Answers
The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).
What is the axis and foci about?The term 'foci' is known to be the point at which there is the coming together of light or any other kinds of electromagnetic radiation, particles, etc.
It is also seen as the point from which they seems to go apart.
[tex]\frac{x^{2} }{144} + \frac{y^{2} }{169} = 1[/tex]
[tex]\frac{x^{2} }{12^{2} } + \frac{y^{2} }{13^{2} }[/tex]
Hence, major axis is = (0, ± 13)
e = [tex]\sqrt{1 -\frac{12^{2} }{13^{2} } }[/tex]
= 5/13
Foci is: (0± 13 x [tex]\frac{5}{13}[/tex])
Foci is: (0, ±5)
Therefore, The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).
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Related Questions
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
Answers
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Answer: x = 6
NS = 8.5
Step-by-step explanation:
JK = KL= KP + LP
26 = 13 + 2x + 1
2x = 12
x = 6
NS = PS
PS = 8.5
NS = 8.5
Simplify the expression using the proper order of operations
5[6 ÷ 2^2 ∙ 3 - 1]
Answers
The simplification of the expression 5(6 ÷ 2² × 3 - 1) using the proper order of operation is 3.75
Simplification5(6 ÷ 2² × 3 - 1)
Bodmas
B - BracketO - ofD - divisionM - MultiplicationA - AdditionS - Subtraction= 5(6 ÷ 4 × 3 - 1)
= 5(6 ÷ 4 × 2)
= 5(6 ÷ 8)
= 5(0.75)
= 3.75
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There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1-dollar bills is five times the number of the 5-dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $2.00?
Answers
Answer:
the number of 1 dollars bills was 5 si make 1 more 5 dollars so 8n total it is 10 dollars.
Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.
a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.
Answers
The additional information needed to calculate ORS are the measures of SPR and PSR
The special names of the linesThe lines are given as:
Lines a, b, c and d
The special names of the lines are as follows:
Line a: A secant. This is because the line divides the circle into unequal segmentsLine b: A tangent: This is because the line touches the circle at a point on the circumferenceLine c: A diameter. This is because the line divides the circle into equal segmentsLine d: A secant. This is because the line divides the circle into unequal segmentsThe additional information neededThe angle is given as:
OPS= 139 degrees
Start by calculating SPR using
SPR = 180- 139
SPR = 41 degrees
So, the additional information needed to calculate ORS are the measures of SPR and PSR
How to calculate the lengths RO, RS, RV, and RTThe theorem 65 is not stated.
So, the question cannot be answered
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Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Answers
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
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Hi I would like to know how I can solve this problem.
Answers
The [tex]n[/tex]-th term is
[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]
so the 39th term is
[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]
Observe that
[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]
which suggests that
[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]
I need help with my homework please!!
Extremely confused!
I need all the equations imputations and how to solve for everything!
Answers
Answer:
what do you need person jjff
Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.
Answers
The equations which completes the left-hand column of the table are;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Which equations and identities complete the left-hand column of the table?The given expression on the right is written as follows;
First row;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
The definition of the sum and difference of cosine are;
cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)
cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)
Therefore;
Second row;
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)
Which gives;
[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
Third row;
sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Learn more about trigonometric functions here:
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8 through 10 thank you answers only
Answers
Answer:
8) - 8z^3 - 3z^2 - 2z + 13
9) g^3 - 3g^2 + 3g + 6
10) (14n + 21) - (8n + 7) = 6n + 14
Consider the following figure:
What is the value of x + y?
Answers
The value of the sum of the angles x + y of the given triangle is; 220°
How to find the angles in a triangle?We know that the sum of angles in a straight line is equal to 180°. Thus;
∠CFE + ∠OFE = 180
140 + ∠OFE = 180
∠OFE = 180 - 140
∠OFE = 40°
Similarly, we can use the same principle to get;
∠OEF + ∠BEF = 180°
∠OEF + y = 180°
∠OEF = 180 - y
Similarly,
∠AOF + ∠EOF = 180°
x + ∠EOF = 180°
∠EOF = 180 - x
Sum of angles in a triangle is equal to 180°. Thus;
40 + 180 - y + 180 - x = 180
Rearranging gives;
x + y = 180 + 180 + 40 - 180
x + y = 220°
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Gcf of 12h3,36h3,12h6
Answers
The greatest common factor from the given information is 12h³.
What is the greatest common factor?The greatest common factor (GCF) of a given set of whole numbers is the largest value that can be divided by the set of numbers.
From the information given, we are to find the GCF of:
12h³ = (1 , 2, 3, 4, 6 , 12 )h³
36h³ = (1, 2, 3, 4, 6, 9, 12, 18, 36)h³
12h⁶ = (1, 2, 3, 4, 6, 12)h³ * h³
Therefore, we can conclude that the greatest common factor is 12h³.
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A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $5, 0.3 for $25, 0.2 for $50, and 0.004 for $75. What
are the odds that the ticket is worth at least $25?
Answers
Answer:
0.7
Step-by-step explanation:
Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7
Which equation is represented by the graph below?
A y=In x-3
B y=In x-4
C y=e^3 -3
D y=e^3 -4
Answers
Answer:
D
Step-by-step explanation:
I assume that for C and D, you meant e^x.
Since the function is defined at 0, eliminate A and B (since ln 0 is undefined)
Between C and D, we know that when x=0, e^x = 1. Since the y intercept of the graph is -3, this means the equation is y = e^x - 4.
a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 5 48 22 Cold 8 12 5 What is the probability that a customer ordered a large given that he or she ordered a cold drink? Rounded to the nearest percent, [? ]% Enter
Answers
Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:
p = 5/25 = 0.2 = 20%.
20% probability that a customer ordered a large given that he or she ordered a cold drink.
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5
364,860
0/1 point
Camila has finally found a house she adores! The cost of the home is $210,000, which she intends to purchase on a 30-year fixed mortgage. Blinded by her adoration for the
property, she has agreed to a 5.5% interest rate. Round all answers to the nearest cent.
How much will Camila pay in interest over the lifetime of the mortgage?
Answers
The total interest on the mortgage loan is $219,249.60
What is a mortgage loan?
It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.
Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.
PV=monthly repayment*(1-(1+r)^-N/r
PV=loan amount=$210,000
monthly repayment=unknown(assume it is X)
r=monthly interest rate=5.5%/12=0.00458333333333333
N=number of monthly payments in 30 years=30*12=360
$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-0.19277525234572900)/0.00458333333333333
$210,000=X*0.80722474765427100/0.00458333333333333
$210,000=X*176.12176312456800000
X=$210,000/176.12176312456800000
X=monthly payment=$1,192.36
total repayments(360 months)=$1,192.36*360
total repayments(360 months)=$429,249.60
Total interest=total repayments(360 months)-loan amount
Total interest=$429,249.60-$210,000
Total interest=$219,249.60
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A grove of redwood tree has an estimated 3,400,000 board feet of lumber at the
start of 2022. If redwoods grow at an exponential rate of 9% each year, then what
would be the growth formula? Within which year will the grove reach one billion board
feet of lumber?
Answers
The exponential growth formula is 3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet is 63.16 years.
What is the exponential growth formula?The exponential growth formula usually has this form:
FV = P (1 + r)^n
FV = Future growth P = Present growth R = rate of growthN = number of years3,400,000 x (1.09^t).
The year in which the grove would reach one billion board feet = (In 1,000,000,000 / 3,400,000) / 0.09 = 63.16 years
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1/2x + 1/4y = 3 solve for y
Answers
Answer:
y=-2x+12
Step-by-step explanation:
First, subtract 1/2 from each side
1/4y = -1/2x + 3 --> multiply each side by 4
y = -2x + 12 is your final answer
The inside dimensions of a box are 12 inches long, 5 inches wide, and 2 inches deep.
How many cubic inches does it contain?
60
110
120
240
none of these
Answers
On average, an American hummingbird flaps its wings about 3,180 times per minute.
About how many times per second does it flap its wings?
Enter your answer in the box.
times
Answers
Answer:
53 times per second
Step-by-step explanation:
There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.
3180 / 60 = 53
10yy'=x y(10)=4
Find the solution of the differential equation that satisfies the given initial condition.
Answers
Answer:
Step-by-step explanation:
10yy'=x
[tex]10y\frac{dy}{dx} =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\\frac{10y^2}{2} =\frac{x^2}{2} +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=\frac{60}{2} =30\\10y^2=x^2+60\\10y^2-x^2=60[/tex]
What is 13 2/3 subtracted from 49 1/3
Answers
Answer:
35 2/3
Step-by-step explanation:
49 1/3 - 13 2/3
First convert both into improper fractions, which is
148/3 - 41/3
Then subtract!
107/3
Next simplify the fraction.
35 2/3
Fill in the missing term in the pair of equivalent ratios. *
5:30 15:
Your answer
The state low temperatures for five states are as follows: -42
Answers
Find the missing length indicated. need help
Answers
The missing length of given right triangle is equal to 25.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
From Pythagorean Theorem you can find h (heigth). Thus,
15²=9²+h²
h²=225-81
h²=144
h=12
If h=12 and m=9, from h²=m*n you can find n.
h²=m*n
12²=9*n
144=9n
n=144/9
n=16
Therefore, x= m+ n= 9+16=25.
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Carlos spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction hours doing his math homework. He spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction as much time practicing piano.
How many hours did Carlos spend practicing piano?
write as a fraction
Answers
The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.
FractionA fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).
Time Carlos spent doing his math homework = 1 1/4 hoursTime spent practicing his multiplication facts = 1/4 of 1 1/4 hours
= 1/4 × 1 1/4
= 1/4 × 5/4
= (1 × 5) / (4 × 4)
= 5/16 hours
Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.
Complete question:
Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.
How many hours did Carlos spend practicing his multiplication facts?
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9
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%?
97.51
102.53
101.78
105.25
Answers
The price of a two-year bond is 101.78 and the correct option is C.
Given that a 9% annual coupon and a yield to maturity of 8%.
Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.
Implicit Face value, FV=$100
Time, N=2 years
Coupon, C=(9/100)×$100=9
The yield of maturity, r=8%=0.08
Now, we will find the bond price using the formula
Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ
Substitute the values in this formula, we get
Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²
Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²
Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664
Price of bond=9×[(1-0.857)/0.08]+85.73
Price of bond=9×[0.143/0.08]+85.73
Price of bond=9×1.7875+85.73
Price of bond=16.0875+85.73
Price of bond=101.78
Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.
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If m4 = 108°, what is the measure of 26?
Answers
Answer:
108
Step-by-step explanation:
When the lines cut through by a transversal are parallel, alternate interior angles are congruent. angle 4 = angle 6 = 108
( WILL GIVE BRAINLIEST ) a dog trainer compared the mean numbers of lessons for two groups of dogs which statement is true about the data?
Answers
Answer:
Answer number 1
......................
To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
Answers
Answer : 5/9
Hope it helps !
The divisor of the expression 2/3 ÷ 6/5 is 9.
We have,
Expression:
2/3 ÷ 6/5
The concept used.
a/b ÷ c/d = ad / bc
Now,
2/3 ÷ 6/5
This can be written as,
= 2/3 x 5/6
= (2 x 5) / (3 x 6)
= 10 / 18
= 2 x 5 / 2 x 9
Cancel the common factor.
= 5 / 9
This can be read as,
Dividend = 5
Divisor = 9
Thus,
The divisor of the expression is 9.
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The sum of five consecutive integers equals 5.5 times the middle integer. Find the integers.
Answers
The integers are therefore -2, -2, 0, 1 and 2
Linear equationLet the five consecutive integers be x-3, x-2, x-1, x and x+1
If the sum of five consecutive integers equals 5.5 times the middle integer, then;
x-3+x-2+x-1+x+x+1 = 5.5(x-1)
5x - 5 = 5.5x - 5.5
Collect the like terms
5x-5.5x = -5.5 + 5
-0.5x = -0.5
x = 1
The integers are therefore -2, -2, 0, 1 and 2
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