Answers
The cotangent of angle θ is given as follows:
cot(θ) = 4.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle, which can also be interpret as the sine divided by the cosine.Considering that the terminal side passes through the point (4,1), the hypotenuse is given as follows:
h² = 4² + 1².
h = sqrt(17).
Considering that x is the adjacent coordinate to the angle while y is the opposite coordinate to the angle, the sine and the cosine of the angle are given as follows:
sin(θ) = 1/sqrt(17).cos(θ) = 4/sqrt(17).The cotangent is the inverse of the tangent, hence it is given by the cosine divided by the sine, thus:
cot(θ) = (4/sqrt(17))/(1/sqrt(17))
cot(θ) = 4.
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Related Questions
Population density is a measure of how crowded an area is. The population density of Australia is approximately 7.6 people per square mile. If Bangladesh has 2,949.7 more people per square mile than Australia, what is the population density of Bangladesh?
2942.10 people per square mile
2957.30 people per square mile
3025.70 people per square mile
3709.70 people per square mile
Answers
Answer:
B
Step-by-step explanation:
Answer:
B) 2957.30 people per square mile
I don't need brainly btw
:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answers
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
\(\frac{x}{3} + z = 14\)
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
\(x + y = 44\)
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
\(\frac{x}{3} + z = 14\)
\(\frac{x}{3} = 14 - x\)
\(x = 3(14 - z)\)
\(x = 42 - 3z\)
And
\(y = z + w\)
In which
\(w = 10 + z\)
So
\(y = z + 10 + z\)
\(y = 2z + 10\)
Replacing:
\(x + y = 44\)
\(42 - 3z + 2z + 10 = 44\)
\(-z + 52 = 44\)
\(z = 52 - 44\)
\(z = 8\)
The number of female faculty in the Department with a PhD is 8.
Two Trends pay the restaurant bill in the ratio of 16:4. If more paying friend pays
Rs 140 find the total amount paid by them.
Answers
Answer:
Cici O i itcivouvitci cc tfurx
Step-by-step explanation:
vhihciycyivovitcu
The ordered pairs show amounts y (in inches) of rainfall equivalent to x inches of snow.(16, 1.5), (12, 1.3), (18, 1.8), (15, 1.5), (20, 2.1),(23, 2.4) About how many inches of rainfall are equivalent to 6 inches of snow? Round your answer to the nearest hundredth, if necessary.
Answers
Answer:
0.57 inches of rainfall is equivalent to 6 inches of snow
Step-by-step explanation:
The given data are presented here as follows;
\(\begin{array}{cc}x&y\\16&1.5\\12&1.3\\18&1.8\\15&1.5\\20&2.1\\23&2.4\\\end{array}\)
The data points are approximately linear
From the the trend line of the plotted points of the graph, created with Microsoft Excel, with Forecasting, when there is 6 inches of snow the rainfall is 0.575 inches
By linear regression, we have;
Y = a + b·X
Where;
\(b = \dfrac{n \cdot \sum XY - \left (\sum X \right ) \cdot \left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}\)
\(a = \dfrac{\sum Y - b \cdot \sum X}{n}\)
∑x = 104
∑y = 10.6
∑(x·y) = 191.7
(∑x)·(∑y) = 1102.4
(∑x)² = 10816
n = 6
SigX^2 = 1878
Plugging in the values, gives;
\(b = \dfrac{6 \times191.7 - 1102.4}{6 \times 1878 - 10816} \approx 0.10575\)
\(a = \dfrac{10.6 - 0.10575 \times 104}{6} \approx -0.06637\)
Therefore;
Y = 0.10575·x - 0.06637
When x = 6 inches, we have;
Y = 0.10575 × 6 - 0.06637 = 0.56813
Y = 0.56813 inches ≈ 0.57 inches of rainfall
Therefore;
0.57 inches of rainfall is equivalent to 6 inches of snow
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 3.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 86 square centimeters? The base is changing at cm/min.
Answers
Answer:
-1.88cm/min
Step-by-step explanation:
Given
dh/dt = 1.5cm/min
dA/dt = 3.5cm²/min
Height h = 10cm
Area A = 86cm²
Required
db/dt
b is the base
h is the height.
Area of a triangle A = 1/2bh
dA/dt = dA/db•db/dt + dA/dh •dh/dt
dA/db = h/2 = 10/2 = 5cm
Get the base
86 = 1/2(10)b
5b = 86
b = 17.2cm
dA/ dh = 1/2b = 1/2(17.2)
dA/dh = 8.6cm
.substitute given values into the formula above;
dA/dt = dA/db•db/dt + dA/dh •dh/dt
3.5 = 5 db/dt + 8.6(1.5)
3.5 = 5 db/dt + 12.9
5 db/dt = 3.5-12.9
5 db/dt = -9.4
db/dt = -9.4/5
db/dt = -1.88cm/min
Hence the base is changing at -1.88cm/min
5 On a scale drawing, the height of a tree is 3.75 inches.
Part A
If the scale of the drawing is 1 in.: 50 ft, how tall is the tree?
A
13.3 in.
B
13.3 ft
C 187.5 in.
D 187.5 ft
Part B
If the same tree is shown as 6 inches tall in a new scale drawing, mademulov ort
what is the new scale?
1 in.:.what about part b
Answers
Part A:
We are given that the height of a tree in a scale drawing is 3.75 inches. The scale of the drawing is 1 inch: 50 feet.
To find the height of the actual tree, we can use the ratio of the drawing scale to the real-life scale. For every 1 inch on the drawing, there are 50 feet in real life.
Therefore, we can set up a proportion:
\($\frac{1 \ \text{inch}}{50 \ \text{feet}} = \frac{3.75 \ \text{inches}}{x \ \text{feet}}$where $x$ is the height of the actual tree in feet.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot x = 3.75 \ \text{inches} \cdot 50 \ \text{feet}$$x = \frac{3.75 \ \text{inches} \cdot 50 \ \text{feet}}{1 \ \text{inch}} = 187.5 \ \text{feet}$Therefore, the height of the tree is $\boxed{D \ 187.5 \ \text{ft}}$.\)
\(Part B:We are now given a new scale drawing where the height of the same tree is 6 inches. We need to find the new scale.Since the tree's height in the new drawing is different, we can use a new proportion to find the new scale.Let the new scale be $1$ inch to $x$ feet. We can set up a proportion:\)
\($\frac{1 \ \text{inch}}{x \ \text{feet}} = \frac{6 \ \text{inches}}{187.5 \ \text{feet}}$where $187.5$ feet is the height of the tree in real life.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot 187.5 \ \text{feet} = 6 \ \text{inches} \cdot x \ \text{feet}$$x = \frac{1 \ \text{inch} \cdot 187.5 \ \text{feet}}{6 \ \text{inches}} = 31.25 \ \text{ft}$Therefore, the new scale is $\boxed{1 \ \text{inch} : 31.25 \ \text{ft}}$.\)
Answer:
Step-by-step explanation:
Part A:
We can use a proportion to solve for the height of the tree:
1 inch on the drawing represents 50 feet in real life.
So, 3.75 inches on the drawing would represent:
3.75 inches * (50 feet/1 inch) = 187.5 feet
Therefore, the height of the tree is 187.5 feet.
The answer is D) 187.5 ft.
Part B:
The ratio of the height of the tree on the new scale drawing to its actual height must be the same as the ratio of the height of the tree on the original scale drawing to its actual height.
Let the new scale be 1 in. : x feet.
Then, we have the proportion:
1 in. / 50 ft. = 6 in. / (x) ft.
Solving for x, we get:
x = (6 in. * 50 ft.) / 1 in.
x = 300 ft.
Therefore, the new scale is 1 in. : 300 ft.
The answer is 1 in. : 300 ft.
i really need help i have till 11:00
Answers
The expression that represents the combined inventory of these two stores is given as follows:
A. 7g²/2 - 4g/5 + 15/4.
How to obtain the combined inventory?The combined inventory is obtained adding the inventories for each store, combining the like terms.
The addition of the like terms for g² is given as follows:
1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².
The term with g is given as follows:
-4g/5.
The constant like terms are combined as follows:
7/2 + 1/4 = 14/4 + 1/4 = 15/4.
Hence the simplified expression is given as follows:
7g²/2 - 4g/5 + 15/4.
Meaning that the correct option is given by option A.
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5. The total length of a beach towel is 28 inches. If there are o beaches
towels laid right next to each other side-by-side, what is the total length o
the towels?
Answers
Which of the following statements describes the value of the expression 71 – 5x, when x = 3?
Answers
Answer:
56
Step-by-step explanation:
when 71-5x=? If x=3 then you would put 3 in the position of the x. Making the equation now 71-5(3) then you can start to solve
71-5(3)
71-15
56
The answer to this equation is 56
Hey there!
71 - 5x
= 71 - 5(3)
≈ 71 - 5 + 5 + 5
≈ 71 - 10 + 5
= 71 - 15
= 56
Therefore, your answer is: 56
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
I need help please!!!
Answers
Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.
I prefer Wills method because it is easier and less complicated.
How to solve differences?Wills method:
(5x + 6x) - (2x - 1)
Subtract both 2x and -1
5x + 6x - 2x - - 1
5x + 4x + 1
In conclusion, Wills method is preferred when both methods are compared.
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Out of 20 people how many would you expect to say that they like all seasons
Answers
Answer:
None
Step-by-step explanation:
Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.
Answer:
One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.
Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.
One way to construct a confidence interval for a proportion is to use the formula:
p ± z * sqrt(p * (1 - p) / n)
where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:
0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)
which simplifies to:
0.6 ± 0.22
or:
(0.38, 0.82)
This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.
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Liam is currently twice as old as Sally. 4 years ago, Liam was three times as old as Sally. How old is Liam now?
Answers
Answer:
16
Step-by-step explanation:
L = 2 * S
L-4 = (S-4) * 3
L-4 = 3S - 12
L = 3S - 8
2S = 3S - 8
-S = -8
S = 8
L = 16
Answer:
16
Step-by-step explanation:
If a ring costs a jeweler $2100, at what price should it be sold to yield a profit of 50% on the selling price?
Answers
2100/2 = 1050
Meaning 50% is $1050
A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$, what are the coordinates for point $C$? Express your answer as an ordered pair.
Answers
Answer:
C = (18, 6)
Step-by-step explanation:
You have ...
AB : BC = 1 : 1/3 = 3 : 1
(B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation
B -A = 3(C -B) . . . . . . . . . multiply by (C-B)
4B -A = 3C . . . . . . . . . . . add 3B
C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C
C = (4(14, 4) -(2, -2))/3 = (54, 18)/3
C = (18, 6)
Find the number of outcomes in the complement of the given event.
Out of 270 apartments in a complex, 174 are subleased.
Answers
Answer:
96
Step-by-step explanation:
Out of 270 apartments in a complex, 174 are subleased.
Given that :
Total number of apartments in complex = 270
Number subleased = 174
The complement of event A = not A
Therefore, The complement in this scenario is NOT SUBLEASED ;
Hence, the Number of apartments in complex not subleased is :
Total apartment in complex - number subleased
270 - 174 = 96
At a summer job, Maya is painting houses. She charges a $100 fee to start a job and $25 per
hour for each hour she spends on the job. Complete the table belly to show how much
money Maya makes painting one house.
Answers
Answer:
the answer would 125
Step-by-step explanation:
Answer:
I think the answer will be 225. Because 1st she got 100 for starting the job and 25 $ for per hour. She did 5 hours. So five times 25 . It will be 125 and 100 . The answer is 225
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Which statements about events in World War II are true?
Choose all answers that are correct.
Responses
German and Japanese scientists succeeded in breaking the Allies' most secret codes.
Nazi terror weapons, called V-1s and V-2s, killed thousands of people in Great Britain.
Germany's industries and cities were devastated by Allied bombing raids.
American forces used new types of ships to attack Japanese-held islands in the Pacific.
Answers
hope that helps
244-33456/3456*345+13.55-2=
Answers
The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:
244 - (33456 / 3456) * 345 + 13.55 - 2
= 244 - 97.02 * 345 + 13.55 - 2
= 244 - 33494.1 + 13.55 - 2
= -33238.55
Therefore, 244-33456/3456*345+13.55-2 = -33238.55.
Solve each equation -3x + 2 = -1
Answers
-3x=-1-2 - -3x=-3
x=1
Help me I don't get it ..........................................
Answers
Answer:
5/7
Step-by-step explanation:
Answer:
130/231
Step-by-step explanation:
you just plug in the values of x, y, and z so:
\(\frac{-\frac{2}{3}*\frac{5}{7} }{-\frac{11}{13} }\)
start by simplifying the top:
\(\frac{-\frac{10}{21}}{-\frac{11}{13} }\)
divide:
\(-\frac{10}{21}\)÷\(-\frac{11}{13}\)
= \(-\frac{10}{21} * -\frac{13}{11}\)
= \(\frac{130}{231}\)
Match the special segment in triangles
Answers
The required special segment in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
The question seems to be incomplete, so we assume that there are two congruent triangles.
For the congruent triangles, special segments in triangles are congruent to each other.
Thus, the required special segments in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.
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Evaluate the expression when y=−2 and z=−5.
10y2z
that is 10y to the second power divided by z
Answers
Answer:
4
Step-by-step explanation:
10y^2/ z
10(-2)^2/-5
10 ×-2 =-20
-20÷-5=4
The value of the expression is -8.
The expression when y=−2 and z=−5 in 10y²/z will be gotten by putting the values of y and z into the expression that's given. This will be:
10y²/z = 10(-2)²/-5
= 10(4)/-5
= 40/-5
= -8
In conclusion, the value of the expression is -8.
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Consider the line 5x+2y=−4. What is the equation of the line parallel to the given line that passes through the point (−2, 6) in slope-intercept form? Enter your answer by filling in the boxes to complete the equation.
Answers
Answer:
y = -5/2x +1
Step-by-step explanation:
You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.
Parallel lineThe equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:
5(-2) +2(6) = c
-10 +12 = c
2 = c
Now we know the equation of the parallel line can be written as ...
5x +2y = 2
Slope-intercept formSolving for y puts this in slope-intercept form:
2y = -5x +2 . . . . . . . . subtract 5x
y = -5/2x +1 . . . . . . . . divide by 2
We don't know what your boxes look like, but we can separate the numbers to make it look like this:
\(\boxed{y=\dfrac{-5}{2}x+1}\)
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Given that 4x – 5y = 21
Find x when y = -4
Give your answer as a fraction in its
simplest form.
Answers
A Chevrolet Sonic Hatchback costs $14,800.00. With a 12 % down payment, you can have an amortized loan for 6 years at a rate of 4.5%. What will the monthly payment be? car cost in total, money paid in interest
Answers
Based on the loan amount and the number of years, the monthly payment, total cost of the car, and amount of interest to be paid are as follows:
Payment each month: $206.74Total cost of the car was $14, 885.$1, 861.52 must be paid in interest.How do I calculate the required interest?Find the loan amount first:
= Car expense x ( 1 - down payment percent)
= 14, 800 x ( 1 - 12%)
= $13024
the monthly rate and the total number of periods, then:
Daily rate calculation:
= Annual Rate / Twelve-Month Period
= 4.5% / 12
= 0.375%
Counting periods:
= Years multiplied by Months per year
6 years times 12
72 months
These enable the following formula to determine the monthly payment:
= Loan Amount / 72-period Annuity Present Value Interest Factor of 0.375%
13024 / 62.995976235992
= $206.74
Total amount repaid on the auto loan:
= Amount Due Each Month x The Number of Months
= 206. 74 x 72
= $14, 885. 52
Accordingly, the total amount of interest paid was:
= Amount borrowed - Amount paid toward the car's cost
= 14, 885.52 - 13, 024
= $1, 861.52
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A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate. Let y be the number of kg of salt in the tank after t minutes. Write the differential equation for this situation
Answers
Let A(t) denote the amount of salt (in kg) in the tank at time t.
At the start, there are 80 kg of salt in the tank, so A(0) = 80.
Solution flows into the tank at a rate of 8 L/min at a concentration of 0.04 kg/L, so that salt flows in at a rate of
(8 L/min) * (0.04 kg/L) = 0.32 kg/min
Solution flows out at the same rate, but its concentration depends on the amount of salt in the tank. The concentration of the solution is the proportion of salt in the liquid to the total volume of the liquid. Solution flows in and out at 8 L/min, so the volume of liquid (1000 L) stays the same. A(t) is the amount of salt in the tank, so the concentration is A(t)/1000 kg/L. Hence salt flows out at a rate of
(8 L/min) * (A(t)/1000 kg/L) = 0.008 A(t) kg/min
The net rate at which salt flows through the system is then given by the differential equation,
dA(t)/dt = 0.32 - 0.008 A(t)
(Don't forget to include the initial condition)
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Answers
Sorry my kid needs help with this
Answers
Answer:
700,000
Step-by-step explanation:
Well, \(10^{4}\) as we know is 10(10)(10)(10), or 10 multiplied by itself 4 times.
The easiest way to solve this, is knowing that because 10 is being multiplied by itself 4 times, it'll have the outcome of 10000, which has 4 zeroes. This is very good to remember, so I recommend remembering it :) Just like if the question was about \(10^{5}\), it would be 100000, which has 5 zeroes.
So now we add on all of those zeroes to 70.
700000 would be your answer because we added on 4 more zeroes.
I NEED HELP AND QUICK.
Answers
Answer:
1. 40-p+w
2. $4 left
I'm not sure about the first one, but I'm pretty sure about the second one.
Step-by-step explanation:
What is the meaning of "the notion of finiteness"?
Answers
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
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