Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.
Answers
Solution
Step 1
The terminal side, containing point (-3, 4) is located in Quadrant 2.
sine is positive
cosine and tangent are both negative.
Step 2
Draw a diagram to illustrate the information
Step 3
[tex]\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }\sqrt{25} \\ \text{d = 5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} sine\text{ = }\frac{Opposite}{Hypotenuse} \\ Sin\theta\text{ = }\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} Cosine\text{ = }\frac{Adjacent}{Hypotenuse}\text{ = }\frac{x}{d} \\ Cos\theta\text{ = }\frac{-3}{5} \end{gathered}[/tex][tex]\begin{gathered} tangent\text{ = }\frac{Opposite}{Adjacent}\text{ = }\frac{y}{x} \\ tan\theta\text{ = }\frac{-4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} sin\theta\text{ = }\frac{4}{5} \\ cos\theta\text{ = }\frac{-3}{5} \\ tan\theta=\frac{-4}{3} \end{gathered}[/tex]
Related Questions
a. If Ax = b has a solution and Aᵀy = 0, then y is perpendicular to ___.
b. If Aᵀy = c has a solution and Ax = 0, then x is perpendicular to ___.
Answers
The answer to question (a) that is if Ax = b has a solution and [tex]A^{T}[/tex] y = 0 then y is perpendicular to b
Answer to question (b) that is if [tex]A^{T}[/tex] y = c has a solution and Ax = 0 then x is perpendicular to c.
a) As Ax = b has a solution for x this means b lies in the column space of A. We also know that [tex]A^{T}[/tex] y = 0. This means y lies in the orthogonal complement of the column space of A or in the left null space of A. Therefore y is perpendicular to b
b) We see [tex]A^{T}[/tex] y = c has a solution. This tells us that c lies in the row space of A and also from the given Ax = 0 we can deduce that x lies in the null space of A or the orthogonal complement of row space of A. Therefore evidently x will be perpendicular to c
Determine whether AT has a row space same as column space of A
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Solve and check the equation X-23=16
Answers
Answer:x=39
Step-by-step explanation:
x-23=16
x=16+23
x=39
LetW = the set of whole numbersF = the set of (non-negative) fractionsI = the set of integersN = the set of negative integersQ = the set of rational numbersSelect each set that is closed under addition.
Answers
Verify each set
W ---------> are closed under addition
F ------> are closed under addition
I ------> are closed under addition
N ----> are closed under addition
Q ----> are closed under addition
The slope of like A is m=9 & the slope of line B is m-9. What is their relation?
O Parallel
O Perpendicular
O Neither
Answers
Use the law of cosines to solve the following problem.The robot arm shown in the figure places packages on a conveyer belt. What is the distance x?
Answers
SOLUTION
Using cosine rule it follows:
[tex]x^2=3.00^2+2.25^2-3(2.25)\cos110[/tex]Simplify the equation for x
[tex]x=\sqrt{3.00^2+2.25^2-3(2.25)\cos110}[/tex]Therefore the required answer is
[tex]x=\sqrt{3.00^2+2.25^2-3(2.25)\cos(110)}[/tex]can you give me some examples of how to simplify
Answers
Let's check out the expression
[tex]2x+4+6y+7+2+3x[/tex]To simplify, you have to add up similar terms. That is, add up everything that has an x, add up everything that has a y, and add up every independent term (no variable), as following:
[tex]\begin{gathered} 2x+4+6y+7+2+3x\rightarrow2x+3x+6y+4+7+2 \\ \rightarrow5x+6y+13 \end{gathered}[/tex]And there we have the simplified expression.
Juan rented a truck for one day. There was a base fee of $9.00, and there was an additional charge of 7 cents for each mile driven. The total cost, C (in dollars), for driving x miles is given by the following function.
C (x) = 9.00 + 0.07x
What is the total rental cost if Juan drove 30 miles?
Answers
Answer:
$11.10
Step-by-step explanation:
Ez
The mass of an atom or molecule is measured in atomic mass units. Which is greater, a carat or a milligram?
Answers
Notice that:
[tex]\begin{gathered} -23<-21, \\ 8.3<10. \end{gathered}[/tex]Therefore:
[tex]8.3\times10^{-24}<10\times10^{-24}=10^{-23}<10^{-21}<1.66\times10^{-21}\text{.}[/tex]Then a carat is greater.
Now, since:
[tex]1atomic\text{ mass unit=8.3}\times10^{-24}carat.[/tex]Then:
[tex]\frac{1}{8.3}\times10^{24}\text{atomic mass unit=1carat.}[/tex]Simplifying the above result we get:
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]Also, since:
[tex]1\text{atomic mass unit=1.66}\times10^{-21}milligram[/tex]then:
[tex]\frac{1}{1.66}\times10^{21}\text{atomic mass unit=1 milligram.}[/tex]Simplifying the above result we get:
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]Answer:
A carat is greater.
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]and
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]and
Help please and thank you
Answers
Hence coordinates of x interfept = (-2,0)
On the y intercept, the x coordinate is 0. Hence 4(0) -2y = -8
-2y= -8
y=-8/-2 = 4
Y intercept coordinate is (0.4)
Which of the following would result in an integer?
O a.) 120
O b.) √144
O c.) √52
O d.) √24
Answers
The answer is either Option (a) or option(b) or both the options i.e, 120 or √144
What is Integer ?
An integer is a whole number from the set of -ve , non-negative , +ve and 0 numbers.
Let's see how both the option is correct
we know, integers are 0,1, 2, 3, .... or -1, -2 , -3 ......
Means the number which is not in fraction or decimal value or root.
so, by seeing option(a) we can say it's an integer
but in option(b) it's the root so how it is integer
The answer is simple it's perfect square of 12 so √144 = 12 so that means it have the value which is not in fraction. By that we can say that option(b) is also an integer
Now, in option(c) and (d) they are not the perfect square and their root results in decimal values. so we cannot tell them as an integer value.
Hence, the answer is either Option (a) or option(b) or both the options.
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Given the graph above, what is the slope of this line?
Question 2 options:
1.m = -2
2. m = 3
3. m = 0
4. m = -3/2
Answers
Answer:
my answer would be m=-3/2
Step-by-step explanation:
given the coordinates
(0,0) - this is the origin and the first coordinate it will be treated as x1=0,y1=0
(-2,3)- this is the second given coordinate and will be treated as x2=-2,y2=3
To find the slope(m) we use the formula
m=y2-y1/x2-x1
m=3-0/-2-0
m=-(3/2)
m=-3/2
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what is the distance of (-23, -14 ) and ( -18,2)
Answers
From the given question,
There are given that two point, (-23, -14) and (-18, 2).
Now,
For finding the distance between two point,
Here use distance formula.
From the distance formula,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]x_1=-23,y_1=-14,x_2=-18,y_2=2[/tex]Put the all values into the above formula,
Then,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-18_{}-(-23_{})^2+(2_{}-(-14)_{})^2} \\ d=\sqrt[]{(-18_{}+23_{})^2+(2_{}+14_{})^2} \end{gathered}[/tex]Then,
[tex]\begin{gathered} d=\sqrt[]{(-18_{}+23_{})^2+(2_{}+14_{})^2} \\ d=\sqrt[]{(5_{})^2+(16_{})^2} \\ d=\sqrt[]{25+256} \\ d=\sqrt[]{281} \end{gathered}[/tex]Hence, the distance of given
Can you help me ?
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
The cost of a school lunch is $2.50.
Complete the table to show the total cost of 1, 2, 3, and 4 lunches.
Lunches Bought 1 2 3 4
Total Cost ($)
Part B
Select the correct choices to complete the sentence.
The total cost is , 1 of 2.
Select Choice
to the number of lunches bought because the ratios between the quantities , 2 of 2.
Select Choice
the same unit rate.
Answers
The cost for the lunches will be:
1 lunch = $2.50
2 lunches = $5
3 lunches = $7.50
4 lunches = $10
How to calculate cost?From the information, the cost of a school lunch is $2.50. Therefore, the cost of 1 lunch will be:
= 1 × $2.50
= $2.50
The cost of 2 lunches will be:
= 2 × $2.50
= $5.00
The cost of 3 lunches will be:
= 3 × $2.50
= $7.50
The cost of 4 lunches will be:
= 4 × $2.50
= $10
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In the diagram below, if < 2 = 123 °, what would be the measure of < 7?
Answers
Given:
[tex]\angle2=123^{\circ}[/tex]To find:
The angle 7.
Explanation:
We know that,
The sum of the exterior angles is supplementary.
So, we can write
[tex]\begin{gathered} \angle2+\angle7=180 \\ 123^{\circ}+\angle7=180 \\ \angle7=180-123 \\ \angle7=57^{\circ} \end{gathered}[/tex]Therefore, angle 7 is 57 degrees.
Final answer:
Angle 7 is 57 degrees.
49. Calculate the limit. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.
lim x^lnx
x→0+
Answers
The limit of xlnx when x is tending towards zero is zero.
What is limit in mathematics?
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.
Given limit is:
[tex]\lim_{x \to 0} x lnX[/tex]
Considering f = x, and g = ln x
The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.
The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as
[tex]\frac{lnx}{1/x}[/tex]
We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as
The limits
[tex]\lim_{x \to 0^+} lnx= - \infty[/tex], and
[tex]\lim_{x \to 0^+} \frac{1}{x}[/tex]
The limits [tex]\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}[/tex] exists as:
[tex]\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0[/tex]
Hence the answer is 0.
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Maria expandió el siguiente cuadrado (x+3)^2=x^2 Está correcta la forma que usò?
Answers
No, the form that Maria expanded is not correct.
What does it mean to "extend and simplify"?
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out.
Given:
(x+3)²
= x² + 2 . 3 . x + 3²
= x² + 6x + 9
Therefore the correct expansion is x² + 6x + 9.
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Question:
Maria expanded the following square (x+3)^2=x^2 Is the form she used correct?
10. A 300-room hotel collects $125 per occupied room and does not collect any money for vacantrooms. Which of the following functions best represents how many dollars, d, the hotel generates ifthere are v vacant rooms in the hotel?O d = 125(300 + V)O d = 300(75 - v)O d = 300(75+)O d = 125(300 - V)
Answers
If there are v vacant rooms, the number of occupied rooms is 300-v (in total there are 300 rooms).
As every occupied makes the hotel collect 125, the dollars the hotel generates are:
[tex]d=125(300-v)[/tex]It means that the correct answer is the last option.
I need help on this question?
Answers
By definition, [tex](f \circ g)(x)=\boxed{f(g(x))}[/tex]. So, if [tex]g(2)=6[/tex] and [tex]f(6)=17[/tex], then [tex](f \circ g)(2)=f(g(2))=f(6)=\boxed{17}[/tex].
Question 2-20
Mrs. Kimsey purchased a bushel of large apples that weighs about 48 pounds. The bushel contains 96 apples. What is the approximate
weight, in ounces, of one apple?
02
O 16
32
Answers
Weight of one apple is 8 ounces.
We have to calculate the weight of one apple. For that firstly, we have to calculate the weight of one apple in pounds because we have been given the weight of 96 apples in pounds. After that, we will convert it into ounces and we know that one pound is equal to 16 ounces.
A bushel has 96 apples.
We have been given weight of 1 bushel which is 48 pounds.
Weight of 96 apples = 48 pounds
We have to calculate weight of one apple.
Weight of one apple = 48/96 = 1/2 pound
1 pound = 16 ounces.
Now, we have to convert pounds into ounces
Weight of one apple = 1/2 * 16 ounces
= 8 ounces
Hence, the answer is 8 ounces.
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I NEED HELP ASAP, I DONT KNOW HOW TO DO THIS.
Answers
Answer:
slope = 5/2
Step-by-step explanation:
Locations of points: (-4 , -4) and (-2 , 1)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (1 - (-4)) / (-2 - (-4))
slope = 5/2
Find the range PLEASE HELP!!! EXTRA POINTS
Answers
the domain is the interval or set of all valid values for x (the input variable).
the range is the interval or set of all valid values for y or f(x) (the function result variable).
the functional result values for the first piece :
x - 4 for 0 <= x < 2
for x = 0 we get y = -4
for x = 2 we get y = -2
the range for this piece is [‐4, -2).
we use the round bracket to indicate -2 itself is not included, as we have x < 2 (and not x <= 2).
the functional result values for the second piece :
x² - 3x + 4 for 2 <= x < 4
for x = 2 we get 4-6+4 = 2
for x = 4 we get 16-12+4 = 8
the range for this piece is [2, 8)
again, because of x < 4 we use the ")" for 8 (not included).
the functional result values for the third piece :
5 for 4 <= x < 7
the range is simply [5) = [5] because the set contains only one element.
and 5 is already contained in the range of the second piece.
so, the range is just the combination of the ranges of the first 2 pieces :
[-4, -2) U [2, 8)
The state transportation commission counted cars traveling east and west across a toll bridge. 75% of the 588 cars counted were traveling east. How many eastbound cars did the commission count?
Answers
Answer: the answer is 441
Step-by-step explanation: 75% of 588 is 441
Hello I need help please.The choices for f(-6): A. f(-6) ; B. The answer is not a real number
Answers
Given the function:
[tex]f\mleft(x\mright)=\sqrt{x-1}[/tex]First part:
You need to substitute the following value of "x" into the function:
[tex]x=1[/tex]In order to find:
[tex]f(1)[/tex]Then, substituting and evaluating, you get:
[tex]\begin{gathered} f(1)=\sqrt[]{1-1} \\ f(1)=\sqrt[]{0} \\ f(1)=0 \end{gathered}[/tex]Second part:
Substitute this value of "x" into the function:
[tex]x=-6[/tex]And then evaluate, in order to find:
[tex]f(-6)[/tex]You get:
[tex]\begin{gathered} f(-6)=\sqrt[]{-6-1} \\ f(-6)=\sqrt[]{-7} \end{gathered}[/tex]Since the Radicand is negative, it is not a Real Number.
Therefore, the answers are:
First part:
A.
[tex]f(1)=0[/tex]Second part:
B. The answer is not a real number.
I really need help with this question!! How do you solve it?In 1985, they discovered a new sea creature. It was found to have an initial population of 832. Assuming the population was growing at a rate of 2.3% each year, when will the population exceed 1500?
Answers
Solution:
The growth rate is given below as
[tex]r=2.3\%[/tex]The initial population is
[tex]P_0=832[/tex]The exponential growth formula is given below as
[tex]\begin{gathered} P=P_0(1+r)^t \\ 832(1+\frac{2.3}{100})^t=1500 \\ 832(1.023)^t=1500 \\ (1.023)^t=\frac{1500}{832} \\ (1.023)^t=1.803 \\ take\text{ ln of both sides} \\ ln(1.023)^t=ln(1.803) \\ tln(1.023)=ln(1.803) \\ t=\frac{ln(1.803)}{ln(1.023)} \\ t=25.9years \\ \end{gathered}[/tex]Hence,
The final answer is
The population will exceed 1500 in approximately 26 years' time
From 1982 to 2004, the number
B
of federally insured banks could be approximated by
B
(
t
)
=
−
326.6
t
+
13783
where t is the year and t=0 corresponds to 1982.
How many federally insured banks were there in 1987?
Find the slope of the graph of B.
Answers
There were 120150 federally insured bank in the year 1987. The slope of the graph of B is -326.6.
The provided function B(x) states the number of federally insured banks from 1982-2004.
The function B(x) is,
B(x) = -326.6t + 13783
Here t is representing the year,
This function is a linear function corresponding to an equation of line,
If according to the situation,
t = 0, signifies the year 1982,
Then the year 1983 should be represented by t = 1.
On continuing the pattern the year 1987 should be represented by t = 5.
So, the number of federally insured banks in year 1987 can be found by putting t = 5 in B(x),
B(5) = -326.6(5) + 13783
B(5) = 12150.
The number of banks federally insured in year 1987 is 12150.
The function is B(x)= -326.6t + 1783,
This is representing the point-slope form of the line,
y = mx + c,
On comparing the provided function with the standard equation we can see,
Slope m = -326.6
So the slope of the function is -326.6.
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The table below shows the population of the state of Washington for several decades starting in1900.Year1900191019201930194019501960Populationin millions0.521.151.371.571.742.392.86If the population is modeled by an exponential function of the form P(t) = a(b)^t, where t is yearssince 1900, which of the following would be a reasonable value for a?0.522.860.0351900
Answers
a represents the initial value of the function. Since the function starts at 1900, the associated population value for this year should be the answer. The answer is 0.52.
anyone know this one i was having troble
Answers
The zero of the linear function will be at (1, 0).
A linear function is the one which can be represented in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. The zero of a line is the point where the line crossed the x-axis which is also known as the x intercept. The equation of the line in slope intercept form is given as y = mx + c where m is the slope and c is the y intercept. The slope of line from points (0, 5) and (2, -5) can be found by m = -5 - 5/2 -0
m = -10/2
m = -5
Now, putting this and the point (0, 5) in y = mx + c we get
5 = -5×0 + c
=> c = 5
Now, equation of line is y = -5x + 5 and for x intercept we put y = 0
0 = -5x + 5
5x = 5
=> x = 1
=> (1, 0) which is the required point
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HELP ME WITH IS PROBLEM THANK YOU
Answers
The solution to the given expression is 10√5 - 4√10 which is the correct answer would be an option (C)
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
The given expression as:
⇒ √5(10 - 4√2)
Open the parentheses and apply the distributive property of multiplication to get,
⇒ 10√5 - 4√5√2
⇒ 10√5 - 4√(5 × 2)
⇒ 10√5 - 4√10
Therefore, the solution to the given expression is 10√5 - 4√10.
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Here are two expressions whose product is a new expression, A: 1. What could we put in the boxes to make A be a polynomial?
Answers
We are given the following product:
[tex](-2x{}^3+B)(x^n+15)=A[/tex]For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:
[tex]ax^n[/tex]We will use a constant. We will substitute the first box for "1":
[tex](-2x^3+1)(x^n+15)=A[/tex]For the second box, we need to use an exponent that is a positive whole number.
We will use 2:
[tex](-2x^3+1)(x^2+15)=A[/tex]With these values, the result of the product is a polynomial.
just 34 unless you want to help me with more?
Answers
M is the midpoint of the line segment FG.
Being the midpoint means that M divides the line in two equal halves so you know that the distance between F and M is equal to the distance between M and G, symbolically:
FM=MG
And of you add them you'll be able to calculate the length of the whole line FG
34.
Given the expressions
FM= 5y+13
MG=5-3y
We know that FM=MG, so the first step is to replace this equivalency with the given expressions. This way you'll determine an equation with one unknown y.
Once you have the equation you can clear the value of y:
[tex]\begin{gathered} FM=MG \\ 5y+13=5-3y \end{gathered}[/tex]Pass all terms with the unknown to one side of the equation and all others to the other side:
[tex]\begin{gathered} 5y+3y=5-13 \\ 8y=-8 \\ y=-1 \end{gathered}[/tex]y=-1
Now that you know the value of y, you can replace it in the given expressions to calculate the length of FG
[tex]\begin{gathered} FG=FM+MG \\ FG=(5y+13)+(5-3y) \\ FG=5y+13+5-3y \\ FG=2y+18 \\ \text{Replace with y=-1} \\ FG=2(-1)+18 \\ FG=16 \end{gathered}[/tex]The length of the line segment FG is 16 units.