Plot the foci of the hyperbola represented by the equation x^2/625 − y^2/3600 =1 100pts

Answers

Answer 1

The attached image represents the foci of the hyperbola

How to determine the foci?

The equation of the hyperbola is given as:

[tex]\frac{x^2}{625} - \frac{y^2}{3600} = 1[/tex]

Rewrite as:

[tex]\frac{x^2}{25^2} - \frac{y^2}{60^2} = 1[/tex]

A hyperbola is represented as:

[tex]\frac{(x - h)^2}{b^2} - \frac{(y - k)^2}{a^2} = 1[/tex]

This means that:

h = 0

k = 0

b = 25

a = 60

Next, calculate c the distance from the center to the focus using:

[tex]c = \sqrt{a^2 -b^2}[/tex]

This gives

[tex]c = \sqrt{60^2 -25^2}[/tex]

Evaluate

[tex]c = \pm \sqrt{2975}[/tex]

This means that:

Foci = (0, -√2975) and (0, √2975)

See attachment for the hyperbola and the foci

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Plot The Foci Of The Hyperbola Represented By The Equation X^2/625 Y^2/3600 =1 100pts

Related Questions

Evaluate:
lim h->0 (√(x+h) - √x) / h

Answers

Rationalizing the numerator, it is found the result of the limit is given as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{1}{2\sqrt{x}}[/tex]

What is a limit?

A limit is given by the value of function f(x) as x tends to a value.

The first step to find the limit is replace the variable by the value, hence:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{0}{0}[/tex]

Undefined limit, hence we have to find another way. The numerator includes square roots, hence it should be rationalized using the subtraction of perfect squares, as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{(\sqrt{x + h})^2 - (\sqrt{x})^2}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}[/tex]

Then we simplify the h, so:

[tex]\lim_{h \rightarrow 0} \frac{1}{\sqrt{x + h} + \sqrt{x}} = \frac{1}{2\sqrt{x}}[/tex]

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Find ZABC
00
A
38⁰
32⁰

Answers

Answer:

The answer will be 38° + 32° = 70°

Please mark me as the brainliest

What is 0.000345 expressed in scientific notation?

3.45 × 102
3.45 × 104
3.45 × 10–2
3.45 × 10–4

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Expression in scientific notation :

[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 0.000345[/tex]

[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]

[tex] \textsf{Correct option - D} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

3.45 x 10-4

Step-by-step explanation:

A coordinate plane is labeled street on the x-axis and avenue on the y-axis. ping is at point (3, 6) and ari is at point (21, 18). a line is drawn from ping to ari. ping lives at the corner of 3rd street and 6th avenue. ari lives at the corner of 21st street and 18th avenue. there is a gym two-thirds the distance from ping's home to ari's home. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 where is the gym? 9th street and 10th avenue 12th street and 12th avenue 14th street and 12th avenue 15th street and 14th avenue

Answers

The gym location is (15th street, 14th Avenue). so the option D is correct.

What is graph ?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location is 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home will be

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari will be

= (18th , 12th )

We know that

Gym distance = 2/3 × (18),  2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

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I'm having problems because our teacher is making us do this monstersety 391.92x10372.45-918+12.5

Answers

Answer:

4064265.104

Step-by-step explanation:

Use PEMDAS :

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

We only have multiplication and addition/subtraction to do. Multiplication and Division can go in either order depending on which comes first reading left to right. It's the same with Addition and Subtraction: we will first subtract 918 and then add 12.5.

Let's start by Multiplying. 391.92 x 10372.45 = 4065170.604.

Now, subract 918. 4065170.604-918 = 4064252.604.

Finally, add back 12.5. 4064252.604. +12.5 = 4064265.104 !

If the size of a storage box is 50 cm by 10 cm by 20 cm. What is the volume of the box?

Answers

Answer:

l×b×h

50×10×20

10000cm^3

Step-by-step explanation:

please mark me as brainlest

Answer:

10000 cm³

Step-by-step explanation:

Volume of rectangular box:

         To find the volume of box,  multiply the length, width and height of the box and its unit is cubic units

         [tex]\sf \boxed{\bf Volume \ of rectangular \ box = l *w*h}[/tex]

                                                         = 50 * 1 0 * 20

                                                          = 10000 cm³

Select the correct answer.
The cost of renting a community center is $100, with an additional cost of $10 per guest.
Which graph has the most appropriate scales and units for this situation?
О А.
B.
Total Rental Cost ($)
tal Cost ($)
500
400
300
200
100
50
40
30
0
10 20 30 40 50
Number of Guests

Answers

The cost of renting a community center for x guest is given as y = 10x + 100

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the y intercept.

Let y represent the cost of renting a community center for x guest. Hence:

y = 10x + 100

The cost of renting a community center for x guest is given as y = 10x + 100

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After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds

Answers

Answer:

3 seconds

proofi took the test

The object reaches its maximum height after 3 seconds.

The correct option is 3 seconds.

To find the time at which the object reaches its maximum height, we need to determine the vertex of the parabolic function[tex]h(t) = -16t^2 + 96t + 6[/tex] . The vertex form of a parabola is given by [tex]h(t) = a(t - h)^2 + k[/tex], where (h, k) represents the vertex.

In this case, a = -16, so the vertex is given by t = -b/2a. Plugging in the values, we get t = -96/(2 x (-16)) = 96/32 = 3 seconds.

Therefore, the object reaches its maximum height after 3 seconds.

Option B, 3 seconds, is the correct answer.

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The complete Question:

The function [tex]h(t) = -16t^2 + 96t + 6[/tex] represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

After how many seconds does the object reach its maximum height?

A. 2 seconds

B. 3 seconds

C. 6 seconds

D. 9 seconds

bill $42 , tax 9% , tip 18%

Answers

Answer:

Tax 3.78 $ and tip 7.56 $

Step-by-step explanation:

42*0.09 = 3.78

42*0.18 = 7.56

find the value of cosec^2 30 degree - sin^45 - sec^60

Answers

For this question, I will be writing 'csc' instead of 'cosec'

[tex]\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}[/tex]

Will you do the hard questions

Answers

Answer:

No

Step-by-step explanation:

I will not do hard questions

yes i will do the easy questions if u do the hard ones

If the nth term of a sequence is 11n+2 what is the 12th term

Answers

Answer:

134

Step-by-step explanation:

the "nth" term of a sequence means that you can plug in the term number to get the term value

so, if

  11n + 2 is the sequence

  11(12) + 2 is the 12th term

  132 + 2 is the 12th term

  134 is the 12th term

By plugging in the term "place" (1st, 2nd, 3rd, 4th, etc.) for the variable "n", we get a term value.

hope this helps!!

The 12th term of the sequence is 133

How to determine the 12th term?

The nth term is given as:

Tn = 11n + 1

The 12th term is calculated as:

T(12) = 11(12) + 1

Evaluate

T(12) = 133

Hence, the 12th term of the sequence is 133

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the bearing of two points x and y from z are 45° and 135° respectively . if |zx|=8cm and |zy|=6cm, find |xy|.

Answers

Answer:

[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:

[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].

Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:

[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].

What is the range of the function y=-x² +1?
A) y≤ -1
B) y²-1
C) y≤ 1
D) y≥ 1

Answers

Answer:

Option (C)

Step-by-step explanation:

The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.

So, this means that adding 1 to this, the range matches with option C.

which expression is equivalent to. 5 32x^5 y ^10 z^15

HURRY NOW

Answers

Answer:

the answer is B

Step-by-step explanation:

5th root of 32 = 2

5 / 5 = cancels

10 / 5 = 2

15 / 5 = 3

2xy²z³

Answer:

2xy^2z^3

Step-by-step explanation:

What is the slope of the line represented by the equation y = -x + 1/2x+1/4

- 1/2

- 1/4

1/4

1/2

Answers

I don’t know it to bad………

2. Draw a picture to show how many 1/5s there are in 7/10.​

Answers

2. 7/10 ÷ 1/5 = 7/2

7/10 × 5 = 1/2

hope it helps u

Which function represents exponential growth?
O f(x) = 3x
O f(x) = x³
Of(x) = x + 3
O f(x) = 3x

Answers

Answer:

b step by step explanation

The function that represents exponential growth is:

f(x) = x³

What is Exponential Growth?

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Exponential growth is a phenomenon that occurs when the rate of change of a quantity is proportional to its current value. In other words, as the value of the quantity increases, the rate at which it increases also increases. This can be represented mathematically using an exponential function of the form f(x) = abˣ, where a is the initial value, b is the growth factor, and x is the time or number of periods.

The function that represents exponential growth is:

f(x) = x³

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An experiment consists of rolling a standard six-sided die once. Event A is "rolling a 5{}^{\prime\prime} and event B is "rolling an odd number." Are the events dependent or independent? Why? Select the option that correctly answers both questions.

O Events A and B are independent, because P(B) = P(B|A) = 1/2.
O Events A and B are independent, because P(A) = P(B|A) = 1/12.
O Events A and B are dependent, because P(A) =/ P(B|A).
O Events A and B are dependent, because P(B) =/ P(B|A).

Answers

Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.

Is event B independent of event A?

Events are independent if P(B) = P(B|A)

The probability of event B is:

= 3 odd numbers / 6 numbers

= 1 / 2

The probability of A is:

= 3 prime numers / 6

= 1/2

P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)

= 1/2

So P(B) = P(B|A) = 1/2.

The events are independent.

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You have $40.00. You wish to buy a T-shirt costing $14.50. You would also like to buy a pair of jeans. There
is a 6% sales tax on clothing. What is the top tag price (excludes sales tax) you could pay for the jeans?

Answers

Tax is 1.54

Including tax = 39.99
Excluding tax= 38.5

Hope this helps

The following data is a randomly selected sample of 20 state populations. find the measures of central tendency. you may use technology to find the measures.

Answers

The mean is  6394530.35 and the median is = 3355572.5

The missing data is attached in the answer.

What is Mean ?

Mean is the average value of the data points , it is determined by dividing the total sum of the data points to the number of data points.

Mean and Median is the measure of the central; tendency of the data.

Mean is given by

Sum of the observations/number of observations

= (741894 + 6931071....)/20

= 6394530.35

2) To find median

The data needs to be arranged in ascending order

Then the median is the middle number of the arranged data

Here the median is = 3355572.5

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Find the value of cos N rounded to the nearest hundredth, if necessary.

Answers

cos N = 14/20 = 0.70

if AB= 51, and AC = 120. find BC.
A
B
C

Answers

Answer:

Step-by-step explanation:

AB = 51

AC = 120

BC = AC - AB

BC = 120-51

BC = 69 units

Help ASAP, really stuck

Answers

The total length of the wire needed to make this shape is 162cm

Perimeter of a triangle

The perimeter of a triangle is the sum of the external side of the triangle.

Given the following parameters

Length of one side of the outside shape = 24cm

The side length of the smaller triangle = 24/4 = 6cm

The perimeter of the smallest triangle  3(6) = 18cm

The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm

Total length of wire needed. = 3(24) + 3(18) + 36

Total length of wire needed = 72 + 54 + 36

Total length of wire needed = 162cm

Hence the total length of the wire needed to make this shape is 162cm

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What function is represented below?
HELP ASAP!!

Answers

f(x)= (1/4)^x -2 the negative two is not with the x

Answer:

C

Step-by-step explanation:

(1/4)^x-2 is the answer

Two number cubes are rolled for two separate events:
Event A is the event
that the sum of numbers on
both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional-probability formula for
event B given that event A occurs first by writing A and B in the blanks:

Answers

Answer:

Good idea for thanks......

The jet stream is traveling nearly due south from Wyoming to Colorado at 110 knots. If the plane’s speed is 400 knots, what will be its ground speed if it travels from Wyoming to Colorado?

Answers

Considering the direction of the wind, it is found that the ground speed needs to be of 510 knots.

What is the ground speed?

The ground speed, considering that the wind is flowing from Wyoming to Colorado, and the same direction as the trip, is given by:

G = Plane speed + Wind speed.

In this problem, we have that the speeds are given as follows:

Plane: 400 knots.Wind: 110 knots.

Hence the ground speed is given by:

G = 400 + 110 = 510 knots.

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Question 2(Multiple Choice Worth 1 points)
(02.02 LC)
If g(x)= x² + 3, find g(4).
11
19
16
8

Answers

Answer: 19

Step-by-step explanation:

g(4) = 4² + 3

g(4) = 16 + 3

g(4) = 19

Z varies directly as x and y, z=6 when x=2 and y=6 find the value of z when x=3 and y=8

Answers

Answer:

12

Step-by-step explanation:

Direct Variation. I think it's gonna be like this.

SInce Z is not inversely to y , its varies directly to both.

Then it's,

Z=kxy, where k is constant.

subst. Z=6,x=2 and y=6.

6=k×2×6

6=k×12=12k

6=12k=½

the formula connecting them is

Z=½xy

Z=½×3×8

Z= 1×3×8÷2

Z=24÷2

Z=12.

That's my solution.

​The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is required to make 1 litre of fuel?​​​

Answers

The amount of oil required for 1 liter of fuel is 111.11 mL.

Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.

Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.

The total part of the fuel is 8+1=9

the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9

the portion of the oil = parts of oil /total parts of the fuel= 1/9

Now we have to calculate the amount of oil required for 1 liter of fuel.

As discussed before, 1/9 parts of the fuel is oil.

So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL

Similarly, we can calculate the amount of petrol which will be

the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL

Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.

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