Answers
Answer:
To prove the trigonometric identity (tan x + cot x)/(csc x * cos x) = sec^2 x, we can simplify the expression step by step:
(tan x + cot x)/(csc x * cos x)
= (sin x / cos x + cos x / sin x) / (1 / sin x * cos x)
= [(sin^2 x + cos^2 x) / (sin x * cos x)] / (1 / sin x * cos x)
= [(sin^2 x + cos^2 x) / (sin x * cos x)] * (sin x * cos x / 1)
= sin^2 x + cos^2 x
= 1
= sec^2 x
Hence, we have shown that the left-hand side (LHS) is equal to the right-hand side (RHS), proving the trigonometric identity.
Related Questions
According to this diagram, what is tan 62°?
Answers
Answer:
12
Step-by-step explanation:
i think that is the answer
Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?
A 200.96 in.2
B 525.76 in.2
C 375.04 in.2
D 576 in.2
Answers
Answer:
A
AAAAAAAAAAAAAAZSAAAAAAA
what greater than 476 and less than 598
Answers
Answer:
Any numbers 477 to 597
I could pick 500 i mean its greater than 476 and less that 598.
Most likely I would pick 597 because its close.
The length of a rectangle is 1 units more than the width. The area of the rectangle is 72 units. What is the length, in units, of the rectangle?
Answers
How do you write 2.8 × 10^5 in standard form?
Answers
Answer:
280,000
Step-by-step explanation:
10^5=100,000
2.8 x 100,000=280,000
The intensity of an earthquake wave passing through the Earth is measured to be 2.8×106 J/m² .s at a distance of 53 km from the source.
(B) At what rate did energy pass through an area of 1.0 m^2 at 2.0 km?
Answers
The rate at which the energy pass through an area of 1.0 m² at 2.0 km is equal to 1.97 × 10⁹ J/s.
How to calculate the intensity of the earthquake from the source?At a constant power, the intensity of a wave is inversely proportional to the distance from the source. Mathematically, the intensity of a wave with respect to the distance from a source can be modeled (represented) by this mathematical expression;
I ∝ 1/r²
Where:
I represents the intensity of a wave.r represents the distance from a source.Next, we would re-write the mathematical expression and then determine the intensity of a wave from source as follows;
I₁/I₂ = r₂²/r₁²
I₁ = I₂(r₂²/r₁²)
Note: We know that its intensity when it passed a point from the source is 2.0 km.
Substituting the given parameters into the formula, we have;
I₁ = 2.8 × 10⁶ × (53²/2²)
I₁ = 1.97 × 10⁹ J/m²s.
Now, we can calculate the rate of the energy by using this formula;
Power = intensity × area
Power = 1.97 × 10⁹ × 1.0
Power = 1.97 × 10⁹ J/s.
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. Higher Order Thinking This Venn diagram
shows the relationship of ratios to rates to unit
rates. Describe a real-world situation involving
a ratio relationship. Then write the ratio as
2 different equivalent rates and as a unit rate.
Answers
The ratio relationship of a car's fuel efficiency can be expressed as equivalent rates of miles per gallon and gallons per mile, or as a unit rate of either 30 miles per gallon or 1/30 gallons per mile.
What is a Real-World Situation that Involves a Ratio Relationship?A real-world situation involving a ratio relationship could be the fuel efficiency of a car. For example, suppose a car travels 60 miles using 2 gallons of gas.
To express this ratio relationship as equivalent rates, we can write:
60 miles ÷ 2 gallons = 30 miles per gallon
2 gallons ÷ 60 miles = 0.0333 gallons per mile
To express the ratio as a unit rate, we can divide the numerator and denominator by the same amount to simplify the fraction. Let's choose to divide by 2 to get:
60 miles ÷ 2 gallons = 30 miles per gallon
2 gallons ÷ 60 miles = 1/30 gallons per mile
In both cases, the ratio represents the same relationship between miles traveled and gallons of gas used, but it is expressed in different units or rates.
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The moon is in an orbit around the earth, and the length of this
orbit is 3.844 × 100,000 kilometers.
1. What is the shortcut for multiplying 3.844 by 100,000?
Answers
The product of given numbers is 384400.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Given that, the moon is in an orbit around the earth, and the length of this
orbit is 3.844×100,000 kilometers.
Here, 3.844 multiplied by 1 we get 3.844
When multiplying decimals by 100000, the digits shift five places to the left.
That is, 384400.0
Therefore, the product of given numbers is 384400.
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tan(x+y)=x. (2 3) , what is dy/dx
Answers
Answer:
0/0
Step-by-step explanation:
Unsure, used a calculator to help
Determine whether 548 is greater than or less than 373. Then write the expression showing this using < or >.
Answers
Answer:
548 > 373
Step-by-step explanation:
548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.
The ">" symbol is used to represent "greater than" in mathematical comparisons.
Hope this helps!
Question
A watermelon is assumed to be spherical in shape while it is growing. Its mass, M kg, and radius, rcm, are related by the formula M = kr³, where k is a constant. It is also assumed that the radius is increasing at a constant rate of 0.1 centimetres per day. On a particular day the radius is 10 cm and
the mass is 3.2 kg. Find the value of k and the rate at which the mass is increasing on this day.
Answers
Thus, the mass is increasing at a rate of 0.15625 kg per hour, and the mass on this day is 4.5 kg.
Let's consider a general formula for finding the rate of increase:Rate of increase = k x original valueHere, k is a constant that represents the rate of increase per unit of time, and the original value is the initial value of the quantity being measured.
For example, if the original value is 3.2 kg and the rate of increase is 0.5 kg per hour, we can use the formula to calculate the mass at any time t as follows: Mass at
time t = 3.2 + (0.5 x t)
where t is the time elapsed in hours.In order to find k, we need to know the rate of increase and the original value.
Once we have these values, we can rearrange the formula to solve for
k:k = rate of increase / original value
For example, if the mass is increasing at a rate of 0.5 kg per hour and the original value is 3.2 kg, we can calculate k as follows:
k = 0.5 / 3.2k = 0.15625
To find the rate of increase on a specific day, we need to know how much time has elapsed since the original value was measured. Once we have this information, we can plug it into the formula we derived earlier:Mass at time t = 3.2 + (k x t)For example, if 8 hours have elapsed since the original value was measured, we can calculate the mass on that day as follows:
Mass at time t = 3.2 + (0.15625 x 8)
Mass at time t = 4.5 kg
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Write an expression to represent the product of 6 and the square of a number plus 15. In your expression what is the value of the coefficient? A. 1 B. 6 C. 15 D. 2
Answers
Answer:
B) 6
Step-by-step explanation:
Let the number be x
Product of 6 and square of number plue 15 : (6x²) + 15
Coefficient of x² = 6
Identify percent of change. 20 is decreased to 6.
Answers
Answer:
70%
Step-by-step explanation:
the formula for percent of change is:
New value - Old value divided by Old value
we can write this algebraically as:
(6-20)/20 which is -14/20
the negative simply implies a 'decrease' from old to new
14/20 equals 70/100 or 70%
Answer:
The answer to your question is 70% decrease
Step-by-step explanation:
I hope this helps and have a wonderful day!
complete the partial two-way frequency table below that shows the extracurricular activities of high school students. Based on the data in the table, how many students do not play an instrument
Answers
According to the information, the missing number from the box is number 40.
How to find the missing number in the box?To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.
According to the above we can infer that the missing number is 40.
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I need help with the both of these please If you help I will mark you brainLIEST
Answers
Answer:
Step-by-step explanation:
Assuming the data distribution is normal with a median lifetime income of $25800 and standard deviation of $14000. Use the chart to find the probability that a person chosen at random has a median lifetime income between 1 to 2 standard deviations below the mean.
Answers
Answer: To find the probability that a person chosen at random has a median lifetime income between 1 to 2 standard deviations below the mean, we need to calculate the area under the normal distribution curve within that range.
First, let's define the variables:
μ = Mean lifetime income = $25800
σ = Standard deviation = $14000
We want to find the probability of having a median lifetime income between 1 to 2 standard deviations below the mean.
1 standard deviation below the mean would be μ - σ, and 2 standard deviations below the mean would be μ - 2σ.
μ - σ = $25800 - $14000 = $11800
μ - 2σ = $25800 - 2 * $14000 = $-2200
Next, we need to find the z-scores for these values. The z-score represents the number of standard deviations a given value is from the mean in a standard normal distribution.
For μ - σ:
z1 = (11800 - μ) / σ = (11800 - 25800) / 14000 ≈ -1.5714
For μ - 2σ:
z2 = (-2200 - μ) / σ = (-2200 - 25800) / 14000 ≈ -2.2857
Using a standard normal distribution table or a statistical software, we can find the corresponding probabilities associated with these z-scores.
The probability of having a median lifetime income between 1 to 2 standard deviations below the mean is the difference between the probabilities corresponding to z1 and z2.
P(1 to 2 standard deviations below the mean) = P(z1 < Z < z2)
You can refer to a standard normal distribution table or use statistical software (such as Excel, R, or Python) to calculate the probabilities. The exact values may vary depending on the specific table or software used.
An artist is building a pedestal out of wood that will be used to display a piece of sculpture. She plans to cover the pedestal with tile. How much tile will it take to cover the pedestal, including the bottom?
224 square feet
192 square feet
144 square feet
288 square feet
Answers
tile will it take to cover the pedestal, including the bottom is 288 square feet
How much tile will it take to cover the pedestal, including the bottom?It depends on how big the pedestal is and how big the tiles are that are being used. It would require 192 square feet of tile to cover the pedestal, including the bottom, if the tiles were one foot square and the pedestal was four feet tall.To cover the pedestal, however, would require 224 square feet of tile if it were five feet tall and the chosen tiles were two feet square.Similar to this, 144 square feet of tile would be required to cover a pedestal that is three feet tall and two feet square. The pedestal would require 288 square feet of tile to cover it, including the bottom, assuming the tiles were one foot square and the pedestal was five feet tall.As you can see, the size of the pedestal and the tiles being used both affect how many tiles are needed to completely cover the pedestal.To learn more about a tiling project refer to:
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(1) A reference angle of 82˚ is used to construct 4 angles in a coordinate plane, with 1 angle per quadrant, where all of the angles have a positive measure less than 60 degrees. In keeping in mind the requirement of showing the steps you took to calculate the answers, what are the measures of each of the angles in (a) through (d) below, filling in the blank?
(a) The angle in Quadrant I is _______˚;
(b) The angle in Quadrant II is ________˚;
(c) The angle in Quadrant III is ________˚;
(d) The angle in Quadrant IV is ________˚.
(2) Find tan(θ) to four decimal places, provided that sin(θ) is equal to 2/9.
Answers
(a) The angle in Quadrant I:
The angle in Quadrant I has the same measure as the reference angle because both angles are positive and less than 90˚.
Therefore, the angle in Quadrant I is 82˚.
(b) The angle in Quadrant II:
The angle in Quadrant II is equal to 180˚ minus the reference angle, as angles in this quadrant are greater than 90˚ and less than 180˚.
Therefore, the angle in Quadrant II is 180˚ - 82˚ = 98˚.
(c) The angle in Quadrant III:
The angle in Quadrant III is equal to 180˚ plus the reference angle, as angles in this quadrant are greater than 180˚ and less than 270˚.
Therefore, the angle in Quadrant III is 180˚ + 82˚ = 262˚.
(d) The angle in Quadrant IV:
The angle in Quadrant IV is equal to 360˚ minus the reference angle, as angles in this quadrant are greater than 270˚ and less than 360˚.
Therefore, the angle in Quadrant IV is 360˚ - 82˚ = 278˚.
The measures of the angles in each quadrant are:
(a) Quadrant I: 82˚
(b) Quadrant II: 98˚
(c) Quadrant III: 262˚
(d) Quadrant IV: 278˚
(2) Given sin(θ) = 2/9, we can use the Pythagorean identity to find cos(θ) and then calculate tan(θ):
sin²(θ) + cos²(θ) = 1
(2/9)² + cos²(θ) = 1
4/81 + cos²(θ) = 1
cos²(θ) = 1 - 4/81
cos²(θ) = 77/81
cos(θ) = √(77/81)
Since sin(θ) and cos(θ) are both positive, we can determine that θ lies in the first quadrant.
Now, to find tan(θ):
tan(θ) = sin(θ) / cos(θ)
tan(θ) = (2/9) / √(77/81)
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √81:
tan(θ) = (2/9) / (√(77/81) * √(81/81))
tan(θ) = (2/9) / (√(77*81) / 81)
tan(θ) = (2/9) / (√6237 / 81)
tan(θ) = (2/9) * (81 / √6237)
tan(θ) = 162 / (9√6237)
tan(θ) ≈ 1.0809 (rounded to four decimal places)
Therefore, tan(θ) ≈ 1.0809.
Enter a positive value for d that makes this statement true: 34×d is less than 34 but greater than zero HELP PLSS FASTT
Answers
Answer:
0.5 (any number between 0 and 1)
Step-by-step explanation:
34 * 0.5 = 17
34 > 17 > 0
Find the area of the pentagon
Answers
Answer:
A=1
45(5+25)a2
Step-by-step explanation:
EASY!!! What is (8+4)+24 / 2^3
Answers
Answer:
4 1/2.Step-by-step explanation:
Given equation:
(8 + 4) + 24 ÷ 2³.Solve:
(8 + 4) + 24 ÷ 2³= 12 + 24 ÷ 2³= 36 ÷ 2³= 36 ÷ 8= 4 R4= 4.5= 4 1/2.PLS HELP:)
Solve 2x - 5 = 7
Answers
Answer:
6
Step-by-step explanation:
2x-5=7
add 5 on both sides:
2x-5+5=7+5
2x=12
divide both sides by 2
2x/2=12/2
x=6
Answer:
6
Step-by-step explanation:
2−5=72x-5=7
2x−5=72−5+5=7+5
DUE NOW ASAP PLS The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a. bus
b. car
c. subway
d. train
Answers
The type of transformation that is the least likely to take more than 30 minutes is given as follows:
c. Subway.
What does a box and whisker plot shows?A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:
The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.For the subway box and whisker plot, we have that 30 minutes is the 75th percentile, meaning that only 25% of the subway rides take more time than that.
For the other types, we have that 30 is less than the 75th percentile, hence a higher percentage of rides that more than 30 minutes.
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Suppose your net income every month is $3,750. In the 20-50-30 Model, how much of
your net income would be in each category?
Answer in three complete sentences to explain how much of your income is in each category.
Answers
In the 20-50-30 Model, $1,875 is allocated for needs, $1,125 for wants, and $750 for savings and debt repayment.
According to the 20-50-30 Model, your net income should be allocated as follows:
Needs (50% of net income): In this case, 50% of $3,750 would be allocated to cover essential expenses such as rent/mortgage, utilities, groceries, transportation, and healthcare.Therefore, $1,875 would be allocated to cover these necessary expenses.
Wants (30% of net income): The 30% category is for discretionary spending on non-essential items and experiences that bring you joy and improve your quality of life.In this case, 30% of $3,750 would be allocated for wants, which amounts to $1,125. This portion can be used for activities such as dining out, entertainment, travel, hobbies, and personal indulgences.
Savings and Debt Repayment (20% of net income): The remaining 20% of your net income, which amounts to $750, should be allocated towards savings, investments, and paying down debt.It is important to prioritize building an emergency fund, saving for future goals, and reducing any outstanding debt, such as credit card balances or student loans.
By following the 20-50-30 Model, you can ensure that your income is distributed in a balanced manner, addressing your immediate needs, providing for your wants, and securing your financial future through savings and debt reduction.
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A triangle has no congruent sides and one angle measuring 108°.
What is this triangle's classification according to its sides and angles?
Answers
answer: acute
Step-by-step explanation:
none of the sides are equal
PLEASE HELP!!!!!!!!!!!!!
The vertex of a quadratic function g(x) is (3, 4) what is the vertex of f(x)=g(x)+1?
Answers
Check the picture below.
well, g(x) + 1 is simply a vertical shift upwards of 1 unit, if the vertex before that had a y-coordinate of 4, then later on became 4+1 or 5, so the new vertex is simply (3 , 5).
Consider the following story:
Three men walk into a hotel and ask to share a room. The cost is going to be $270 for
the night. Each man puts in a $100 bill and they get 3 $10 bills in change. The bell boy
carries their luggage and they each decide to be generous and tip the bell boy their change.
The front desk realizes they miss-charged the men, so the bell boy takes a $20 bill change to
the room. The men realize that you can’t split the $20 bill evenly 3 ways so they add it onto
the tip. The bell boy is happy but then thinks to himself: ”If the room is $270 and they had
this extra $20 that’s only $290, where did the other $10 go?”
Explain what is wrong with the Bell Boy’s thoughts, and what is the correct math here.
Answers
Answer:
Step-by-step explanation:
The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip
Total money of the three men: 3($100) = $300
They paid $270 for the room: $300 - $270 = $30
Tip for the bell boy: $30 - $30 = $0
Amount overcharged to them: $0 + $20 = $20
Tip to the bell boy: $20 - $20 = $0
They were left with no more money from the original $300.
ignore this:isnsjsbjs sjsdjsnsnssnsnnsnsns
Answers
Answer:
4
Step-by-step explanation:
i dont wanna explain but the answer is 4
Dorothy organises a charity raffle she sells 800 tickets for £2 each 4% of the tickets win a prize it cost £20 65% of the profit goes to charity A and the rest goes to charity be how much of the money does Dorothy raise for charity day
Answers
By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336
What is Percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.Total ticket sold = 800
Cost of each ticket is £ 2
Total fund raised (raw) = 2 * 800 = £1600
4% of the ticket won a prize of £20 each
so total number of tickets winning a prize = 4 % of 800 = 32
Total prize money distributed = 32 * 20 = £ 640
Total amount to distribute to charity = 1600 - 640 = £ 960
Total profit that goes to Charity A is = 65 % of 960 = £624
And rest to charity B is = £ 336
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The terminal point of 0 is (0,1). What is tan 0?