Find all angles 0 theta such that 0 degrees is less than or equal to theta less than or equal to 360 degrees A) cos 0 = -square root of 3/2B) sin 0 = - square root of 2/2
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ANSWER :
A. 150 degrees and 210 degrees
B. 225 degrees and 315 degrees
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} \cos\theta=-\frac{\sqrt{3}}{2} \\ \\ and \\ \\ \sin\theta=-\frac{\sqrt{2}}{2} \end{gathered}[/tex]Note that the cosine of an angle is negative if the angle is in Quadrants II and III.
Reference angles are angles in the x-axis.
So we are looking for the angles when the cosine is negative.
Recall the identity :
[tex]\cos30=\frac{\sqrt{3}}{2}[/tex]So we can say that the angle adjacent to the x-axis is 30 degrees.
The first angle (blue) is 180 less 30 degrees.
That's 180 - 30 = 150 degrees
The second angle (red) is 180 + 30 degrees.
That's 180 + 30 = 210 degrees
Therefore, we have :
A. 150 degrees and 210 degrees
For B, with the sine function :
The sine of an angle is negative if the angle is in Quadrants III and IV.
So we have angles on quadrants III and IV, of course, the angles are adjacent to the x-axis.
Recall the identity :
[tex]\sin45=\frac{\sqrt{2}}{2}[/tex]So we can say that the angle is equal to 45 degrees.
The first angle (blue) is 180 + 45 degrees.
That's 225 degrees
The second angle is 360 less 45 degrees.
That's 360 - 45 = 315 degrees
So we have :
B. 225 degrees and 315 degrees
Related Questions
8select all correct answers what is 9,150, 000, 000, 000, 000, 000 Express in scientific notation
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the numbers should be
[tex]9.15\times10^{18}[/tex]or
[tex]9.15E18[/tex]because you move the point 18 places to obtain 9.15(the dot is initially at the end of the number)
Mitch has already run 16 miles on his own, and he expects to run 1 mile during each track practice. How many track practices would it take for Mitch to run 23 miles?practices.
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If he expects to run 1 mile during each track practice, the ratio of speed would be 1 mile per track. Knowing this, we just have to divide to find the answer.
[tex]\frac{23}{1}=23[/tex]Therefore, Mitch has to take 23 track practices.Find the slope of the line passing through the points (-3, 3) and (5, 9).
Answers
Answer:
3/4
Step-by-step explanation:
plot the points on the graph use those points do rise over run 3= rise 4= run
Answer:
Slope = 3/4 OR 0.75x
How much salsa is missing from the can below? Hint: You may need to subtract the heights. 5 cm for 10 cm
Answers
Answer
Amount of salsa missing = 471.3 cm³
Explanation
The volume of a cylinder is given as
Volume = πr²h
π = 3.142
For the missing salsa,
r = radius of the cylinder = 5 cm
h = height of the missing salsa = 10 - 4 = 6 cm
Volume = πr²h
Volume = (3.142) (5²) (6) = 471.3 cm³
Hope this Helps!!!
1. a/6 = 15/2 2. 10/7 = 8/kuse the cross property to solve the proportion for both problems
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just need to answers to double check my work :)
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Bank account 1: $3000 (5% interest)
Bank account 2: $7000 (4% interest)
At the end of 1 year, the interests are:
Bank 1: 5% of $3000 = 5*3000/100
Interest 1 = $150
Bank 2: 4% of $7000 = 4*7000/100
Interest 2 = $280
The total interest is: Total = Interest 1 + Interest 2 = 150 + 280
Total = $430
The total deposited is $3000 + $7000 = $10 000
If the total interest is $430, then the percent is:
430*100/10 000 = 4.3%
Part 1 of 4Suppose the data represent the inches rainfall in April for a certain city over the course of 20 yearsGiven the quartiles Q1= 1.970, Q=3.380, and Q3 = 4.770, determine the lower and upper fences. Are there any outliers, according to this criterion?0.330.771.251.541.822.122.452.883.053.233.533.844.064.534.684.865.225.435.816.27
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For this problem, we were given a certain dataset, as well as the quartiles Q1, Q, and Q3. From this information, we need to determine the lower and upper fences.
The fences are given by:
[tex]\begin{gathered} \text{lower}=Q_1-(1.5)\cdot\text{IQR} \\ \text{upper}=Q_3+(1.5)\cdot\text{IQR} \end{gathered}[/tex]Therefore, we need to calculate the value of the IQR, which is the subtraction between Q3 and Q1.
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1=4.77-1.97 \\ \text{IQR}=2.8 \end{gathered}[/tex]With this, we have all the data to determine the lower and upper fences. The calculations are shown below:
[tex]\begin{gathered} \text{lower}=1.97-(1.5)\cdot2.8 \\ \text{lower}=-2.23 \\ \text{upper}=4.77+\cdot(1.5)\cdot2.8 \\ \text{upper}=8.97 \end{gathered}[/tex]Since there aren't any values that are lower than the lower fence or higher than the upper fence, we don't have any outlier on this data.
Try it
Use the graph and table to write the equation that
describes the line graphed.
5
y
X
4.
1
3
-2
N
2
2
-1
الم
3
0
3
4
5
4
-5
-3 2-1
- 1
5
-2
2
-3
4
The equation of the line is
y = x + 1
y=-x+1
y = -x +3
y = x + 3
Done
Answers
Given:
Find-:
Equation of a line.
Sol:
General equation of a line.
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m=\text{ slope} \\ \\ m=\frac{x_2-x_1}{y_2-y_1} \\ \\ c=\text{ y-intercept.} \end{gathered}[/tex]Choose any two-point then:
[tex]\begin{gathered} (-2,1)=(x_1,y_1) \\ \\ (-1,2)=(x_2,y_2) \end{gathered}[/tex]So the slope of the line is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{-1-(-2)} \\ \\ m=\frac{1}{-1+2} \\ \\ m=1 \end{gathered}[/tex]So the equation become:
[tex]\begin{gathered} y=mx+c \\ \\ y=(1)x+c \\ \\ y=x+c \end{gathered}[/tex]So y-intercept is:
[tex]\begin{gathered} (x,y)=(-2,1) \\ \\ y=x+c \\ \\ 1=-2+c \\ \\ c=1+2 \\ \\ c=3 \end{gathered}[/tex]So final equation of a line:
[tex]\begin{gathered} y=mx+c \\ \\ m=1 \\ \\ c=3 \\ \\ y=x+3 \end{gathered}[/tex]Equation of line is y = x + 3
1. Express each of the following complex numbers in the form of a + ib a) (2 + 5i) + (1-i)
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Given:
(A)
[tex](2+5i)+(1-i)[/tex]Solve:
[tex]undefined[/tex]$0.42 x 0.5 helppp...
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First, multiplicate the numbers ignoring the decimals:
Rewrite the product with 3 decimal places. (since there are 3 decimal places in both numbers)
0.210 = 0.21
How wide is a rectangular strip of land with length 1 1/2 kilometers and area 3/4 square kilometers?
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Answer: The wideness of the rectangular strip of land is 1/2 km
The length of the rectangular strip = 1 1/2 kilometers
The area of the rectangular strip = 3/4 square kilometers
Area of a rectangle = Length x width
Let the width of the rectangular strip = x
[tex]\begin{gathered} \text{Length = 1}\frac{1}{2}\text{ km} \\ \text{Convert the length to an improper fraction} \\ \frac{(1\text{ x 2) + 1}}{2} \\ \frac{2\text{ + 1}}{2} \\ \frac{3}{2}\text{ km} \\ \text{ Since, area = 3/4 } \\ \frac{3}{4}\text{ = }\frac{3}{2}\cdot\text{ x} \\ \frac{3}{4}\text{ =}\frac{3x}{2} \\ \text{Cross multiply} \\ 3\text{ x 2 = 3x }\cdot\text{ 4} \\ 6\text{ = 12x} \\ \text{Divide both sides by 12} \\ \frac{12x}{12}\text{ = }\frac{6}{2} \\ x\text{ = }\frac{1}{2}\text{ kilometer} \end{gathered}[/tex]The widenes of the rectangular strip is 1/2 km
Sophie says, "To find 8 X 8, I can find 8 X (4 + 4)."Do you agree? Explain.3rd grade subject
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Step 1
Given:
[tex]8\times8[/tex]Required:
[tex]\begin{gathered} To\text{ agre}e\text{ that if I can find 8}\times(4+4)_{} \\ \text{then I can find 8}\times8 \end{gathered}[/tex]Step 2
Find out if you agree or disagree
[tex]\begin{gathered} 8\times(4+4) \\ =\text{ (8}\times4)+(8\times4) \\ =\text{ 32 + 32 = 64} \\ or \\ 8\times(4+4) \\ \text{But (4+4) = 8} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ 8\times(4+4)\text{ = 8}\times8 \\ \text{Therefore, To find 8}\times8,\text{ I can find 8 }\times(4+4) \end{gathered}[/tex]Hence, I agree.
33. Suppose that the scores on a statewide standardized test are normally distributed with a mean of 78 and a standard deviation of 3. Estimate the percentage of scores that were (a) between 75 and 81. % (b) above 87. % (c) below 72. % (d) between 75 and 84. %
Answers
Given the scores on a statewide standardized test are normally distributed
Mean = μ = 78
Standard deviation = σ = 3
Normalize the data using the z-score by using the following formula and chart:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Estimate the percentage of scores of the following cases:
(a) between 75 and 81
so, the z-score for the given numbers will be:
[tex]\begin{gathered} 75\rightarrow z=\frac{75-78}{3}=\frac{-3}{3}=-1 \\ 81\rightarrow z=\frac{81-78}{3}=\frac{3}{3}=1 \end{gathered}[/tex]As shown, the percentage when (-1 < z < 1) = 68%
(b) above 87
[tex]87\rightarrow z=\frac{87-78}{3}=\frac{9}{3}=3[/tex]The percentage when (z > 3) = 0.5%
(c) below 72
[tex]72\rightarrow z=\frac{72-78}{3}=\frac{-6}{3}=-2[/tex]The percentage when (z < -2) = 0.5 + 2 = 2.5%
(d) between 75 and 84
[tex]\begin{gathered} 75\rightarrow z=\frac{75-78}{3}=-\frac{3}{3}=-1 \\ 84\rightarrow z=\frac{84-78}{3}=\frac{6}{3}=2 \end{gathered}[/tex]The percentage when ( -1 < z < 2 ) = 68 + 13.5 = 81.5%
Translate the figure 7 units left and 5 units down.Plot all of the points of the translated figure.You may click a plotted point to delete it.12 35 6 7 8 9 10
Answers
Explanation:
This translation is:
[tex](x,y)\rightarrow(x-7,y-5)[/tex]In the graph we have 3 points. The points and their translations are:
[tex](1,6)\rightarrow(-6,1)[/tex][tex](8,9)\rightarrow(1,4)[/tex][tex](9,1)\rightarrow(2,-4)[/tex]Answer:
The original figure is in black and the image is in pink:
In each equation, which move would you make first? Why?466-3) 202(m+10) -- 4(m-15)5(x + 2) = 3x - 82x 10- 21% 15)432212345
Answers
In each equation, which move would you make first?
[tex](1)4x-12=20[/tex][tex](2)2m+20=4m-60[/tex][tex](3)5x+10=3x-8[/tex][tex](4)2x+10=2x+10[/tex][tex](5)4x-3x+6=21[/tex]In ∆PQR, the measure of
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The trigonometric ratio sin(θ) which applies to right triangles, is given by
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically,
Therefore, the ratio that represents the sine of angle P is
[tex]\sin (P)=\frac{45}{53}[/tex]Which input in this table is incorrect?Cost ofTax onItem Item1.00.082.00 .163.00 .246.00 .5610.00.80Noter all entries are in dollarsTotal Costof Item1.082.163.247.5610.80A. 6.00B. 3.00C. 2.00D. 10.00I
Answers
From the table, we can observe that the formula for the total cost of item is
[tex]\text{Total cost of item = Cost of item + Tax on item}[/tex]From the data in the table, cost of item 6.00 has the input incorrect because the sum of the cost of its item and tax on the item is,
[tex]\text{Total cost of item=6.00+56=6.56}[/tex]but the total cost was incorrectly inputed as 7.56.
Hence, the correct option is Option A.
may I please have someone to help me with Apcalc.
Answers
The given expression is,
[tex]y=6x^5-x+10[/tex]We have the rule,
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]Differentiating with respect to x, we have,
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(6x^5-x+4) \\ \text{ = 5}\times6(x^{5-1})-1 \\ \text{ =30x}^4-1 \end{gathered}[/tex]The answer is
[tex]30x^4-1[/tex]Bill buys a weekly bus pass for $20 it cost Bill $2.75 each way to ride the bus from home to work and back Bill rides the bus 5 days a week how much money does he save with the weekly pass $5 $7.50 or $10
Answers
If he walks 5days a week, then ride to and fro is equal to 10
If it cost him $2.75 each way to ride from home to work and back,
Then; The cost for ride in a week = 10 x $2.75 = $27.5
The amount save with the weekly pass = $27.5 - $20 = $7.50
Hence he saved $7.50 with the weekly pass
determine how many miles from the terminal the two types of pipe should meet so that the total cost is minimized
Answers
ANSWER:
24 miles
STEP-BY-STEP EXPLANATION:
The first thing is to make a graph of the situation, like this:
Therefore, the function of total cost will be:
[tex]C(x)=143000\cdot\sqrt[]{x^2+12^2}+55000\cdot(29-x)[/tex]To minimize we must calculate the derivative of the function, like this:
[tex]\begin{gathered} C^{\prime}(x)=\frac{d}{dx}143000\cdot\sqrt[]{x^2+12^2}+55000\cdot(29-x) \\ C^{\prime}(x)=\frac{143000d}{\sqrt[]{x^2+144}}-55000 \end{gathered}[/tex]Now we set the derivative equal to 0 and solve for d, like this:
[tex]\begin{gathered} \frac{143000d}{\sqrt[]{x^2+144}}=55000 \\ 143000x=55000\sqrt[]{x^2+144} \\ 143^2x^2=55^2\cdot(x^2+144) \\ 20449x^2=3025x^2+435600 \\ 20449x^2-3025x^2=435600 \\ 17424x^2=435600 \\ x^2=\frac{435600}{17424} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]Distance from terminal the two types of pipe meet is 29 - x, therefore would be:
[tex]\begin{gathered} d=29-5 \\ d=24\text{ miles} \end{gathered}[/tex]Question 1 (1 point)RATEY is a way of graphing rational functions.TrueFalse
Answers
Given the following question:
The given statement is indeed true. RATEY is a way to graph rational functions and is often referred to as a graph organizer which you factor the numerator and the denminator should be c
Denise found a job listed in the classified section that pays a yearly salary of $51K.What is the weekly salary based on this annual salary?
Answers
The yearly salary is $51k
1 year = 12 months
The slary for 12 months = $51k
Since,
1 year = 52 weeks
That means
Salary of Denise in 52 weeks = $51k
Now to find the salary of denise in one week, we divide the total salary in 52 weeks by the number of weeks
[tex]\begin{gathered} \text{ Salary of Denise in One w}eek\text{ =}\frac{Salary\text{ in 52 w}eeks}{Total\text{ number of w}eeks} \\ \text{Salary of Denise in One w}eek\text{ =}\frac{51}{52} \\ \text{Salary of Denise in One w}eek\text{ =0.980K Dollars} \end{gathered}[/tex]So, the salary of Denise on weekly based is $0.980 K
C(t) = 2(t − 4)(t + 1)(t − 9)(t, C(t)) = (smallest t-value)(t, C(t)) = (t, C(t)) = (largest t-value)
Answers
Explanation
Given the function
[tex]C(t)=2(t-4)(t+1)(t-9)[/tex]The t values becomes
[tex]\begin{gathered} (t-4)=0\Rightarrow t=4 \\ (t+1)=0\Rightarrow t=-1 \\ (t-9)=0\Rightarrow t=9 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} (-1,0) \\ (4,0) \\ (9,0) \end{gathered}[/tex]B ( a little 3 on the top) - 2ac + d (a little two on the top) evaluate this polynomial if a=2,b= -3,c= 4 and d = -5.
Answers
b³ - 2ac + d²
a = 2
b = -3
c = 4
d = -5
In order to evaluate the given polynomial, we need to replace each letter by its corresponding value:
b³ - 2ac + d²
(-3)³ - 2 * 2 * 4 + (-5)²
(-3) * (-3) * (-3) - 4 * 4 + (-5) * (-5)
9 * (-3) - 16 + 25 , because the product of two negative numbers equals a positive number
-27 - 16 + 25
-27 + 9
-18
The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d=4n-2, where n is the length (in inches) of the nail.A) Solve the equation for n.B) use the equation from part a) to find the length of nails with the following penny sizes: 3, 6, and 10.
Answers
Given: The penny size d is given by the equation
[tex]d=4n-2[/tex]where n is the length of the nail.
Required: a) To solve the equation for n
b) To use the equation to find out the length of the nail with the following penny sizes: 3, 6, and 10.
Explanation: The given equation can be solved for n as follows
[tex]\begin{gathered} d-4n=-2 \\ -4n=-2-d \\ 4n=2+d \\ n=\frac{2+d}{4} \end{gathered}[/tex]Now putting the value of d=3 we get
[tex]\begin{gathered} n=\frac{2+3}{4} \\ n=\frac{5}{4} \end{gathered}[/tex]Again putting d=6 we get
[tex]n=\frac{2+6}{4}[/tex][tex]\begin{gathered} n=\frac{8}{4} \\ n=2 \end{gathered}[/tex]Finally putting d=10 we get
[tex]\begin{gathered} n=\frac{2+10}{4} \\ n=3 \end{gathered}[/tex]Final Answer: a) The equation for n is
[tex]n=\frac{2+d}{4}[/tex]b) The length of the nail with penny sizes 3,6, and 10 is 5/4, 2, and 3 respectively.
Can you help me draw the loci fitting this description? A circle that is concentric to the given circle and that has a radius that is d units longer than that of the given circle.
Answers
In the previous image you can identify two concentric circles. One of them has a radius that is d units longer that the radius of the smaller circle.
The diameter of a circle is 20 inches. What is the area?Give the exact answer in simplest form.___ square inches.
Answers
Answer
Area = 314 square inches
Explanation
The area of a circle is given as
Area = πr²
π = pi = 3.14
r = radius of the circle = ½ (Diameter) = ½ (20) = 10 inches
Area = πr²
Area = 3.14 × (10²)
Area = 314 square inches
Hope this Helps!!!
Find the area of a regular octagon whose radius is 15yds and the side length is 8yds.
Answers
Problem
Find the area of a regular octagon whose radius is 15yds and the side length is 8yds.
Solution
The area is given by:
A= 1/2 Perimeter* Apothem
The perimeter is:
P= 8*8 yd = 64 yd
And the area would be:
A= 1/2 * 64 yd * 15 yd= 480 yd^2
select the correct answer Brenda has a square shaped photo frame if the area of the square frame is 123 square inches which statement is true
Answers
Since the shape of the frame is a square we know that its area is given as:
[tex]A=l^2[/tex]where l is the length of each side, plugging the value of the area into the equation and solving for l we have:
[tex]\begin{gathered} 123=l^2 \\ l=\sqrt[]{123} \\ l\approx11.09 \end{gathered}[/tex]Therefore we notice that the length of the sides is between 11 and 12 inches, hence the answer is C.
Answer: The length of the photo frame is between the 11 inches and 12 inches.
Step-by-step explanation: 123 square root = 11.0905
answer choices for the first one:reflected across the y-axisreflected across the line y=xrotated 180 degrees about the originanswer choices for the second one:reflected across the x-axistranslated 3 units downrotated 90 degrees counterclockwise about the originanswer choices for the third one:both rigidnot both rigidanswer choices for the last one:congruentnot congruent
Answers
The first transformation can be:
- Reflected across the y-axis: seeing in the graph, the y-axis is not a reflection axis.
- Reflected across the line y=x: it could be, but it is not reflected, as the points are not equally distance and perpendicular to the line y=x, as if they were reflected.
(we can conclude looking at both triangles that there is not reflection, but a rotation).
- Rotated 180 degrees about the origin: this is the right answer. We can draw a line between each point and the origin, and if it is rotated 180 degrees, we get the transformed point.
Answer first one: Rotated 180 degrees about the origin.
The second transformation can be:
- Reflected across the x-axis: not right. The triangle is not reflected but translated.
- Translated 3 units down: This is the right answer. The triangle is translated.
- Rotated 90 degrees counterclockwise about the origin: The triangle is not rotated.
Answer second one: Translated 3 units down.
Third and fourth options.
As the triangles are not scaled, the transformations are both rigid and the resulting triangles are congruent (equal angles and sides).