Answer:
[tex]r^2 sin2\theta = 12[/tex]
Step-by-step explanation:
Given
[tex]xy = 6[/tex]
Required
Get polar equivalent
Polar coordinate [tex](r, \theta)[/tex] and rectangular coordinate [tex](x,y)[/tex] are related in such a way that:
[tex]x = rcos\theta[/tex] and [tex]y = rsin\theta[/tex]
So, substitute [tex]x = rcos\theta[/tex] and [tex]y = rsin\theta[/tex] in [tex]xy = 6[/tex]
[tex]rcos\theta * rsin\theta = 6[/tex]
This can be rewritten as:
[tex]r * cos\theta * r * sin\theta = 6[/tex]
Reorder
[tex]r * r * cos\theta * sin\theta = 6[/tex]
[tex]r^2 * cos\theta * sin\theta = 6[/tex]
Multiply both sides by 2
[tex]2 * r^2 * cos\theta * sin\theta = 6 * 2[/tex]
[tex]2 * r^2 * cos\theta * sin\theta = 12[/tex]
Reorder
[tex]r^2 * 2 * cos\theta * sin\theta = 12[/tex]
[tex]r^2 * 2cos\theta sin\theta = 12[/tex]
In trigonometry:
[tex]sin2\theta = 2sin\theta cos\theta = 2cos\theta sin\theta[/tex]
So, the expression becomes
[tex]r^2 * sin2\theta = 12[/tex]
[tex]r^2 sin2\theta = 12[/tex]
Hence, the equivalent of [tex]xy = 6[/tex] is [tex]r^2 sin2\theta = 12[/tex]
It is known that 10% of the UNIVERSITY students own their own car. If a random sample of 10 students is taken, what is the probability that at most 2 have their own vehicle?
Probability of students having their own vehicle
= 2/10
= 1/5
if i have 1000 dollars and lose 1000 dollars how much do i have left 100 points
The mathematical answer would happen to be... 0
Answer:
0
Step-by-step explanation:
PICTURE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
Because WY⊥YZ and WY⊥WV ⇒ WV║YZ ⇒ ∠YZX ≅ ∠WVX ⇒ ΔXWV ~ ΔXYZ (AAA similarity theorem)
Can you help with the 2 that are not correct?
Answer:
MPO=MNO
NPO=MNP
Step-by-step explanation:
MPO=MNO because MPO opposite angles of a parallelogram are congruent.
MNO is the top right angle of the parallelogram and so the opposite side of that is MPO or OPN whatever way you want to write it.
NPO=MNP because they are alternate interior angles. (If you don't understand what that means I can come back and explain it)
Sales of video games and consoles fell from $1.15 million to $1.03 million in 1 year. Find the percent decrease.
Answer:100 times 7
Step-by-step explanation: because
For the function y = 7 − 3x, what is the ordered pair for x = 5?
9514 1404 393
Answer:
(x, y) = (5, -8)
Step-by-step explanation:
The value of y is found by evaluating the equation for x=5.
y = 7 -3(5) = 7 -15 = -8
For x = 5, y = -8. As an ordered pair, this is (x, y) = (5, -8).
Michael owns dogs, hamsters and fish in the ratio 2:3:6
If he has 6 hamsters, how many pets does he have?
Answer:
11
Step-by-step explanation:
I think you just add the ratios together.
Use Newton's method to approximate the given number correct to eight decimal places. 4√73
Answer:34.17601498.
Step-by-step explanation:
Newton's method of approximation is used to approximate values.
The value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
Let the number be x.
So, we have:
[tex]\mathbf{x = 4\sqrt{73}}[/tex]
Square both sides
[tex]\mathbf{x^2 = 1168}[/tex]
Subtract 1168 from both sides
[tex]\mathbf{x^2 - 1168 = 0}[/tex]
Express as a function
[tex]\mathbf{f(x) = x^2 - 1168 }[/tex]
Set x1 to 73/2.
So, we have:
[tex]\mathbf{x_1 = \frac{73}{2} = 36.5}[/tex]
Where:
[tex]\mathbf{x_{n+1} = x_n- \frac{x_n^2-1168}{2x_n}}[/tex]
So, we have:
[tex]\mathbf{x_{1+1} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
[tex]\mathbf{x_{2} = x_1- \frac{x_1^2-1168}{2x_1}}[/tex]
This gives
[tex]\mathbf{x_{2} = 36.5- \frac{36.5^2-1168}{2 \times 36.5}}[/tex]
[tex]\mathbf{x_{2} = 34.25}[/tex]
[tex]\mathbf{x_{3} = x_2- \frac{x_2^2-1168}{2x_2}}[/tex]
[tex]\mathbf{x_{3} = 34.25- \frac{34.25^2-1168}{2 \times 34.25}}[/tex]
[tex]\mathbf{x_{3} = 34.1760948905}[/tex]
[tex]\mathbf{x_{4} = x_3- \frac{x_3^2-1168}{2x_3}}[/tex]
[tex]\mathbf{x_{4} = 34.1760948905- \frac{34.1760948905^2-1168}{2\times 34.1760948905}}[/tex]
[tex]\mathbf{x_{4} = 34.1760149814}[/tex]
[tex]\mathbf{x_{5} = x_4- \frac{x_4^2-1168}{2x_4}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149814- \frac{34.1760149814^2-1168}{2\times 34.1760149814}}[/tex]
[tex]\mathbf{x_{5} = 34.1760149813}[/tex]
The values of x4 and x5 are the same up till the 8th decimal place.
Hence, the value of [tex]\mathbf{4\sqrt{73}}[/tex] is 34.17601498
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Computer use.
A random sample of 197 12th-grade students from across the United States was surveyed, and it was observed that these students spent an average of 23.5 hours on the computer per week, with a standard deviation of 8.7 hours. If we plan to use these data to construct a 99% confident interval, the margin of error will be approximately.
(a.) 0.07
(b.) 0.62
(c.) 1.6
(d.) 8.7
Answer:
The margin of error will be approximately =
(c.) 1.6
Step-by-step explanation:
Sample of 12th-grade students = 197
Average hours spent on computer per week = 23.5 hours
Total hours spent = 4,625 (197 * 23.5) hours
Standard deviation = 8.7 hours
Confidence interval = 99%
Square root of sample size = [tex]\sqrt{x}[/tex] = 14.04
Standard deviation/square root of sample size = 8.7/14.04 = 0.6196
Z value at 99% confidence = 2.58
Margin of error = 0.6196 * 2.58
= 1.59857
= 1.6
This question can be determined by the concept of standard deviation. The margin of 1.6 error will be approximately.
Given:
Random sample of 12th-grade students = 197
Average hours spent on computer per week = 23.5 hours
Therefore,
Total hours spent by 12th grade students = [tex]\bold{(197 \times23.5=4629.5)hours}[/tex]
Standard deviation = 8.7 hours (Given)
Confidence Interval =99% (Given)
Square root of random sample size = = 14.04
[tex]\bold{\dfrac{Standard\: deviation}{Square\: root\: of\: sample\: size} =\dfrac{8.7}{14.04 } = 0.6196}[/tex]
Therefore,
Z value at 99% confidence = 2.58
Margin of error = [tex]0.6196 \times2.58[/tex]
= 1.59857 error
= 1.6 error
Thus, the correct option is (c) 1.6 error.
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If the ages in a classroom were 11, 12, 12, 13, 13, 14 - what would the median age be if you added someone that was 10 years old?
Answer: 12 years old
Step-by-step explanation:
10,11,12,12,13,13,14
The middle in these numbers is 12
Solve this equation.
[tex]\frac{x + 4}{6x} = \frac{1}{x}[/tex]
A. x = -2
B. x = 0, -2
C. x = 2
D. x = 0, 2
Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
Answer:
The correct option is a. Amy’s balance would be greater than Hank’s in the end.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Amy invested $500 per month in a 401k that earned 6% annual return for 40 years. Hank invested $1,000 per month in a 401k that also earned 6% annual return, but for 20 years. Which of the following would be true?
a. Amy’s balance would be greater than Hank’s in the end.
b. Amy’s balance is $5,142 and Hank’s balance is $3,207.
c. Hank’s balance would be greater than Amy’s in the end.
d. The investment and balance would be the same.
e. None of these are true
The explanation to the answer is now given as follows:
The balance in the end for each can be determined using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where;
For Amy:
FV = Future value or balance in the end = ?
M = Monthly investment = $500
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 40 years * 12 months = 480
Substituting the values into equation (1), we have:
FV = $500 * (((1 + 0.005)^480 - 1) / 0.005)
FV = $500 * 1,991.49
FV = $995,745.37
Therefore, Amy’s balance would be $995,745.37 in the end.
For Hank:
FV = Future value or balance in the end = ?
M = Monthly investment = $1,000
r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
n = number of months the investment will be made = 20 years * 12 months = 240
Substituting the values into equation (1), we have:
FV = $1,000 * (((1 + 0.005)^240 - 1) / 0.005)
FV = $1,000 * 462.04
FV = $462,040.90
Therefore, Hank’s balance would be $462,040.90 in the end.
Conclusion
Since Amy’s balance of $995,745.37 is greater than Hank’s balance $462,040.90, it therefore implies that the correct option is a. Amy’s balance would be greater than Hank’s in the end.
anybody understand this ? please help me .
Answer:its a or b
Step-by-step explanatio
Answer:
The answer is (2)
Step-by-step explanation:
We know that to the distance between two numbers on a number line, we subtract the smaller number from the larger number. For instance, the difference between [tex]5[/tex] and [tex]3[/tex] is simply [tex]5-3[/tex], which is [tex]2[/tex]. With that being said, variables such as [tex]p[/tex] or [tex]q[/tex] differ from a question to another. Sometimes, the [tex]p[/tex] is larger, but sometimes the [tex]q[/tex] is. If we don’t know which one is which, we can subtract them in any order and take the absolute value of that result. If the result of subtraction is positive, great! The absolute value of that is still positive ([tex]5-3=2\\|5-3|=2[/tex]) If it’s not, now it is! (e.g., [tex]|3-5|=2[/tex]! Therefore, the answer is (2) [tex]|p-q|[/tex].
Find the value of x in the triangle shown below.
X=?
Answer:
68
Step-by-step explanation:
Given triangle is an isoceless 56=56
So
X+56+56=180
X=180-112
X=68
So value is X is 68
Describe two differences in the atomic structure of nitinol and the atomic structure of either nickel or titanium that result in different physical properties of the elements used to make nitinol. CAN ANYONE HELP, PLEASE!!!!
Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
What is nitinol?Nitinol is an alloy containing an equal quantity of elements of nickel and titanium.
It is a superelastic alloy and has shape memory capacity.
It retains its shape after reforming into another shape by an increase in temperature.
Thus, the difference is that Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
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Expand and simply (x + 3) (x + 5)
What value of θ makes the statement true?
cos(θ)=sin(θ/3−10)
The required value of θ for the trigonometric function cos(θ)=sin(θ/3-10) is 60°.
What are trigonometric functions?The basic Trigonometric functions are sine, cosine, tangent, secant, cosecant and cotangent.
The given equation is,
cos(θ)=sin(θ/3-10) (1)
To find the value of θ,
Change the whole equation into one trigonometric function,
Since, cos(θ)=sin(90-θ)
Substitute this value in equation (1)
sin(90-θ)=sin(θ/3-10)
⇒90-θ=θ/3-10
⇒4θ/3=80
⇒θ=60
The value of θ is 60°.
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50 points!!! Please Help!!! Will give Brainliest!!!
THAT IS not 50 points, that is just 25 points
Answer:
okay but i dont see the problem
Step-by-step explanation:
the process of finding factors
For every left-handed person, there are about 4-right handed people. If there are 30 students in a class, predict the number of students who are right-handed.
Answer:
There are 24 right handed students
Step-by-step explanation:
This is a ratio question so it would be represented as 1:4.
First you would do 1 + 4 which is 5.
Then do 30 ÷ 5 which is 6.
Finally multiply 6 by 4 and 1.
So 6 × 4 × 1 is 24.
So there are 24 students who are right handed.
Hope this makes sense!
Death Valley, located in California, is the lowest place in North America. It is 282 feet below sea level, or -282 feet. The Dead Sea, in Asia, is the lowest place on Earth. It's elevation is approximately 4.82 times the elevation of Death Valley. What is the approximate elevation of the Dead Sea?
Answer:
1359.24
plz mark brainly
Step-by-step explanation:
Convert 86 to base 5.
Answer:
321
Step-by-step explanation:
Conversion of 86 to base 5 will be done through base 10 to base 5 and it will be (321)₅.
How to convert any number into base 10?To convert any number to base 10 we have to multiply its unit digit by 10⁰ and its tenth digit by 10¹.
After it, we need to add it. It will give us a number of the 10 bases.
Conversion of any 10 base number into base 5
To convert any number to base 5 we need to divide by 5 and write the remainder each time thus we need to write the quotient from down to up.
Converting 86 to base 10
⇒ 8ₓ10¹ +8ₓ[tex]10^0[/tex]
⇒ 86₁₀
Converting 86₁₀ into 86₅
When the number 86 is converted in a base of 5 will be (321)₅
Since we need to go down to up to 321₅ will be the correct answer.
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There are 60 students in a classroom, 50% of the students are
boys. 30% of the boys and 60% of the girls want to buy the
new textbook. How many students want to buy the new
textbooks?
___ students
Answer:
28
Step-by-step explanation:
If 50% of students are boys that means there are 30 boys and 30 girls. Then if 30% of boys are 10 and 60% of girls are 18. You add 18+10 and that gives you 28.
Josh rents a kayak at a nearby state park. He pays a flat rate of $12.99 plus $3.75 for
each hour that he spends in the water. How much did Josh spend if he was on the river
for 4 hours?
Answer:
Whats a kayak?
Step-by-step explanation:
After 10 years, the principal on this mortgage is $136,683. How much of the next payment will go towards interest
Answer: 13,668 i think.
Which of the following equations does not have a solution? Check all that
apply.
A. 7x + 1 = 2x + 6
B. 2x + 12 = 4x
C. 12x = x
D. 6x + 5 = 5x - 10
E. 5x + 6 = 5x - 6
F. x+8 = 3(x + 2)
G. 6(x - 4) + 2x = 8x + 12
H. X= x-1
Answer:
E, G, H
Step-by-step explanation:
...,.....................
Fraction of 7/12 in drawing
Answer:
I dont think we can answer that
Answer: Fraction of 7/12 equals to 58
Step-by-step explanation: When we have a fraction with a denominator of 100 , the numerator gives us the percent, since the word "percent" literally means per 100 .
Identify the following numerical values:
The average height of 10 plants grown with rain water in a study of the effects of all
plants grown with rain water.
Answer:
THE CORRECT ANSWER IS STATISTIC
Step-by-step explananation:
I TRUSTED THE DUDE WHO SAID PARAMETER AND I GOT THE QUESTION WRONG
edit: im pretty sure the answer that said parameter was deleted. Nice!
3) A local school district has 4512 students this year. The student population is declining by 2.5% per year. How many students will the school have next year
Answer:
Number of students(n1)= 4,402
Step-by-step explanation:
Giving the following information:
Number of students= 4,512
Declining rate= 2.5%
To calculate the number of students next year, we need to use the following formula:
Number of students (n+x)= number of students (n0) / [(1+declining rate)^(n+x)
x= number of years
Number of students(n1)= 4,512/1.025
Number of students(n1)= 4,402
Find the area of the shape shown below
Answer:
18 MARK AS BRAINLIEST OR ELSE!!!!
Step-by-step explanation:
area = 1/2h(sum of bases)
area = 1/2x3(3+9)
area = 1/2 of 36
area = 18