Answer:
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression
Required
[tex]\cos(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]
Make [tex]\cos^2(\theta)[/tex] the subject
[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]
Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]
[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]
Evaluate all squares
[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]
Take LCM
[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]
[tex]\cos^2(\theta)= \frac{13}{29}[/tex]
Take square roots of both sides
[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]
cosine is positive in the 4th quadrant;
So:
[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]
Split
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]
Rationalize
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Find the axis of symmetry of the graph of
y = x2 + 2x + 2
A- x= 1
B- y=1
C- x= -1
D- y=-1
Answer:
x = -1
Step-by-step explanation:
The graph's turning point is at ( -1 , 1 ), therefore the line of symmetry is at x = -1.
Answer: x = -1
Step-by-step explanation:
The formula to find the axis of symmetry in a function y = ax² + bx + c is:
[tex]x=\frac{-b}{2a}[/tex]
For y = x² + 2x + 2, where:
a = 1b = 2c = 2The axis of symmetry would be:
[tex]x=\frac{-b}{2a} =\frac{-2}{2(1)} =\frac{-2}{2} =-1[/tex]
help me out, so I can confirm my answers...:)
Answer:
Step-by-step explanation:
i) 18 - 2b = 5a
18 - 2b - 5a = 0
-2b -5a = -18
2b + 5a = 18
5a + 2b = 18
ii) 3a = 5b + 17
3a - 5b = 17
At this time x = 3, y = -5, c= 17
ax + by = c is equivelant to 3a -5b = 17
So another equation is:
3a - 5b = 17
Answer from Gauthmath
Step-by-step explanation:
18-2b=5a
we want to make 5a the subject so first we 5a to the left so our new equation is 5a+18-2b=0
then we move the 2b infront of the +18 so then our new equation is 5a+2b+18=0 then. we move the +18 to the other side to give 5a+2b=18
Simplify: y^-3
a) 3/y
b) - 1/y^3
c) -3y
d) 1/y^3
Answer:
1/y^3
Step-by-step explanation:
We know that a^-b = 1/a^b
y ^-3 = 1/y^3
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.
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.
Find the solutions of x^2+30 = 0
please give detailed steps!
Answer:
x= i√30
Step-by-step explanation:
I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.
Okay, so first you want to subtract 30 from both sides
x^2=-30
Then you take the square root of each side.
√(x^2)=√-30
x=√-30
Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=√-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.
Final answer: x = i√30
PLEASE I HAVE AN HOUR Why might you use the distributive property to simplify 3(30-2)
What is tan 30°?
60
2
1
90°
30"
V3
O A.
B. 1
O c. 2
O D. 7/ 룸
O E
1 / 3
Eg
O E
Answer:
Hello,
What is tan 30°?
[tex]tan(30^o)=\dfrac {\sqrt{3} }{3}[/tex]
Step-by-step explanation:
[tex]sin(30^o)=\dfrac{1}{2} \\\\cos(30^o)=\dfrac{\sqrt{3} }{2} \\\\\\tan(30^o)=\dfrac{sin(30^o)}{cos(30^o)} \\tan(30^o)=\dfrac{\dfrac{1}{2} } { \dfrac{\sqrt{3} }{2} }\\\\ =\dfrac {1*2}{2*\sqrt{3} }\\\\ =\dfrac {\sqrt{3} }{3}[/tex]
The value of tan 30° is 1/√3
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.
Tan 30° = sin 30° / cos 30°
We know that, sin 30° = 1/2
cos 30° = √3/2
Therefore,
Tan 30° = 1/2 ÷ √3/2
Tan 30° = 1/2 x 2/√3
Tan 30° = 1/√3
Hence, the value of tan 30° is 1/√3
Learn more about tangent of an angle, click;
https://brainly.com/question/10053881
#SPJ7
What information is NOT necessary to find the area of a circle?
a.
pi
c.
diameter
b.
radius
d.
height
Answer:
D. Height
General Formulas and Concepts:
Geometry
Area of a Circle: A = πr²
r is radiusStep-by-step explanation:
In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.
It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.
∴ our answer is D.
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5240 permanent dwellings on an entire reservation showed that 1613 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.) What is the lower limit? What is the upper limit?
Answer:
Step-by-step explanation:
point est. 0.307824427
99% 2.58
Confidence Interval - "P" values
(0.2914 , 0.3243 )
Farah is x years old. Ibtisam is 3 years younger than Farah. Muna is twice as old as Ibtisam. Write and expression in terms of x, for
(a) Ibtisam's age,
(b) The sum of their three ages, giving your answer in its simplest form.
Answer:
Farah: x
Ibtisam: x-3
Muna: 2(x-3) or 2x-6
Sum of all their ages: 4x-6
Step-by-step explanation:
Farah is x, so we don't need an expression for that.
Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.
Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6
Now, you have all their ages in expression form, now you need to simplify by adding:
x+x+2x-6
We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:
4x-6
Hope this helps!
--Applepi101
Answer:
a) X -3
b) 4x - 9
Step-by-step explanation:
a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah
b) Farah is X years old
Ibtisam is X - 3 years old
Muna is 2(X -3) since she is 2 times older than Ibtisam.
the sum of Thier ages will be
X + X -3 + 2(x-3)
= 2x - 3 + 2x - 6
= 4x - 9
Can someone help me with this?
9514 1404 393
Answer:
CNBD -- using the given statement regarding perpendicularityΔLAW ≅ ΔWKL by ASA -- using the markings on the figureStep-by-step explanation:
The given information tells us there is one congruent side in the two right triangles. That is not sufficient to claim congruence of the triangles.
CNBD
__
The figure shows one congruent angle in addition to one congruent side, so the figures can be shown to be congruent using the ASA theorem.
ΔLAW ≅ ΔWKL
_____
Additional comment
We don't know which answer is expected. You should discuss this question with your teacher, since it appears to be missing the statement that
∠ALW ≅ ∠KWL
verify sin2θ/1+cos2θ =tanθ
Answer:
LHS.= Sin 2x /( 1 + cos2x )
We have , sin 2x = 2 sinx•cosx
And. cos2x = 2cos^2 x - 1
i.e . 1+ cosx 2x = 2cos^2x
Putting the above results in the LHSwe get,
Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x
=sinx / cosx
= Tanx
.•. sin2x/(1 + cos2x)= tanx
Step-by-step explanation:
On Fridays, Jerry stops at Steak & Taco Shack before he goes home. This week
his order was 1 steak sandwich, 2 orders of cheese fries, and 2 taco salads. He was
charged $11.50 before tax. One week ago, his order was 2 steak sandwiches, 3
orders of cheese fries, and 1 taco salad, and he was charged $15.25. Two weeks ago
he ordered 1 steak sandwich, 4 orders of cheese fries, and 1 taco salad, and was
charged $13. How much is 1 steak sandwich? How much is 1 cheese fries? How
much is 1 taco salad?
Answer:
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
Step-by-step explanation:
Let :
Steak sandwich = x
Cheese fries = y
Taco salad = z
This week:
x + 2y + 2z = 11.50 - - - - (1)
Last week :
2x + 3y + z = 15.25 - - - (2)
Two weeks ago :
x + 4y + z = 13 - - - - - (3)
Taking (1) and (2)
x + 2y + 2z = 11.50 ___(1)
2x + 3y + z = 15.25 ___(2)
Multiply (1) by 2 and (2) by 1 and subtract
2x + 4y + 4z = 23
2x + 3y + z = 15.25
_______________
y + 3z = 7.75 - - - - (4)
Taking (2) and (3)
2x + 3y + z = 15.25 - - (2)
x + 4y + z = 13 - - - - - (3)
Multiply (2) by 1 and (3) by 2 and subtract
2x + 3y + z = 15.25
2x + 8y + 2z = 26
______________
-5y - z = - 10.75 - - - - - (5)
Lets solve (4) and (5)
y + 3z = 7.75 - - - - (4) - - - multiply by 5
-5y - z = - 10.75 - - - - - (5) - - - multiply by 1
Then add the result :
5y + 15z = 38.75
-5y - z = - 10.75
____________
14z = 28
z = 28 / 14
z = 2
To find y ; put z = 2 in (4)
y + 3z = 7.75
y + 3(2) = 7.75
y + 6 = 7.75
y = 7.75 - 6
y = 1.75
From equation 3 ;
x + 4y + z = 13 - - - - - (3)
x + 4(1.75) + 2 = 13
x + 7 + 2 = 13
x + 9 = 13
x = 13 - 9
x = 4
Hence,
Steak sandwich = x = 4
Cheese fries = y = 1.75
Taco salad = z = 2
Rearrange to make P the subject, :)..
Answer: [tex]P = \frac{25}{E^2}-Q\\\\[/tex]
Work Shown:
[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]
Simple geometry please help
Find KL. Round to the nearest hundredth.
Answer:
KL ≈ 1.94
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{JL}{KL}[/tex] = [tex]\frac{1.3}{KL}[/tex] ( multiply both sides by KL )
KL × cos48° = 1.3 ( divide both sides by cos48° )
KL = [tex]\frac{1.3}{cos48}[/tex] ≈ 1.94 ( to the nearest hundredth )
If 25 burgers feed 15 kids how many burgers would feed 55 kids
Answer:
1375
Step-by-step explanation:
If
f (x) = 3x +1 and 1-1 = *?
then f-'(7) =
O 22
O-2
02
According to my calculations answer is -2
Geometry something about chords but I don’t understand this whatsoever
Answer:
x = 5
Step-by-step explanation:
A radius is the distance from the center of a circle to the circumference (out edge) of a circle. Within the same circle, all radii are congruent. As per the given image, the radius of the circle is (5). As per its definition, the chord (a line in a circle that spans from one end of the circle to the other) with a measure of (x) is also another radius. Since all radii in a circle are congruent, (x) must also equal (5).
28. A boy decided to cut 10 pieces of wood from a length of wood so tha the first piece was 5cm the second 10cm, the third 15cm, the fourth 20cm and so on until he had cut TO pieces, each one 5cm longer than the one he had cut before. What length of the wood did he use? (a) 50cm (b) 55cm (c) 70cm (d) 200cm (e) 275cm
Step-by-step explanation:
he use 50cm length of the wood
The fraction 64/72 is a
Answer:
proper fraction
Step-by-step explanation:
This is a proper fraction, which has a numerator smaller than the denominator
a mixed number has a whole number in front such as 1 3/5
An improper fraction has a numeration greater than a denominator such as 7/6
The point A(−8,−4) is reflected over the origin and its image is point B. What are the coordinates of point b?
9514 1404 393
Answer:
B(8, 4)
Step-by-step explanation:
Reflection across the origin negates both coordinate values.
(x, y) ⇒ (-x, -y) . . . . . reflection across the origin
A(-8, -4) ⇒ B(8, 4)
(a+b)2= c+d
answer
answer
Answer:
a+b=c+d/2
i cant understand what answer you want
Please show your steps
Answer:
M of aftershock = 4.90
Step-by-step explanation:
5.6 = log(x/1)
[tex]10^{5.6} = 398107.1 \\[/tex]
1/5 * 398,107.1 = 79,621.4
[tex]10^{m} =[/tex] 79,621.4
m = log (79,621.4) = 4.90
Calvin and Jamel each havr cats as pets. Calvin buys cat food in cylindrical can that are 6 centimeters in diameter and 12 centimeters high. Jamel buys cat food in cylindrical can that 12 centimeters in diameter and 6 centimeters high. What is the ratio of the volume of one of Calvin's cans of to the volume of one of Jamel's cans?
Answer:
see below
Step-by-step explanation:
CALVIN
v=[tex]\pi[/tex]× r ² × h
v=3.14 × 3² × 12
v=3.14×9 × 12
v=3.14 × 108
v = 339.12
JAMEL
v=[tex]\pi[/tex] × r ²×h
v=3.14× 6 ² × 6
v=3.14 × 36×6
v=3.14×216
v=678.24
Use distributive property to remove parantheses
9(2/3-3x)
The curve y=2x^3+ax^2+bx-30 has a stationary point when x=3. The curve passes through the point (4,2).
(A) Find the value of a and the value of b.
#secondderivative #stationarypoints
A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have
dy/dx = 6x ² + 2ax + b
and so when x = 3,
0 = 54 + 6a + b
or
6a + b = -54 … … … [eq1]
The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have
2 = 128 + 16a + 4b - 30
or
16a + 4b = -96
4a + b = -24 … … … [eq2]
Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :
(6a + b) - (4a + b) = -54 - (-24)
2a = -30
a = -15 ===> b = 96
Correct
Suppose it takes John 27 minutes to run 3 miles. How long would it take him to run 4 kilometers? Round your answer to the nearest minute,
lil Keypad
Answer
Keyboard Shortcuts
min
Submit Answer
© 2021 Hawkes Learning
O
Type here to search
Answer:
Step-by-step explanation:
4km
[tex]\frac{3 }{27} \frac{miles}{minutes}[/tex] * [tex]\frac{60}{1} \frac{min}{hour}[/tex] * [tex]\frac{1}{.6213} \frac{km}{mile}[/tex]
4km ÷ 10.73 km/hr = .37 hr = 22.3 minutes
PLEASE HELP VENN DIAGRAM!
Look at attached for the diagram!!!
In his diagram BH represents the students that have brown hair and W represents the students that are wearing a watch.
Is having brown hair independent of wearing a watch?
Please show some work if possible
Answer:
Yes.
Step-by-step explanation:
Since there is an overlap, that does mean some people with brown hair do wear watches, but not all of them do. Hence it's independent.
КУ
11
10
A
9
8
7 구
6
5
4
A А
C
3
B'
2
1
B
C с
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
A ABC is dilated about the origin./
What scale factor was used to make the image A A'B'C?
Answer:
3
Step-by-step explanation:
The dilation factor is 3
There are five cities in a network. The cost of building a road directly between i and j is the entry ai,j in the matrix below. An infinite entry indicates that there is a mountain in the way and the road cannot be built. Determine the least cost of making all the cities reachable from each other.
0 3 5 11 9
3 0 3 9 8
5 3 0 [infinity] 10
11 9 [infinity] 0 7
9 9 10 7 0
Solution :
Given :
There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex] is the entry [tex]a_{i,j}[/tex]
[tex]a_{i,j}[/tex] refers to the matrix.
Road cannot be built because there is a mountain.
The given matrix :
[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]
The matrix on the left above corresponds to the weighted graph on the right.
Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.
Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7 is available.
The edge of the weight 8 completes a minimum spanning tree and total weight 21.
If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.
