Answer:
cosΘ = - [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
Given that Θ is in the third quadrant then cosΘ < 0
Given
tanΘ = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
Then 5 and 12 are the legs of a right triangle (5- 12- 13 ) with hypotenuse = 13
Thus
cosΘ = - [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{12}{13}[/tex]
Please help! Will give brainliest to correct answer! (1/3) - 50 POINTS - please no wrong answers.
Answer:
( 6, pi/6)
Step-by-step explanation:
( 3 sqrt(3), 3)
To get r we use x^2 + y ^2 = r^2
( 3 sqrt(3) )^2 + 3^2 = r^2
9 *3 +9 = r^2
27+9 = r^2
36 = r^2
Taking the square root of each side
sqrt(36) = sqrt(r^2)
6 =r
Now we need to find theta
tan theta = y/x
tan theta = 3 / 3 sqrt(3)
tan theta = 1/ sqrt(3)
Taking the inverse tan of each side
tan ^-1 ( tan theta) = tan ^ -1 ( 1/ sqrt(3))
theta = pi /6
Find the measure of the indicated angle to the nearest degree. Thanks.
Answer:
θ ≈ 40°
Step-by-step explanation:
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
In the picture attached,
Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.
tanθ = [tex]\frac{19}{23}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]
θ = 39.56
θ ≈ 40°
In 2009 the number of vehicle sales in the United States was 10,002 thousand and in 2013 it was 17,884 thousand.a. [3 pts] Determine the average rate of change (slope) from 2009 to 2013.b.
Answer:
1970.5 thousand
Step-by-step explanation:
Given
Vehicle sales in 2009 = 10,002 thousand
Vehicle sales in 2013 = 17,884 thousand
Required
Determine the average rate of change;
From the given parameters, it can be seen that the number of vehicles is a function of year
Let x represent the years and y represent the number of vehicles;
Such that;
[tex]x_1 = 2009;\ y_1 = 10,002[/tex]
[tex]x_2 = 2013;\ y_2 = 17,884[/tex]
The rate of change is calculate as follows;
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{10002 - 17884}{2009 - 2013}[/tex]
[tex]m = \frac{-7882}{-4}[/tex]
[tex]m = \frac{-7882}{-4}[/tex]
[tex]m = 1970.5[/tex]
Hence, the average rate of change is 1970.5 thousand
In △ABC,c=9, m∠B=65°, and a=105. Find b.
Answer:
b ≈ 101.52
Step-by-step explanation:
Given two sides and the angle between, the Law of Cosines is useful.
b^2 = a^2 +c^2 -2ac·cos(B)
b^2 = 105^2 +9^2 -2·105·9·cos(65°) ≈ 10307.251
b ≈ √10307.251
b ≈ 101.52
For questions 13-15, Let Z1=2(cos(pi/5)+i Sin(pi/5)) And Z2=8(cos(7pi/6)+i Sin(7pi/6)). Calculate The Following Keeping Your Answer In Polar Form. 13. z1z2 14. z2 15. z1/z2
Answer:
Step-by-step explanation:
Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;
a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))
Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }
Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }
since i² = -1
Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }
Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }
From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and sin(A+B) = sinAcosB + cosAsinB
The equation becomes
= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }
= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }
= 18{cos((41π)/30) + isin(41π)/30)) }
b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))
c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))
let A = pi/5 and B = 7pi/6
z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))
On rationalizing we will have;
= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))
= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}
= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}
From trigonometry identity; cos²B+sin²B = 1
= 16{cos(A+ B)-i(sin(A+B)}/64
= 16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64
= 16{ (cos 41π/30)-isin(41π/30)}/64
Z1/Z2 = (cos 41π/30)-isin(41π/30)/4
Answer:
13. 16(cos(41 π/30)+ isin(41 π/30))
14. Mine asked for z2 magnitude so I got 8 (magnitude is the same as modulus which is r)
15. 1/8 (cos(29 π/30)+ isin(29 π/30))
Step-by-step explanation:
13. Since we’re multiplying z1, and z2, use De Moivre’s theorem by multiplying the r values (2 and 8) and adding the theta values (π/5 and 7π/6). Adding the angle values should lead you to have 41 π/30, and the rest is self-explanatory.
14. Explanation is in the answer, just take the r value from z2 for magnitude (at least that’s what’s on my practice assignment)
15. Use De Moivre’s theorem again, this time with division, so you will divide the r values (2 divided by 8) and subtract the theta values (π/5 minus 7π/6). 2/8 simplifies to 1/8 and when subtracting with 6π/30 - 35π/30 (finding common denominators) you should get 29π/30.
Which linear function represents the line given by the point-slope equation y-8 = {(x - 4)?
O f(x)=x+4
Of(x)= x+6
O fx) = x-10
O f(x) = {x-12
Answer:
[tex]f(x) = x + 4[/tex]
Step-by-step explanation:
[tex]y - 8 = x - 4[/tex]
Add 8 to both sides to isolate the y
[tex]y = x - 4 + 8[/tex]
then you're left with y = x + 4
n
The nth term of a sequence is given by
T = -19n - 3.
(a) Which term of the sequence has a value
of -250?
b) Is-344 a term in the sequence? Why?
Answer:
a)13 b)no because at 18th term its -345
Using traditional methods, it takes 9.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 15 students and observed that they had a mean of 10.0 hours with a standard deviation of 1.6. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Answer:
Step-by-step explanation:
Null hypothesis: u = 9.5hrs
Alternative: u =/ 9.5hrs
Using the t test
t = x-u/sd/√n
Where x is 10hrs, u is 9.5, sd is 1.6 and n is 15
t = 10-9.5 / (1.6/√15)
t = 0.5 / (0.4131)
t = 1.21
In order to make a conclusion, we have to find the p value at a significance level lot 0.1. The p value is 0.2263 which is greater than 0.1. This, we will fail to reject the null hypothesis and conclude that there is not enough statistical evidence to prove that the technique performs differently than the traditional method.
Factor.
-7x2 + 49x
-7(x - 7)
01 - 7x2 + 49x)
-x(x – 7)
-7x(x – 7)
Answer:
Option 1: -7x (x - 7)
Step-by-step explanation:
Factor -7x out of -7x^2.
= -7x (x) + 49x
Factor -7x out of 49x.
= -7x (x) -7x (-7)
Factor -7x out of -7x (x) - 7x (-7).
= -7x (x - 7)
(Also I took the test and got this answer right)
help please winth this will give bralienst
Answer:
1rst way they give is CORRECT WAY
The rest of the options are the INCORRECT WAY.
Step-by-step explanation:
When you do 620*7 + 6 = 4376 is the answer you get.
When you do the other math - you do not get the same initial value.
I need help, I don’t need an explanation, just the answer
Answer:
[tex]x = 48 \: \: \: \: \: \: y = 16[/tex]
Step-by-step explanation:
[tex]y = - x + 4y[/tex]
[tex]y + x = 4y[/tex]
[tex]y + x - 4y = 0[/tex]
[tex] - 3y + x = 0[/tex]
[tex] - x + 4y = 16[/tex]
[tex] - 3y + x = 0[/tex]
[tex] - 3y = - x[/tex]
[tex]y = - \frac{1}{3} ( - 1)x[/tex]
[tex]y = \frac{1}{3} x[/tex]
[tex]4 \times ( \frac{1}{3} )x - x = 16[/tex]
[tex] \frac{1}{3}x = 16 [/tex]
[tex]x = 48[/tex]
[tex]y = \frac{1}{3} \times 48[/tex]
[tex]y = 16[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
x = 48, y = 16
Step-by-step explanation:
You are flying a kite on a line that is 350 feet long. Let's suppose the line is perfectly straight (it never really is) and it makes an angle of 65 degrees with the horizontal direction. The kite is flying at an altitude of feet.
Answer:
We can think that the line of the kite is the hypotenuse of a triangle rectangle, and the altitude is one of the cathetus of the triangle.
And we know that it makes an angle of 65° with the horizontal (i guess this is measured between the hypotenuse and the horizontal adjacent to the kite.
This angle is complementary to the top angle of our triangle rectangle, such that A + 65° = 90°
A = 90° - 65° = 25°
Then the altitude of the kite is the adjacent cathetus to this angle.
We can use the relation:
sin(A) = Adjacent cathetus/hypotenuse.
Sin(25°) = X/350ft
Sin(25°)*350ft = X = 147.9m
The kite is flying at an altitude of approximately 317.20 feet.
The situation will form a right angle triangle.
The hypotenuse of the triangle is the will be the line of the kite which is 350 ft long.
The line makes an angle of 65° with the horizontal direction. The horizontal direction is the adjacent of the triangle formed.
Using trigonometric ratio, the altitude of the kite can be found below.
The altitude of the kite is the height/ opposite side of the triangle.
Therefore,
sin 65° = opposite / hypotenuse
sin 65° = opposite / 350
cross multiply
opposite = 350 × sin 65
altitude of the kite = 350 × 0.90630778703
altitude of the kite = 317.207725463
altitude of the kite ≈ 317.20 ft
read more; https://brainly.com/question/13835041?referrer=searchResults
Lana has a friend who is deaf and uses sign language to communicate. She can
sign about 36 concepts per minute. How many concepts can she sign in a 15
minute period?
Information given:
1. 36 concepts per minute
2. The question is telling us how many concepts can she sign in 15 min period.
_________________________________________
So we know that we have to multiply to find the answer.
36x15 will give us 540 as the answer.
So the answer to your question is 540
I attached a picture for you to see how I had multiply.
Hope this helps! :)
Find the slope of the line that passes through the following points (show work) E(4, 1 2/3) and F(-2, 2/3)
Answer:
1/6
Step-by-step explanation:
The formula of a slope [tex]\frac{y2-y1}{x2-x1}[/tex] (change in y / change in x)
1. Substitute in the values
(x1, y1) = (4, 1[tex]\frac{2}{3}[/tex])
(x2, y2) = (-2, [tex]\frac{2}{3}[/tex])
([tex]\frac{2}{3}[/tex] - 1[tex]\frac{2}{3}[/tex]) / (-2 - 4)
2. Solve
[tex]\frac{2}{3}[/tex] - 1[tex]\frac{2}{3}[/tex] = -1
-2 - 4 = -6
slope = [tex]\frac{-1}{-6}[/tex] = [tex]\frac{1}{6}[/tex]
5x + y = 6
5x + 3y = -4
The y-coordinate of the solution to the system shown is
-5
-1
1/2
1
Answer:
y coordinate of the solution to the system is -5
Answer:
-5
Step-by-step explanation:
?? help out plssss ill do the thing wtv its called
Steps to solve:
1 = -4 + 3/8x
~Add 4 to both sides
1 + 4 = -4 + 4 + 3/8x
~Simplify
5 = 3/8x
~Multiply 8/3 to both sides
5 * 8/3 = 3/8x * 8/3
~Simplify
13 1/3 = x
As we look through the answer choices, we can see that none resembles any of the steps I did above but by looking at the answers for each one, the only logical answer is B since it has a final answer of x = 40/3 or 13 1/3.
Best of Luck!
The Digit 6 in which numbers repesent a value of 6 ones?
Answer:
B. 16.4
Step-by-step explanation:
Well in 16.4 the digit 6 is the first number meaning it is 6 ones.
Thus,
choice b is correct.
Hope this helps :)
How many even 3 digit positive integers can be written using the numbers 3,4,5,6,and 7?
Answer:
I got 45, but I may be wrong.
Step-by-step explanation:
When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.
To answer this question, we just have to find as many possible combinations following the guidelines provided.
334
344
354
364
374
434
444
454
464
474
534
544
554
564
574
634
644
654
664
674
336
346
356
366
376
436
446
456
466
476
536
546
556
566
576
636
646
656
666
676
736
746
756
766
776
find value of x and y plz do fast ?
Answer:
option C is the right answer
c) 70 and 60
Identify the algebraic series.
A) 10, 23, 36...... B) 4 + 8 + 16 +...... C) 100, 90, 81,...... D) 84 + 73 + 62 +.......
Answer:
Please read the answer below.
each number is the previous one less 11.
Step-by-step explanation:
A)
10, 23, 36, 36 +13 , 36 +13 +13 , 36 +13 +13+13, ...
= 10, 23, 36, 49, 62, 75, ...
each number is the sum of the previous number plus 13.
B)
4 + 8 + 16 + 2^5 + 2^6 +2^7 +2^8 + ... + 2^n
= 4 + 8 +16 + 32 + 64 + 128 +256 ...
each number is a power of 2.
C)
100, 90, 81, 81-9, 81-9-9, 81-9-9-9, ...
= 100, 90, 81, 72, 63, 54, 45, ...
each number is the previous one less 9.
D)
84 + 73 + 62 + (62-11) + (62-11-11) + (62-11-11-11) + ....
= 84 + 73 +62 + 51 + 40 + 39 + ...
each number is the previous one less 11.
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a quiz competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 2, the second goes to 7, the third goes to 4, and the last goes to 10. A) A total of 10 students won all the prizes. B) Four students won 12, 13, 14, 15, 16, or 17 prizes. C) A total of 10 prizes were won by all the students. D) Four prizes were won by 12, 13, 14, 15, 16, or 17 students.
Answer: B.
Four students won 12, 13, 14, 15, 16, or 17 prizes
Answer:
Four students won 12, 13, 14, 15, 16, or 17 prizes!
Step-by-step explanation:
What is the value of x? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
10.2 m
Step-by-step explanation:
180 - 81 - 30 = 69
law of sines
x /sin 30 = 19/sin 69
x = 10.2
A new cola company is testing to see what proportion of their cans contain at least 12 oz. If they want to be within 3% of the actual percentage, how many cans should they measure to be 90% confident
Answer: 752
Step-by-step explanation:
Given that,
Margin of error = 3% = 0.03
confidence level = 90% = 0.90
therefore from the z-table
z = 1.645
Now since no prior estimate of p is given, so we say p = 0.5
Sample size required will be
n = 1.645² × 0.5 ×(1-0.5) / 0.03² = 751.67
n = 751.67 ≈ 752
The energy transfer diagram represents the energy of a person diving into a pool. A wide arrow labeled gravitational potential energy 8000 J with a small arrow turning away from it labeled thermal energy ? J. The rest of the arrow goes forward labeled kinetic energy 7000 J. How much thermal energy is generated? 1000 J 2000 J 7000 J 15,000 J
Answer:
The amount of thermal energy that is generated is 1000 joules.
Step-by-step explanation:
Let consider the person diving into a pool as a closed system, that is, a system with only energy interaction with the surroundings. According to the First Law of Thermodynamics, which is a generalization of the Principle of Energy Conservation, the total energy of the system is neither destroyed, nor created, only transformed. The initial gravitational potential energy is transformed into translational kinetic and thermal energy. That is to say:
[tex]U_{g} - K - Q = 0[/tex]
Where:
[tex]U_{g}[/tex] - Gravitational potential energy, measured in joules.
[tex]K_{tr}[/tex] - Translational kinetic energy, measured in joules.
[tex]Q[/tex] - Thermal energy, measured in joules.
The thermal energy is now cleared:
[tex]Q = U_{g}-K[/tex]
Given that [tex]U_{g} = 8000\,J[/tex] and [tex]K = 7000\,J[/tex], the amount of thermal energy that is generated is:
[tex]Q = 8000\,J - 7000\,J[/tex]
[tex]Q = 1000\,J[/tex]
The amount of thermal energy that is generated is 1000 joules.
Answer:
1000J
Step-by-step explanation:
EDGE2020
Solve application problems using radical equations. A baseball diamond is a square that is 90 feet on each side. What is the distance a catcher has to throw the ball from home to second base?
Answer:
c=127.279
Step-by-step explanation:
c²=a²+b²
c²=90²+90²
c=√90²+90²
c=127.279 feet
1 - Fill the space blanks
If we make a sequence selecting three elements from three different elements
{1, 2, 3} and we permit overlapped elements for the sequence, then the total
number of sequences is [ ] . If we do not take into account the order, the total
number of the selections is [ ] .
I'm totally lost in this, what is overlapped elements? This is about what math content? And what is the answer? Please i need help.
Answer:
The first part is of permutations.
We are selecting 3 elements from three different elements {1,2,3}
Points given:
We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.
So when repetition is allowed and order matters, we use permutations.
Formula to compute permutation is:
Lets say n is the three elements {1,2,3}
We have to select 3 elements so r = 3
Total number of selections using permutations = [tex]n^{r}[/tex] = n × n × n
= 3³ = 3 * 3 * 3
= 27
This means if we have 3 different elements then we have have 3 choices each time for making a sequence.
Hence If we make a sequence selecting three elements from three different elements {1, 2, 3} and we permit overlapped elements for the sequence, then the total number of sequences is 27.
Step-by-step explanation:
The second part indicates combinations.
This is because the statement of the question: If we do not take into account the order.
When the order does not matter, we use combinations.
So when the order does not matter and repetition is allowed we use the following formula:
Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!
= (3 + 3 - 1) ! / 3! (3 - 1)!
= (3 + 2) ! / 3! (2!)
= 5! / 3! 2!
= 5*4*3*2*1 / (3*2*1 ) (2*1)
= 120 / 6 * 2
= 120 / 12
= 10
So these are the number of combinations of 3 elements taken 3 at a time with repetition.
The total number that will be selected in the permutations is 27.
How to calculate the permutations?Based on the information given, the total number of permutations will be:
= n³
= 3 × 3 × 3
= 27
Also, the total number of selection using combination will be:
= (3 + 3 - 1)! / 3!(3 - 1)!
= 120 / (6 × 2)
= 120/12
= 10
Learn more about permutations on:
https://brainly.com/question/1216161
2x + y = 15
x = 15 - 2y
is it no solution?
Answer:
It has a solution.
Step-by-step explanation:
Step 1: Rearrange 1st equation into slope-intercept form
2x + y = 15
y = 15 - 2x
Step 2: Rearrange 2nd equation into slope-intercept form
x = 15 - 2y
2y + x = 15
2y = 15 - x
y = 15/2 - x/2
Step 3: Rewrite systems of equations
y = 15 - 2x
y = 15/2 - x/2
Since the two lines are not parallel, they will have a solution.
What is closest to the area of this section of the garden?
Answer:
117.984ft^2
Step-by-step explanation:
To find the area of a circle the formula is PiR^2 so the area for the full 360 degree circle is. 530.929 ft^2.
Now that we know this we can use a ratio.
530.929/360=x/80
u divide out the left side and multiply it by 80.
so that shows that the area of this circle is
117.984ft^2
logx - logx - 1^2 = x - 4
Answer:
Look at the image below↓
What is the value of the expression iºxi1 x 2 x 3 xi4?
a) 1
b) -1
c) i
d) -i
Answer:
Option b.
Step-by-step explanation:
Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].
Let as consider the given expression is
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that,
[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]
Using these values, we get
[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]
[tex]=i^2[/tex]
[tex]=-1[/tex]
The value of given expression is -1.
Therefore, the correct option is b.