State the domain and range of the sin, cos, tan, functions. State the domain
and range of the inverse sin, cos, and tangent functions.
Answers
The domain and range of trigonometric functions are as follows;
Function Domain Range
sin(x). All real numbers [-1, 1]
cos(x). All real numbers [-1, 1]
tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R
The domain and range of the inverse sine, cosine, and tangent are;
Function Domain Range
arcsin(x). (-1, 1) [-π/2, π/2]
arccos(x). (-1, 1) [0, π]
arctan(x) (-∞, ∞). [-π/2, π/2]
What are the domains and ranges of the trigonometric functions?sin(x)
The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;
All real numbers.The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1
The range is therefore; [-1, 1]cos(x)
Similarly;
The domain of cos(x) is the set of all real numbersThe range of cos(x) is; -1 ≤ cos(x) ≤ 1tan(x)
tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...
The domain of tan(x) is therefore;
{x| x ≠ -3•π/2, -π/2, π/2, 3•π/2...}sin(x) increases as cos(x) decreases, therefore;
The range of tan(x) = sin(x)/cos(x) is therefore;
-∞ < tan(x) < ∞ which is {-∞, ∞}arcsin(x)
The input of arcsin(x) is sin(x)
sin(x) = opposite/hypotenuse
Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude
The domain of arcsin(x) is therefore;
-1 < sin(x) < 1, which is (-1, 1)The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2
The range is [-π/2, π/2]arccos(x)
Similarly;
The domain of arccos (x) is (-1, 1) The range is [0, π]arctan(x)
The input of arctan(x) is tan(x)
tan(x) = sin(x)/cos(x)
The domain of arctan(x) is therefore;
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Related Questions
Daria pays x dollars for a pair of shoes. the tax on shoes is 5%. the expression representing her total cost is x+0.05x.
witch expression is equivalent and why?
A 1.05x because adding $5 to the cost of the shoes is the same as multiplying the cost by 1.05
B 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
C x(0.05) because the cost of the shoes can be factored out
D 1.5x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.5
Answers
The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
PercentageAmount paid for shoes = $xTax = 5%Total cost = x + (5% of x)
= x + (0.05 × x)
= x + (0.05x)
Total cost = 1.05x
Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05
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Find a point-slope form with slope 1/2 and passing through the point (-7,-1)
Answers
Answer:
x-2y+5=0
Step-by-step explanation:
y+1= \(\frac{x+7}{2}\)
y=\(\frac{x+7}{2}\) -1
y=\(\frac{x+7-2}{2}\)
y=\(\frac{x+5}{2}\)
2y=x+5
x-2y+5=0
The equation is:
⇨ y + 1 = 1/2(x + 7)Work/explanation:
Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),
where m is the slope and (x₁, y₁) is a point on the line.
Plug in the data:
\(\rm{y-(-1)=\dfrac{1}{2} (x-(-7)}\)
Simplify
\(\rm{y+1=\dfrac{1}{2}(x+7)}\)
Hence, the equation in point slope is y + 1 = 1/2(x + 7).at a rehearsal dinner the night before a wedding, the bride and groom need to assign 10 people to two tables of five people. how many different groups of five can they form?
Answers
The bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner, as they need to assign them to two tables of five people each.
To determine the number of different groups of five people that can be formed, we can use the concept of combinations. In this scenario, we have 10 people who need to be divided into two groups of five people each.
The number of ways to choose five people out of 10 can be calculated using the combination formula. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n represents the total number of people and r represents the number of people to be chosen. In this case, n = 10 and r = 5.
Plugging these values into the formula, we get:
C(10, 5) = 10! / (5! * (10 - 5)!)
= (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5 * 4 * 3 * 2 * 1)
= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)
= 252
Therefore, the bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner. This means that there are 252 distinct ways to divide the 10 people into two tables of five people each, providing flexibility in creating diverse groups for the dinner.
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ASAP HELP
Find the variance and standard deviation of the data set below:
0 0.107
1 0.352
2 0.400
3 0.141
Answers
If the standard deviation of a set of data is 6, then the value of variance is 36
The formula for determining variance is variance = √Standard deviation
Variance of a set of data is equal to square of the standard deviation.
If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula
variance = √Standard deviation
Take square root on both sides
Standard deviation² = 6²
Standard deviation= 36
Hence, standard deviation of a set of data is 6, then the value of variance is 36
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Complete these Primes Factor trees for 120 and 150
Answers
Answer:
The highest common factor of 120 and 150 Is
30.
Hope it will help ✔
120
/ \
10. 12
/. \. /. \
2 5. 2. 6
/. \
2. 3
Step-by-step explanation:
150
/. \
10. 15
/. \. /. \
2. 5. 3. 5
so its 30
What is the solution to the system of equations below? x + 3 y = 15 and 4 x + 2 y = 30
Answers
Answer:
X=6 y=3 point form (6,3)
Step-by-step explanation:
Answer:
6,3
Step-by-step explanation:
I just took the test and got 100%
3. Problem 2: Suppose a radio manufacturer has the total cost function C (x) = 43x + $ 1850 and the revenue function R (x) = $ 80x. Where "x" is the number of radios manufactured and sold. Find:
plissssssssssssss helpppp
Answers
Given that,
Total cost function, C (x) = 43x + $1850
The revenue function R (x) = $80x
To find,
The number of units that must be produced and sold to break even.
Solution,
At break even, cost = revenue
43x + $1850 = $80x
Subtract 80x from both sides.
43x + 1850 -80x = $80x -80x
1850 = 80x-43x
37x = 1850
x = 50
So, the required number of units are 50.
What does it mean when you write your measurement as the mean ± standard deviation? (i.e., how much of the data fall within this range?)
Answers
When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.
When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.
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1. Consider a damped spring-mass system with m = 1kg, = 2
kg/s^2 and c = 3 kg/s. Find the general solution. And solve the
initial value problem if y(0) = 1 and y′(0) = 0.
Answers
The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).
The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).
To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.
The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).
By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.
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To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
Answers
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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please help ASAP! thank you
Answers
Answer:
c
Step-by-step explanation:
Solve the following equations. i) m + 80 = 175 ii) 14x = 70 iii) 7 = 36 iv) a – 29 = 40
Answers
the question for no (iii) is not complete.
Step-by-step explanation:
Write 4×10-2 as a decimal.
Answers
Answer:
4x10=40-2=38
38% = 0.38 in decimal form. Percent means 'per 100'. So, 38% means 38 per 100 or simply 38/100. If you divide 38 by 100, you'll get 0.38 (a decimal number).
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Which expressions are equal to 62⁰?
☐ 6³
12³
126
2³.33
26.33
Answers
Answer:
2^3 * 3^3 would also be correct if the answer above is 6^6
Step-by-step explanation:
2^3 * 3^3 (multiplying coefficients and adding exponents) 2*3 = 6 and 3+3=6
Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding
Answers
The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.
Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.
The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.
To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.
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the statistical power of a test is the probability that the test will correctly reject a false null hypothesis. that is, if a null hypothesis is false at the population level, the statistical power of a test is the probability that a researcher rejects the null hypothesis in his or her sample too. group of answer choices true false
Answers
The statement provided in the question is true. The statistical power of a test is the probability of correctly rejecting a false null hypothesis. It is the ability of a statistical test to detect a true effect, given that one exists. In other words, it is the likelihood that a study will be able to detect a difference or relationship between variables if such a difference or relationship truly exists in the population being studied.
The statistical power of a test depends on several factors, including the sample size, the effect size, and the level of significance chosen for the test. A larger sample size, a larger effect size, and a smaller level of significance all increase the power of a test. A low statistical power may indicate that the sample size is too small or that the test is not sensitive enough to detect the true effect.
Therefore, it is important to consider statistical power when designing and interpreting studies.
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D.1 Give an estimate for the total volume of food and water you've ingested in the last day, in milliliters. D.2 How many times larger is the amount of blood your heart has pumped in the last day than the amount of food and drink you took in? D.3 How much error do you expect in your answer to 4 b ? You should give an quantitative response to this, but not one generated by a formula. Instead, estimate the error by examining how closely you think you know the values you estimated for food intake and blood flow. You don't need to use advanced error propagation; an approximate response is fine. D.4 What is the relevance of this calculation to the theory that all the blood that flows through your veins is generated in the liver?
Answers
An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.
D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.
D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.
D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.
D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.
The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.
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2x – 3y = 17 –3x + y = –1
Answers
Answer:
can u rewrite the questions
Step-by-step explanation:
i need helpp quickly
A shopper bought the following items at the farmer’s market:
6 ears of corn for $1.80. What was the cost per ear?
12 apples for $2.88. What was the cost per apple?
5 tomatoes for $3.10. What was the cost per tomato?
How do you find out the problem?
What would happen if the decimal was put in the wrong place?
Answers
Answer:
$0.30 per corn
$0.24 per apple
$0.62 per tomato
Step-by-step explanation: you divide the price by the amount to give you the per item cost. If you put the decimal in the wrong spot your coat could go from $.30 per corn to $3 per corn. big difference!
Question 4(Multiple Choice Worth 10 points) (04.05 LC) Based on your research, how many individual battles occurred at the Battle of Philippi
Answers
The only 2 individual battles were between, Mark Antony and Octavian, and Brutus and Cassius at the Battle of Philippi.
With up to 200,000 soldiers, the Battle of Philippi was one of the largest Roman civil wars, consisting of two skirmishes on the plains west of the ancient city of Philippi. The first he occurred in the first week of October. Brutus confronted Octavian while Antony's army fought Cassius' army.
Battle of Philippi (October 3 and 23, 42 BC). In 300 BC, Philippi witnessed the final extermination of those who supported the old Roman republic, the culmination of the wars that followed the assassination of Julius Caesar in 44 BC.
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Given ⊙K with secants NS¯¯¯¯¯¯¯¯ and NR¯¯¯¯¯¯¯¯ , which expression represents PS. A circle with center point K. Two chords PS and QR intersects at point N outside the circle. A. (NQ)(NQ+QR)NP−NP B. (QR)(NQ+QR)NP−NP C. NP+NQ+QRNR−NR D. (NP)(NQ+QR)NR−NR
Answers
After answering the prοvided questiοn, we can cοnclude that PS = circle (QR(NQ - NR))/NR, which is nοt οne οf the given οptiοns.
What is circle?A circle seems tο be a twο-dimensiοnal cοmpοnent defined as such cοllectiοn οf the all pοints in a jet that becοme equidistant frοm the hub. A circle is cοmmοnly pοrtrayed with the capital "O" fοr centre and the lοwer sectiοn "r" fοr the radius, which is the distance frοm the οrigin tο any pοint οn the circle.
Girth (the distance frοm arοund circle) is given by the fοrmula 2r, where (pi) is a prοpοrtiοnality cοnstant rοughly equal tο 3.14159. The fοrmula r² calculates the circle's circumference, which refers tο the amοunt οf rοοm inside οf the circle.
Nοne οf the given οptiοns represent PS directly. Hοwever, we can use the intersecting secant theοrem tο find PS.
(NQ)(NQ+QR) = (NR)(NR+PR)
We can sοlve fοr PR tο get:
PR = (NR)(NR+PR)/(NQ+QR)
PR(NQ+QR) = (NR)(NR+PR)
PRNQ + PRQR = NR² + PRNR
PRNQ = NR² + PRNR - PRQR
PRNQ = NR(NR + PR - QR)
PR = NR(NR + PR - QR)/NQ
PR(NQ) = NR(NR + PR - QR)
PRNQ = NR(NR + PR - QR)
PRNQ - NR(PR - NR - QR) = 0
PR(NQ - NR) = NR(NR + QR)
PR = (NR(NR + QR))/(NQ - NR)
PS(PR + NR) = QR(NR + QR)
PS = (QR(NR + QR))/(PR + NR)
PS = (QR(NR + QR))/((NR(NR + QR))/(NQ - NR) + NR)
PS = (QR(NQ - NR))/NR
Therefοre, the cοrrect expressiοn representing PS is:
PS = (QR(NQ - NR))/NR, which is nοt οne οf the given οptiοns.
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Nathan is going to invest in an account paying an interest rate of 4.8% compounded continuously. How much would Nathan need to invest, to the nearest ten dollars, for the value of the account to reach $1,310 in 13 years?
Answers
Answer:
700
Step-by-step explanation:
Answer:
$712
Step-by-step explanation:
A x (1 + 4,8%)¹³ = 1310
=> A = 1310 : (1 + 4,8%)¹³ = 712,1551532
What is true about points in Quadrants II and III? A. They all have positive x-coordinates. B. They all have negative x-coordinates. C. They all have positive y-coordinates. D. They all have negative y-coordinates.
i dont have much time so pls help
Answers
Answer:
The correct answer is Option B: Quadrants II and III have negative x-coordinates.
Just FYI: Quadrants II and III have both positive and negative y-coordinates.
Find the slope of the line that passes though (-2,5) and (3, 0
Answers
Answer:
the answer is \(m=-1\)
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps :)
Intercept Form
Point (-3,4)
Slope 5/3
m= b=
Answers
Answer:
y = 5/3x + 9
Step-by-step explanation:
y = 5/3x + b
4 = 5/3(-3) + b
4 = -5 + b
9 = b
Please answer the question and help me pass
Answers
Answer:
10 *6= 60
60÷2=30
1÷2×b×h formula
answer- 30
enter the factor under the radical
\((a - b) \sqrt{a - b} \)
Answers
\(\\ \rm\longmapsto (a-b)\sqrt{a-b}\)
\(\\ \rm\longmapsto (a-b)(a-b)^{\frac{1}{2}}\)
\(\\ \rm\longmapsto (a-b)^{1+\dfrac{1}{2}}\)
\(\\ \rm\longmapsto (a-b)^{\dfrac{3}{2}}\)
Answer:
\(\dashrightarrow \: { \tt{(a - b) \sqrt{a - b} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{1} {(a - b)}^{ \frac{1}{2} } }}\)
• from law of indices:
\({ \boxed{ \rm{ ({x}^{n} )( {x}^{m} ) = {x}^{(n + m)} }}}\)
therefore:
\(\dashrightarrow \: { \tt{ {(a - b)}^{(1 + \frac{1}{2} )} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{ \frac{3}{2} } }}\)
Read the problem below. Type in your answer on the box.
The length of a rectangle is (3x - 1) and its width is ( 2x + 5). What is the area of the rectangle?
Answers
Answer:
3x^2 + 13x - 5
Step-by-step explanation:
To find the area, you multiply the length by width. So its is (3x - 1) * (2x + 5)
Then distribute. (3x * 2x) + (3x *5) + (-1 *2x) + (-1 * 5)
So 3x^2 + 15x -2x -5
Final Answer: 3x^2 + 13x - 5
Answer:
30 INCHES
Step-by-step explanation:
Justin's truck was totaled and he needs a new one, but cannot afford it with the money he has in the bank. so he gets a 13.5% per year. How much interest will be charged in the first 10 months? How much will he owe after 10 months assuming he did not make any payments?
Answers
The compound interest formula is:
\(A=P(1+\frac{r}{n})^{nt}\)Where
P is principal
r is rate of interest
n is number of compounding
t is number of years
Putting the given information, we have:
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=13,500(1+\frac{0.135}{12})^{12} \\ A=13500(1.01125)^{12} \\ A=15439.60 \end{gathered}\)Interest amount is:
15,439.60 - 13,500 = $1939.60 (in a year/12 months)
In 10 months:
\(1939.60\times\frac{10}{12}=1616.33\)Justin would owe $1616.33 after 10 months.
Please please help me with this question just help me on (C)
Answers
Answer:
move 3 seconds on your x-axis, and find your intersection with you y axis to determine the height h in m.
Am assuming you drew the function...
substitute 3 in the equation
\(h=-5({t})^{2} +20t\\ h=-5({3})^{2} +20(3)\\h=60-45=15m\)