test are displayed in the histogram.
Which of the following best describes the shape of the data, and why?
The data is symmetric because the average test grade falls in the middle of the data.
The data is not symmetric because the grades are spread out in each of the intervals.
The data is skewed because there is a large amount of data, showing the average grade in the middle.
The data is bimodal because there is a low amount of data in the first and last intervals, showing that many students had low grades.
The histogram provided displays the frequency of grades earned on a Spanish test.
Which of the below best illustrates the data's shape and why?
Based on the given information, the shape of the data is not symmetric because the grades are not evenly distributed in each of the intervals.
The data appears to be skewed to the left because there are fewer students who received higher grades than those who received lower grades. Additionally, the mode of the data is in the 71-80 interval, which is the highest point in the histogram.
Therefore, the correct answer is:
"Because there is a large amount of data, the data is skewed, with the average grade being in the middle i.e, option c"
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Angle b has a measure between 0° and 360° and is coterminal with a â€""865° angle. what is the measure of angle b? 110° 115° 210° 215°
An angle that is coterminal with -865° and has a measure between 0° and 360° is 75°. Since Angle b is coterminal with this angle, we can conclude that the measure of Angle b is 75°.
We must locate an angle that is coterminal with the -865° angle and has a measure between 0° and 360° in order to determine the size of angle b.
To do this, we can add or remove 360-degree multiples until we have an angle that is coterminal with -865° and is between 0° and 360°.
-865° + 360° = -505° (not between 0° and 360°)
-865° + 2(360°) = -145° (not between 0° and 360°)
-865° + 3(360°) = 75° (between 0° and 360°)
As a result, an angle with a measure between 0° and 360° that is coterminal with -865° is 75°. We can infer that Angle b's measure is 75° because it contaminates with this angle.
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A table of values is shown.
X
0
1
2
3
4
Y
y =
-2
-10
-50
- 250
- 1250
Write the equation for the function shown in the table
by typing values in the blank spaces.
)x
The function is an exponential function of the form y = a * b^x, where "a" is the initial value and "b" is the common ratio.
Using the given table, we can see that:
- The initial value is y(0) = -2, so a = -2.
- To find the common ratio, we can divide any term by the previous term. For example:
- b = y(1)/y(0) = (-10)/(-2) = 5
- b = y(2)/y(1) = (-50)/(-10) = 5
- and so on.
Since we get the same value of b for all the ratios, we can conclude that the common ratio is b = 5.
Therefore, the equation for the function shown in the table is: y = -2 * 5^x.
Elephants are born with tusks and their tusks grow 4 inches a year. A 1 year old elephants tusk measured 5 inches. Write a linear equation that represents the situation how long will the elephants tusk be at 6 years old
Answer: y = 4x + 1, 25 inches at 6 years old
Step-by-step explanation:
Our y-intercept will be 1 (5 inches at a year old - 4 inches per year = 1) with a slope of 4 (4 inches a year). Our equation will look like this:
y = 4x + 1
Next, to solve for the length of the tusk at 6 years old, we will input this value of 6 and solve.
y = 4x + 1 = 4(6) + 1 = 25 inches
See attached for a graph.
We can also check our work using a different method.
6 years - 1 year = 5 years
5 years * 4 inches a year = 20 inches
20 inches + current 5 inches = 25 inches at 6 years
When hungry, two puppies can eat a bowl of kibble in 9 seconds. How long do they take individually to eat the same bowl of kibble if one puppy takes 24 seconds longer than the other?
the height of a golf ball after it is hit can be modeled by the equation where represents the number of seconds after the ball is hit, and represents the golf ball height, in feet. a) what is the height of the golf ball at the instant it is hit? feet b) what is the height of the golf ball 2.8 seconds after it is hit? feet c) how long does it take the ball to hit the ground after it is hit? (round answer to three decimal places.) seconds submit question question 3
a. The height of the golf ball at the instant it is hit is 0 feet.
b. The height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.
c. It takes 4 seconds for the golf ball to hit the ground after it is hit.
a) To find the height of the golf ball at the instant it is hit, we need to evaluate the function h when t = 0.
Substituting t = 0 into the given equation, we get:
h = -16(0)² + 64(0) = 0
Therefore, the height of the golf ball at the instant it is hit is 0 feet.
b) To find the height of the golf ball 2.8 seconds after it is hit, we need to evaluate the function h when t = 2.8.
Substituting t = 2.8 into the given equation, we get:
h = -16(2.8)² + 64(2.8) ≈ 62.72
Therefore, the height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.
c) To find how long it takes the ball to hit the ground after it is hit, we need to find the value of t when the height is 0.
Setting h = 0 in the given equation, we get:
0 = -16t² + 64t
0 = t(-16t + 64)
t = 0 or t = 4
Since the golf ball was hit upwards, we are only interested in the positive value of t, which is t = 4.
Therefore, it takes 4 seconds for the golf ball to hit the ground after it is hit.
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The question is -
The height in feet of a golf ball hit into the air is given by h = − 16t² + 64t, where t is the number of seconds elapsed since the ball was hit, and represents the golf ball height, in feet.
a) what is the height of the golf ball at the instant it is hit?
b) what is the height of the golf ball 2.8 seconds after it is hit?
c) how long does it take the ball to hit the ground after it is hit?
what value of x would prove these lines parallel
4. For the function f(x) = -3x + 64,
find x if f(x) = 34.
Step-by-step explanation:
F(x) = 34 so 34 = -3x + 64
- 30 = -3x
x = 10
the time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes. the probability is 90% that it will take at least how long to assemble a component?
For the probability of 90% that it will take at least 68.195 minutes long to assemble an electronic component.
As we have the time it takes to assemble an electronic component is normally distributed.
Mean time, [tex] \mu[/tex] = 17.2 minutes
Standard deviations, [tex] \sigma[/tex]
= 3.1 minutes
We have to determine probability is 90% that it will take at least how long to assemble a component. Now, from the standard normal distribution table value of Z - score for 90% is equals to the 1.645.
Using the Z- score formula in normal distribution, [tex]Z = \frac{ X - \mu}{\sigma }[/tex]
=> 1.645 = ( X - 17.2 )/3.1
=> X - 17.2 = 31 × 1.645
=> X = 17.2 + 50.995
=> X = 68.195
Hence, the required at least the long to assemble a component is equals to the 68.195.
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simplify: [2]
(−3d'2e'4)'3
_________
9d'2e'5
" ' " is used for square..
Answer:
[tex]81 {d}^{4} {e}^{7} [/tex]
Step-by-step explanation:
Use properties of degrees:
1. When multiplying different degrees on one term, the degree indicators must be multiplied, for example:
[tex]( { {x}^{2}) }^{3} = {x}^{2 \times 3} = {x}^{6} [/tex]
2. When dividing like terms (with the same base) with different degrees, the degree indicators must be subtracted, for example:
[tex] \frac{ {x}^{5} }{ {x}^{2} } = {x}^{5 - 2} = {x}^{3} [/tex]
3. When squaring a negative term in parentheses, the minus is eliminated, for example:
[tex]( { - 3x})^{2} = 9 {x}^{2} [/tex]
.
[tex] \frac{ {(( { - 3d})^{2} \times {e}^{4} )}^{3} }{ {9d}^{2} \times {e}^{5} } = \frac{729 {d}^{6} \times {e}^{12} }{9 {d}^{2} \times {e}^{5} } = 81 {d}^{4} \times {e}^{7} [/tex]
Select the correct answer.
This table represents value of a cubic polynomial function.
Based on the information in the table, which sentence best describes the interval [-2, 1]?
A. The function is increasing on the interval [-2, 1].
B. The function is both increasing and decreasing on the interval [-2, 1].
C. The function is decreasing on the interval [-2, 1].
D. The function is constant on the interval [-2, 1].
an automotive manufacturer removes the friction linings from the clutch plates of drag race cars following test runs. a sampling of 10 linings for wear show the following values (in mm): 204.5, 231.1, 157.5, 190.5, 261.6, 127.0, 216.6, 172.7, 243.8, and 291.0. estimate the average wear and its variance. based on this sample, how many clutch plates out of a large set will be expected to show wear of more than 203 mm?
We can estimate the expected number of clutch plates with
wear of more than 203 mm as:
[tex]0.7 \times \text{total number of clutch plates}[/tex]
To estimate the average wear and variance, we first calculate the sample
mean and sample variance:
Sample mean:
[tex]\bar{x} = \frac{1}{n}\sum_{i=1}^{n}[/tex]
[tex]x_i = \frac{204.5 + 231.1 + 157.5 + 190.5 + 261.6 + 127.0 + 216.6 + 172.7 + 243.8 + 291.0}{10} = 213.3[/tex]
Sample variance:
[tex]s^2 = \frac{1}{n-1}\sum_{i=1}^{n}[/tex]
[tex](x_i - \bar{x})^2 = \frac{(204.5 - 213.3)^2 + (231.1 - 213.3)^2 + ... + (291.0 - 213.3)^2}{9} = 3415.5[/tex]
To estimate the proportion of clutch plates with wear of more than 203
mm, we first need to calculate the sample proportion:
[tex]{number of linings with wear more than 203 mm}{\text{total number of linings}} = \frac{7}{10} = 0.7[/tex]
To estimate the proportion for a large set of clutch plates, we assume
that the sample proportion is equal to the population proportion.
Therefore, we can estimate the expected number of clutch plates with
wear of more than 203 mm as:
[tex]0.7 \times \text{total number of clutch plates}[/tex]
However, we don't know the total number of clutch plates in the
population, so we cannot provide a specific estimate.
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Hey- can someone help me with theese 2 questions- i did them yestr and it said that they were wrong?
Answer: 1) C. 1.75
2) C. 5.25
Step-by-step explanation:
For this first question, the answer is C. 1 3/4
First, you will need to calculate how many hours the 3/4-hour students studied versus the 1/4-hour students.
3/4 students: 3/4 · 3 = 9/4
1/4 students: 1/4 · 2 = 2/4
9/4 - 2/4 = 7/4 = 1 3/4
Therefore, your answer for the first question is C.
For the second question, the answer is C
We must calculate how many hours each group of students studied, then add them together. You can add or multiply in this situation.
1/4 students: 1/4 · 2 = 2/4 (No need for simplifying until the end.)
1/2 students: 1/2 · 5 = 5/2
3/4 students: 3/4 · 3 = 9/4
Now, let's change the 5/2 so we can add it to the other fractions.
5/2 ·2 = 10/4
Let's add.
2/4 + 10/4 + 9/4 = 21/4
Simplify.
21/4 = 5 1/4.
Therefore, answer choice C is correct.
Hope this helped!
suppose you add 1 identical room to a pair of houses. the two houses are identical except for square footage. how much does lprice increase for a house with 4000 sqft compared to a house with 1000 sqft?
When adding one identical room to a pair of houses, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.
What is the basis of this problem?
We have two houses, one with a 4000 square foot floor plan and another with a 1000 square foot floor plan. Both of them are identical, and each of them is expected to receive an additional identical room. We must determine how much the price of the house with the 4000 square foot floor plan will increase compared to the house with the 1000 square foot floor plan when both of these are completed.
Let's start by identifying the amount of money needed to construct each house. The amount of money needed to construct the house with the 4000 square foot floor plan is $300,000, and the amount of money required to build the house with the 1000 square foot floor plan is $150,000.The cost of building per square foot in this case is therefore $75/sqft.
As a result, the price for a 4000 sqft house is: $75/sqft × 4000 sqft = $300,000On the other hand, the cost of constructing a 1000 sqft house is:$75/sqft × 1000 sqft = $75,000When each house gets an additional identical room, the increase in the cost of the room is $50,000. As a result, the price of the house with the 4000 square foot floor plan will increase by 4 times, or $200,000, whereas the price of the house with the 1000 square foot floor plan will increase by one, or $50,000. As a result, the price of a 4000 sqft house will be $300,000 + $200,000 = $500,000, whereas the price of a 1000 sqft house will be $150,000 + $50,000 = $200,000.
When we compare these two values, we obtain the following outcome: Suppose you add 1 identical room to a pair of houses. The two houses are identical except for square footage.
When we compare the two values, we get the following result: $500,000 - $200,000 = $300,000
Therefore, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.
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help asap asignment closes soon!!!
Answer:40
Step-by-step explanation:
90= 2x-10
Answer:
40°
Step-by-step explanation:
Measure of angle LOM(aka x) is equal to:
x+x+10 = 90
2x = 80
x = 40°
O 22
O 16
O -0.5
O 40
16. (03.02 MC)
If f(x) = 2x² + 4, find f(3). (1 point)
Answer:
22
Step-by-step explanation:
f(x) = 2x² + 4 f(3)
f(3) = 2(3)² + 4
f(3) = 2(9) + 4
f(3) = 18 + 4
f(3) = 22
Sin(cos^-1[x+1])
Help out solve this math problem
Answer:
sin(cos⁻¹(x+1)) = √(1 - (x+1)²)
Step-by-step explanation:
3
Ten children played arcade games. The table shows the amount of time each child played and the number of tokens each child used in that time.
Child Child Child Child Child Child Child Child Child Child
1
2
3
4
5
6
7
8
9
10
Time
Played
(minutes)
Tokens
Used
1
5
3
5
S 15
12 1 24
S
18
එය
20
1
30
15
35
39
35 S
The correlation coefficient is 0.363 for these data.
Which statement is the best interpretation of the correlation coefficient?
There is a strong negative association between the number of minutes played and the number of tokens used.
There is a weak negative association between the number of minutes played and the number of tokens used.
There is a strong positive association between the number of minutes played and the number of tokens used.
There is a weak positive association between the number of minutes played and the number of tokens used.
The best interpretation of the correlation coefficient is:
There is a weak positive association between the number of minutes played and the number of tokens used.
What is the correlation coefficient?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
The correlation coefficient is 0.363 for these data. Since the correlation coefficient is positive,
we know that there is a positive association between the number of minutes played and the number of tokens used.
However, since the correlation coefficient is less than 0.5, we can conclude that the association is weak.
Therefore, the best interpretation of the correlation coefficient is:
There is a weak positive association between the number of minutes played and the number of tokens used.
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HELP PLEASEEEEE!!! BEST ANSWER WILL GET BRAINLIEST
Step-by-step explanation:
There are SIX sides 3 pairs of equivalent sides
2 * ( 1 1/3 x 3 + 3 * 2 2/3 + 2 2/3 * 1 1/3 ) = 31 1/9 square yards
Sally Brown bought a house with a 10% adjustable rate mortgage for 20 years. She was paying $9.66 monthly per thousand on her original loan. At the end of 4 years she owes the bank $55,000.00. Interest has now gone up to 12%, the bank can renew the mortgage at this rate or Sally can pay the full $55,000.00. Sally renews the mortgage and will pay $11.02 monthly per thousand on this loan.
What is the amount of the old and new monthly payment? What is the percent of increase in her new monthly payment (to the nearest tenth)?
old payment = $
new payment = $
% increase
The old payment is $96.60, and the new payment is $110.20. The percent increase in her new monthly payment is 14.1%.
To calculate the old payment, we multiply the original loan amount by the monthly payment per thousand, which gives us $9.66 x 55 = $531.30.
To calculate the new payment, we divide the renewed loan amount by 1000 and multiply it by the monthly payment per thousand, which gives us $11.02 x 55 = $606.10.
To calculate the percent increase, we use the formula: ((new payment - old payment) / old payment) x 100. Substituting the values, we get ((606.10 - 531.30) / 531.30) x 100 = 14.1%. Therefore, the percent increase in her new monthly payment is 14.1%.
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Members of a basketball team are painting
a design on the floor of the basketball
court. The special paint they are buying
costs $15.80 a pint. One pint of this paint
covers ten square feet of surface.
Answer:
158
Step-by-step explanation:
You pick a card at random. 4 5 6 7 What is P(not odd)? Write your answer as a percentage.
Answer:
50%
Step-by-step explanation:
There are 4 cards. 4 and 6 are not odd, which is 2 cards.
P(not odd) = number of cards that are not odd/ total number of cards
= 2/4 = 1/2 = .5 = 50%
On January 1, 2015, Jose Company purchased a building for $200,000 and a delivery truck for $20,000. The following expenditures have been incurred during 2017:
The capitalized costs for 2017 is $55,000.
Capitalizing means adding the cost of an asset to its book value or cost basis. Not all costs can be capitalized.
Generally, only costs that increase an asset's useful life or productive capacity should be capitalized.
In this case, the building and truck were purchased in 2015 and have been capitalized.
The following costs incurred in 2017 should be analyzed to determine whether they should be capitalized or expensed:
Painting the building for $5,000 - This cost does not increase the useful life or productive capacity of the building.
It is considered a repair and maintenance expense and should be expensed.
Installing new windows in the building for $10,000 - This cost improves the building's insulation and prevents leaking.
It is considered a capital improvement that extends the useful life of the building. Therefore, it should be capitalized.
Installing a new conveyor system for $40,000 - This cost increases the productive capacity of the company's operations. It is considered a capital expenditure and should be capitalized.
Repainting the delivery truck for $1,000 - This cost does not increase the useful life or productive capacity of the truck. It is considered a repair and maintenance expense and should be expensed.
Installing a hydraulic lift system on the truck for $5,000 - This cost allows better handling of large loads and increases the productive capacity of the truck. It is considered a capital expenditure and should be capitalized.
Overhauling the truck's engine for $4,000 - This cost is a repair and maintenance expense and should be expensed.
Therefore, the capitalized costs for 2017 are
$10,000 (new windows in the building) + $40,000 (new conveyor system) + $5,000 (hydraulic lift system on the truck) = $55,000.
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Question:
On January 1, 2015, Jose Company purchased a building for $200,000 and a delivery truck for $20,000. The following expenditures have been incurred during 2017: • The building was painted at a cost of $5,000. To prevent leaking, new windows were installed in the building at a cost of $10,000. • To improve production, a new conveyor system was installed at a cost of $40,000. • The delivery truck was repainted with a new company logo at a cost of $1,000. • To allow better handling of large loads, a hydraulic lift system was installed on the truck at a cost of $5,000. • The truck's engine was overhauled at a cost of $4,000. Required: 1. Determine which of those costs should be capitalized. Assume that all costs were incurred on January 1, 2017.