Answers
Answer:
c = 4√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 30
Opposite = 2√2
Hypothenus = c =?
We can obtain the value of c by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 30 = 2√2 / c
½ = 2√2 / c
Cross multiply
c = 2 × 2√2
c = 4√2
Therefore, the value of c is 4√2.
Related Questions
The vertex form of the equation of a parabola is y =
standard form of the equation?
Y=1/2(x - 4)^2 +13. What is the
O A. y-2x2-8x+29
O B. y=zx2 - 4x +21
O C. y=1* -8x+21
O D. y - 4x2 - 4x +29
Answers
Answer:
Step-by-step explanation:
y = ½(x-4)² + 13
y = ½(x² - 8x + 16) + 13
y = ½x² - 4x + 21
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answers
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
The first term of an A.P is -8.the ratio of the 7th term to the 9th term is 5:8.calculate the numbers
Answers
Answer:
The 7th term is 10 and the 9th term is 16
(and the common difference d = 3)
Step-by-step explanation:
If by calculate the numbers, you mean the 7th term and 9th term, first, you will determine the common difference.
The nth term of an A.P is given by the formula
Tₙ= a+(n-1)d
Where Tₙ is the nth term
a is the first term
and d is the common difference
From the question,
a = -8
T₇ : T₉ = 5:8
From the formula
T₇ = a + (7-1)d = a + 6d
and T₉ = a + (9-1)d = a + 8d
Then.
a + 6d : a + 8d = 5:8
But a = -8
∴ -8 + 6d : -8 + 8d = 5:8
We can write that
(-8 + 6d) / (-8 + 8d) = 5/8
Cross multiply
8(-8+6d) = 5(-8+8d)
-64 + 48d = -40 + 40d
48d - 40d = -40 + 64
8d = 24
d = 24/8
d = 3
∴ The common difference is 3
Now, for the 7th term
From
T₇ = a + 6d
T₇ = -8 + 6(3)
T₇ = -8 + 18
T₇ = 10
and for the 9th term
T₉ = a + 8d
T₉ = -8 + 8(3)
T₉ = -8 + 24
T₉ = 16
Hence, the 7th term is 10 and the 9th term is 16
An amortized loan of RM60,000 has annual payments for fifteen years, the first occurring exactly one year after the loan is made. The first four payments will be for only half as much as the next five payments, whereas the remaining payments are twice as much as the previous five payments. The annual effective interest rate for the loan is 5%. I If the first four payments are X each, calculate the amount of principal repaid in the eighth payment and the amount of interest in the twelfth payment.
Answers
9514 1404 393
Answer:
a) RM2256.09 . . . principal paid by 8th payment
b) RM1791.10 . . . . interest paid by 12th payment
Step-by-step explanation:
First of all, we need to find the payments.
The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.
The future value of a single amount is ...
FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future
The future value of a series of payments is ...
FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r
For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.
__
The first 4 payments will have a future value at the end of the loan period of ...
s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05
s1 = 7.3717764259X
The next 5 payments will have a future value at the end of the loan period of ...
s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05
s2 = 14.8097486997X
The last 6 payments will have a future value at the end of the loan period of ...
s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X
So, the total future value of the series of payments is ...
payment value = 7.3717764259X +14.8097486997X +27.20765125X
= 49.3891763756X
__
The future value of the loan amount after 15 years is ...
loan value = 60,000(1 +0.05)^15 = 124,735.69
In order for these amounts to be the same, we must have ...
49.3891763756X = 124,735.69
X = 124,735.69/49.3891763756 = 2,525.57
__
At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)
In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)
The spreadsheet tells us ...
A) the principal repaid in the 8th payment is RM2,256.09
B) the interest paid in the 12th payment is RM1,791.10
_____
Additional comment
The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.
We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.
Evaluate the following
sqrt(25x169)
Answers
Step-by-step explanation:
[tex]what \: is \: the \: value \: of \: 5 \times 13 = 65 \: is \: the \: answer[/tex]
Answer:
65
Step-by-step explanation:
[tex] \sqrt{25 \times 169} [/tex]
[tex] \sqrt{5 \times 5 \times 13 \times 13} [/tex]
[tex]5 \times 13[/tex]
[tex]65[/tex]
I hope this helps you
Can anyone please help me out?
Answers
Which confidence level would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population?
Answers
Answer:
54% ...
Step-by-step explanation:
this is the answer I guess
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
Option B is the correct answer.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
The width of a confidence interval is proportional to the critical value of the corresponding confidence level.
The critical value is determined by the standard normal distribution or t-distribution, depending on the sample size and whether the population standard deviation is known.
In general,
The wider the confidence interval, the less precise the estimate of the population means.
Therefore, we want to choose the confidence level that produces the widest interval, which corresponds to the largest critical value.
For a given sample size,
The critical value increases as the confidence level increases.
For example, the critical value for a 95% confidence level is larger than the critical value for a 90% confidence level.
Therefore,
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
Learn more about z-score here:
https://brainly.com/question/15016913
#SPJ7
find the missing length indicated
Answers
============================================================
Explanation:
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
--------------------------------
Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
240.
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
What is Pythagorean Theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Learn more about the Pythagorean theorem at
https://brainly.com/question/343682
#SPJ2
For this problem, I got 2 for the median however my answer seems to be incorrect. Can someone help me figure out this problem please? Thank you for your help!
Answers
Answer:
11
Step-by-step explanation:
we have as many numbers as dots
like 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 13 13 14 15 15 16 16 17 18
so in the middle it's 11 and 11
(11+11)÷2=11
Please help 20 points. I will give Brainly to who ever get it right.
Answers
Answer:
Step-by-step explanation:
(-∞,2)
someone help me pls i need to pass summer school
Answers
Answer:
A
Step-by-step explanation:
The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain
14 → 4
12 →5
10 →6
8 →7
An internet provider states that, on average, the daily amount of time an adult spends on the internet is 4.5 hours. A sociologist studying the behaviors of internet consumers believes the average daily amount an adult spends on the internet is different than the amount stated by the internet provider. After completing a study, the sociologist found that the average daily amount of time an adult spends on the internet is 5.9 hours, on average. As the sociologist sets up a hypothesis test to determine if their belief is correct, what is their claim?
a. The average daily amount of time an adult spends on the internet is different than 4.5 hours.
b. The average daily amount of time an adult spends on the internet is different than 5.9 hours.
c. Adults spend a majority of their time on the internet.
d. The average daily amount of time an adult spends on the internet is 4.5 hours.
Answers
Answer:
a. The average daily amount of time an adult spends on the internet is different than 4.5 hours.
Step-by-step explanation:
An internet provider states that, on average, the daily amount of time an adult spends on the internet is 4.5 hours.
At the null hypothesis, it is claimed that the mean is of 4.5 hours, that is:
[tex]H_0: \mu = 4.5[/tex]
A sociologist studying the behaviors of internet consumers believes the average daily amount an adult spends on the internet is different than the amount stated by the internet provider.
At the alternative hypothesis, the sociologist claim, is that the mean is different of 4.5, that is:
[tex]H_1: \mu \neq 4.5[/tex]
Thus, the correct answer is given by option a.
An Experiment to investigate the relation between two physical quantities was performed where 10 data pairs were collected. You are to perform regression analysis to describe the relation between the two quantities using a polynomial. What are the possible values for the order of that polynomial?
a) from 0 to 10
b) from 1 to 9
c) from 1 to 10
d) Any integer
Answers
Answer:
d). Any Integer.
Step-by-step explanation:
Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It
As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.
What type of line is PQ?
A. side bisector
B. angle bisector
C. median
D. altitude
Answers
Answer:
B: I think
Step-by-step explanation:
correct me if im wrong
The line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have a triangle shown in the picture.
As we know,
in terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
From the figure the segment PQ divides the angle into two equal half.
From the definition of the angle bisector, the angle bisector can be defined as a line segment that divides the angle into two half.
Angle P = 40 + 40 = 80 degrees
Thus, the line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.
Learn more about the angle here:
brainly.com/question/7116550
#SPJ5
The length side of xy is?
Answers
Answer:
10
Step-by-step explanation:
ok so you do 12/30 and u get a 0.4 ratio. boom multiply 0.4 by 25 and u get 10. so boom the length is 10
Answer:
XY=10
Step-by-step explanation:
Since they are similar the ratio between each sides should be the same.
Ratio is .4. Found by dividing 12/30.
Multiply .4 by 25= 10
What is the mapping for a reflection in the line y=-1
Answers
Answer:
0
Step-by-step explanation:
the key mapping for a reflection in the line y=-1 is 0
A company is planning its spring advertising campaign. Its marketing team is planning to mail out different types of advertisements, at random, to their town's residents each week. They have the following types of advertisements ready:
Week 1 Week 2 Week 3
Small Poster Brochure Business Card
Brochur Leaflet Postcard
Postcard Small Poster
How many different possible ways can a resident receive an advertisement?
Answers
Answer:
The answer is "18".
Step-by-step explanation:
Amount of different methods a resident could get an advertisement:
[tex]=2\times 3 \times 3\\\\= 18[/tex]
Answer:
The Answer is 18
Step-by-step explanation:
2*3*3
A teacher designs a test so a student who studies will pass94% of the time, but a student who does not studywill pass14% of the time. A certain student studies for91% of the tests taken. On a given test, what is theprobability that student passes
Answers
Answer:
0.868 = 86.8% probability that the student passes.
Step-by-step explanation:
Probability of the student passing:
94% of 91%(when the student studies for the test).
14% of 100 - 91 = 9%(when the student does not study for the test). So
[tex]p = 0.94*0.91 + 0.14*0.09 = 0.868[/tex]
0.868 = 86.8% probability that the student passes.
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)
Answers
Answer:
b
Step-by-step explanation:
ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...
4 votes
ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches
Point-Slope Form of a Line
Answers
Point-Slope Form: y - y1 = m (x - x1) where m = slope y1 = first point of the y intercept and x1 = first points of the x intercept
Step-by-step explanation:
If you want to know more about Point-Slope Form, check this link out:
https://www.albert.io/blog/point-slope-form/#What_is_point_slope_form
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Answers
Answer:
The rental rate for the Fords is of $12 per day.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a Nissan.
y is the cost of a Ford.
z is the cost of a Chevrolet.
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.
This means that:
[tex]3x + 2y + 4z = 106[/tex]
Two Nissans, four Fords, and three Chevrolets cost $107 per day
This means that:
[tex]2x + 4y + 3z = 107[/tex]
Four Nissans, three Fords, and two Chevrolets cost $102 per day.
This means that:
[tex]4x + 3y + 2z = 102[/tex]
From the first equation:
[tex]4z = 106 - 3x - 2y[/tex]
[tex]2z = 53 - 1.5x - y[/tex]
[tex]z = 26.5 - 0.75x - 0.5y[/tex]
Replacing into the third equation:
[tex]4x + 3y + 53 - 1.5x - y = 102[/tex]
[tex]2.5x + 2y = 49[/tex]
From the second equation:
[tex]2x + 4y + 3z = 107[/tex]
[tex]2x = 107 - 4y - 3z[/tex]
[tex]x = 53.5 - 2y - 1.5z[/tex]
[tex]x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)[/tex]
[tex]x - 1.125x = 53.5 - 2y - 39.75 + 0.75y[/tex]
[tex]-0.125x = 13.75 - 1.25y[/tex]
[tex]0.125x = 1.25y - 13.75[/tex]
[tex]x = \frac{1.25y - 13.75}{0.125}[/tex]
[tex]x = 10y - 110[/tex]
Find the rental rate for the Fords.
We have to find y, so:
[tex]2.5x + 2y = 49[/tex]
[tex]2.5(10y - 110) + 2y = 49[/tex]
[tex]25y - 275 + 2y = 49[/tex]
[tex]27y = 324[/tex]
[tex]y = \frac{324}{27}[/tex]
[tex]y = 12[/tex]
The rental rate for the Fords is of $12 per day.
Is interquartile range a measure of center or a measure of variation?
Answers
Answer:
The interquartile range is the middle half of the data that is in between the upper and lower quartiles. ... The interquartile range is a robust measure of variability in a similar manner that the median is a robust measure of central tendency.
please answer this……
Answers
Answer:
no no no no no no no no no no no no
The polygons in each pair are similar. Find the missing side length.
Answers
Let missing one be x
If both are similar
[tex]\\ \sf\longmapsto \dfrac{20}{25}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{4}{5}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto 4x=16(5)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{16(5)}{4}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Part 2.
2. What is a determinant and what role does it play with matrices (Hint: What does a determinant of 0 mean)? How can this be used when solving systems of equations?
Answers
9514 1404 393
Explanation:
Definition
The determinant of a square matrix is a single number that is computed (recursively) as the sum of products of the elements of a row or column and the determinants of their cofactors. The determinant of a single element is the value of that element.
The cofactor of an element in an n by n matrix is the (n-1) by (n-1) matrix that results when the row and column of that element are deleted. The "appropriate sign" of the element is applied to the cofactor matrix. The "appropriate sign" of an element is positive if the sum of its row and column numbers is even, negative otherwise. (Rows and columns are considered to be numbered 1 to n in an n by n matrix.)
Uses
The inverse of a square matrix is the transpose of the cofactor matrix, divided by the determinant. Hence if the determinant is zero, the inverse matrix is undefined. This means any system of equations the matrix might represent will have no distinct solution. (There may be zero solutions, or there may be an infinite number of solutions. The determinant by itself cannot tell you which.)
Cramer's Rule for the solution of linear systems of equations specifies that the value of any given variable is the ratio of the determinants of two matrices. The numerator matrix is the original matrix with the coefficients of the variable replaced by the constants in the standard-form equations; the denominator matrix is the original coefficient matrix. This rule lets you solve a system of 3 equations in 3 variables by computing 3+1 = 4 determinants, for example.
Let's look at an example.
If we wanted to solve this system of equations
[tex]\begin{cases}2x-y = 2\\x+y = 7\end{cases}[/tex]
Then it's equivalent to solving this matrix equation
[tex]\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\7\end{bmatrix}[/tex]
We can then further condense that into the form
[tex]Aw = B[/tex]
Where,
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\w = \begin{bmatrix}x\\y\end{bmatrix}\\\\B = \begin{bmatrix}2\\7\end{bmatrix}[/tex]
------------------------------------------
To solve the matrix equation Aw = B, we could compute the inverse matrix [tex]A^{-1}[/tex] and left-multiply both sides by this to isolate w.
So we'd go from [tex]Aw=B[/tex] to [tex]w = A^{-1}*B[/tex]. The order of multiplication is important.
For any 2x2 matrix of the form
[tex]P = \begin{bmatrix}a & b\\c & d\end{bmatrix}[/tex]
its inverse is
[tex]P^{-1} = \frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Notice the expression ad-bc in the denominator of that fractional term outside. This [tex]ad-bc[/tex] expression represents the determinant of matrix P. Some books may use the notation "det" to mean "determinant"
[tex]P^{-1} = \frac{1}{\det(P)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
or you may see it written as
[tex]P^{-1} = \frac{1}{|P|}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Those aren't absolute value bars, even if they may look like it.
Based on that, we can see that the determinant must be nonzero in order to compute the inverse of the matrix. Consequently, the determinant must be nonzero in order for Aw = B to have one solution.
If the determinant is 0, then we have two possibilities:
There are infinitely many solutions (aka the system is dependent)There are no solutions (the system is inconsistent)So a zero determinant would have to be investigated further as to which outcome would occur.
------------------------------------------
Let's return to the example and compute the inverse (if possible).
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\A^{-1} = \frac{1}{2*1 - (-1)*1}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\A^{-1} = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\[/tex]
In this case, the inverse does exist.
This further leads to
[tex]w = A^{-1}*B\\\\w = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}*\begin{bmatrix}2\\7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}1*2+1*7\\-1*2+2*7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}9\\12\end{bmatrix}\\\\w = \begin{bmatrix}(1/3)*9\\(1/3)*12\end{bmatrix}\\\\w = \begin{bmatrix}3\\4\end{bmatrix}\\\\\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}3\\4\end{bmatrix}\\\\[/tex]
This shows that the solution is (x,y) = (3,4).
As the other person pointed out, you could use Cramer's Rule to solve this system. Cramer's Rule will involve using determinants and you'll be dividing over determinants. So this is another reason why we cannot have a zero determinant.
In ∆ ABC,AD is the altitude from A to BC .Angle B is 48°,angle C is 52° and BC is 12,8 cm. Determine the length of AD
Answers
9514 1404 393
Answer:
7,6 cm
Step-by-step explanation:
The law of sines can be used to find the length AB.
AB/sin(C) = BC/sin(A)
A = 180° -48° -52° = 80°
AB = BC·sin(C)/sin(A) = 12,8·sin(52°)/sin(80°)
The sine function can be used to find AD from AB.
AD/AB = sin(48°)
AD = AB·sin(48°) = 12,8·sin(48°)sin(52°)/sin(80°)
AD ≈ 7,61 cm
__
The dimension of interest is ha in the attachment, the height from vertex A.
Answer by formula please
Answers
Answer:
Step-by-step explanation:
I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:
(a² - b²) tan²θ = b² and then distributed to get:
a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:
a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:
[tex]\frac{a^2sin^2\theta}{cos^2\theta}=b^2+\frac{b^2sin^2\theta}{cos^2\theta}[/tex] and isolated the sin-squared on the left to get:
[tex]a^2sin^2\theta=cos^2\theta(b^2+\frac{b^2sin^2\theta}{cos^2\theta})[/tex] and distributed to get:
***[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex]*** and factored the right side to get:
[tex]a^2sin^2\theta=b^2(sin^2\theta+cos^2\theta)[/tex] and utilized a trig Pythagorean identity to get:
[tex]a^2sin^2\theta=b^2(1)[/tex] and then solved for sinθ in the following way:
[tex]sin^2\theta=\frac{b^2}{a^2}[/tex] so
[tex]sin\theta=\frac{b}{a}[/tex] This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:
[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex] and get the cos²θ alone on the right by subtracting to get:
[tex]a^2sin^2\theta-b^2sin^2\theta=b^2cos^2\theta[/tex] and divide by b² to get:
[tex]\frac{a^2sin^2\theta}{b^2}-sin^2\theta=cos^2\theta[/tex] and factor on the left to get:
[tex]sin^2\theta(\frac{a^2}{b^2}-1)=cos^2\theta[/tex] and take the square root of both sides to get:
[tex]\sqrt{sin^2\theta(\frac{a^2}{b^2}-1) }=cos\theta[/tex] and simplify to get:
[tex]\frac{sin\theta}{b}\sqrt{a^2-b^2}=cos\theta[/tex] and go back to the identity we found for sinθ and sub it in to get:
[tex]\frac{\frac{b}{a} }{b}\sqrt{a^2-b^2}=cos\theta[/tex] and simplifying a bit gives us:
[tex]\frac{1}{a}\sqrt{a^2-b^2}=cos\theta[/tex]
That's my spin on things....not sure if it's what you were looking for. If not.....YIKES
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
y = -1x + 2
Step-by-step explanation:
Mua hàng hóa 10000kg về nhập kho,Đơn giá 200 000đ/kg,thuế gtgt là 10%,trả bằng chuyển khoản 50%,còn nợ người bán.Chi phí vận chuyển 2 100 000 bao gồm thueest gtgt 5% trả tiền mặt
Answers
What percent is modeled by the grid?
A grid model with 100 squares. 33 squares are shaded.
23%
30%
33%
40%
Answers
Answer
33 percent
Step-by-step explanation:
Answer:
33 squares are shaded 23%
Step-by-step explanation:
I hope this answer works out for you if it doesn't I'm really sorry have a great day
