4. Sketch the graph of F(x) = 1 +x/x²-1
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Answers:

[tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1\\\\\displaystyle \lim_{x \to 2^{-}} f(x) = 1\\[/tex]

Both result in the same limit value. This allows us to say [tex]\displaystyle \lim_{x \to 2} f(x) = 1[/tex] without the plus or minus over the 2.

The left and right hand limits may not always match like this.

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Explanation:

The notation [tex]\displaystyle \lim_{x \to 2^{+}} f(x)[/tex] means that we are approaching x = 2 from the right hand side. This is from the positive direction. So we start at say x = 3 and move to x = 2.5 then to x = 2.1 then to x = 2.01 and so on.

Because we started with values x > 2, we will use the third definition of the piecewise function

if x > 2, then f(x) = 3x-5

Plug in x = 2 to get

f(x) = 3x-5

f(2) = 3(2)-5

f(2) = 6-5

f(2) = 1

This shows [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1[/tex]

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For the other limit, we're approaching x = 2 from the negative side. So we could start at say x = 0, then move to x = 1, then to x = 1.5 then to x = 1.9 then to x = 1.99, and so on.

We're using x values such that x < 2 now.

So we'll be using the first definition of the piecewise function

If x < 2, then f(x) = x^2 - 3

f(x) = x^2-3

f(2) = 2^2-3

f(2) = 4-3

f(2) = 1

We end up with [tex]\displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]

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Both right hand limit and left hand limit result in the same value

Because [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = \displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]

We can shorten that to [tex]\displaystyle \lim_{x \to 2^{}} f(x) = 1[/tex] meaning we can approach x = 2 from either direction to arrive at the same limiting value.

A thing to notice is that f(2) is not equal to 1. Instead the second line of the piecewise function says f(2) = 3.

The fact that the limit as x approaches 2 and f(2) don't agree means this function is not continuous at x = 2.

The graph shows this. We have a removable discontinuity where we effectively picked the point off the graph and move it upward.

See the diagram below.

Answer:

  -8

Step-by-step explanation:

Find the ordered pair with 3 as the first element: (3, -8). This tells you ...

  g(3) = -8

Answer:

systematic errors [ A, C], Random errors [B, D]

Step-by-step explanation:

Random errors are errors that cause certain fluctuations around the true values of substances that are measured, as a result of difficulties being experienced while taking measurements.  Systematic errors are mostly associated with the calibration of equipment. It seen to cause consistent deviations from the true value that can be gotten during measurement.

In most cases, random errors cannot be avoided while systematic errors can.

Answer:

Jerry  was paid $10.75 an hour and Leigh-Anne was paid $12.05 hourly

Step-by-step explanation:

Answer:

Set your calculator to Degree mode.

A = 39°

19/sin(39°) = b/sin(97°)

b = 19sin(97°)/sin(39°) = 30.0 m

19/sin(39°) = c/sin(44°)

c = 19sin(44°)/sin(39°) = 21.0 m

Answer:Did u mean plus 36

Step-by-step explanation:

Answer:

187.285714286

Step-by-step explanation:

Step-by-step explanation:

27/57= 0.40350877193

0.40350877193x7=

2.82456140351

rounded ver- 2.82

Step-by-step explanation:

150/1000 and then you you have to simplify it

Answer:

Volume of the figure = 704 units³

Step-by-step explanation:

The figure is composed of a triangular prism and a square prism.

Volume of the figure = volume of triangular prism + volume of square prism

Volume of the figure = ½*a*b*a + a³

Given, that, a = 8 units; b = 6 units, plug in the values into the equation.

Volume of the figure = ½*8*6*8 + 8³

Volume of figure = 4*6*8 + 512

Volume of the figure = 192 + 512

Volume of the figure = 704 units³

Answer:

D.

[tex](x - 4) {}^{2} + (y - 3) {}^{2} = 5 {}^{2} [/tex]

The equation of the circle centered at point (4, 3) with a radius of length 5 is (x - 4)² + (y - 3)² = 5².

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that circle has a center at point (4, 3 ).

Hence:

h = 4

and k = 3

Also given that, the radius has a length of 5

r = 5

Plug these values into the above formula and simplify the equation:

( x - h )² + ( y - k )² = r²

( x - 4 )² + ( y - 3 )² = 5²

Expanding and simplifying, we get:

(x - 4)² + (y - 3)² = 25.

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 5².

Option D)  (x - 4)² + (y - 3)² = 5² is the correct answer.

Learn more about equation of circle here: brainly.com/question/29288238

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First, turn 4 5/8 into an improper fraction.

4 = 32/8

(The fraction bar is basically division)

32/8 + 5/8 = 37/8

Now, flip it to find the answer.

6/37

That is the answer.

Hope I helped

Answer:

u=16

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

]650 divided by 6 = 108

Answer:

he put 3 fish everyday for 6 days

Answer:

x = 6

Step-by-step explanation:

Step 1: Write equation

75 - 3.5x - 4x = 4x + 6

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

75 - 3.5(6) - 4(6) = 4(6) + 6

75 - 21 - 24 = 24 + 6

54 - 24 = 30

30 = 30

Answer:

yes because if they want a bigger pizza or more they can just buy 2 eight inch pizza

Step-by-step explanation:

pizza is lit

The polar coordinates of the Cartesian coordinate (1,3) is (√10, 74.49°).

To convert the Cartesian coordinate (1,3) to polar coordinates, follow the steps below:

Step 1: Plot the point (1,3) in the Cartesian plane. We have;Cartesian Plane

Step 2: Determine the distance (r) of the point from the origin using the distance formula;r = √(x² + y²)r = √(1² + 3²)r = √(1 + 9)r = √10

Step 3: Determine the angle (θ) between the positive x-axis and the line segment connecting the origin to the point (1,3).

We can find θ using any of the following formulas;

θ = tan⁻¹(y/x)θ = cos⁻¹(x/r) if x is positiveθ = cos⁻¹(x/r) + π if x is negative and y is positiveθ = tan⁻¹(y/x) + π if x is negative and y is negativeθ = ½ π if x is zero and y is positiveθ = 3/2 π

if x is zero and y is negativeθ is undefined if x is zero and y is zeroθ = cos⁻¹(1/√10) if x is positiveθ = cos⁻¹(-1/√10) + π if x is negative and y is positiveθ = tan⁻¹(3/1) + π

if x is negative and y is negativeSince x = 1 and y = 3,θ = cos⁻¹(1/√10)θ ≈ 74.49°

Step 4: Write the polar coordinates as (r, θ) using the determined values;r = √10 and θ ≈ 74.49°

To learn more about : polar coordinates

https://brainly.com/question/29840804

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Answer:

في الأسبوع الماضي ، اشترى تشين جالونًا من البنزين للغالون الواحد. هذا الأسبوع اشترى جالونًا من البنزين مقابل الدولار للغالون

Step-by-step explanation:

في الأسبوع الماضي ، اشترى تشين جالونًا من البنزين للغالون الواحد. هذا الأسبوع اشترى جالونًا من البنزين مقابل الدولار للغالون

Answer:

1. 2x + y = 3

2. y = -5

3. x -y = -3

4. 3x -y = 9

5. x + y = -2

6. 6x + y = -5

7. x + y = 2

8. y = -3

9. x + y = 4

10. x - y = -2

Step-by-step explanation:

It will take too long to explain all questions, so if you want more information on how to do these kinds of math problems please comment on this answer.

Answer:

Something

Step-by-step explanation:

Something and something and thats it!

Answer:

solution:

Here,7+4-2-8=13-9

or, 9-B=4

or, -B=4-9

or-B=-5

*B= 5

Answer:

7040

Step-by-step explanation:

You do 5280 times 4 which is 21120.  Then you do 21120 divided by 3 and get 7040.

Answer:

c. -10/7

Step-by-step explanation:

-v-23/21=1/3

-v=1/3+23/21

-v=10/7

v=-10/7

Answer:

Step-by-step explanation:

Statements:

A. The ratio of ginger ale to the entire punch bowl is 1 to 4

B. The ratio of orange juice to ginger ale is 2 to 2

C. The ratio of juices to the ginger ale is 2 to 2

D. The ratio of the entire punch bowl to the juices is 2 to 4

E. The ratio of the orange juice to the raspberry juice is 1 to 1

Answer:

Showing results for plants

Search instead for plsntd

Map of plants

Burson Feed & Seed Inc

4.7  

(26) · Garden center

124 Rome St

Open ⋅ Closes 5PM · (770) 832-6252

Sold here: plants

Pat's Place

3.3  

(3) · Garden center

60 Old Airport Rd

Open now · (770) 836-0597

Sold here: plants

Garden Center at The Home Depot

5.0  

(2) · $ · Garden center

1332 S Park St

Open ⋅ Closes 9PM · (770) 832-1796

Step-by-step explanation:

Answer:

A) 585 miles

B) 584 miles

Step-by-step explanation:

We are told that the satellite pass directly over two tracking stations A and B, which are 90 mi apart.

This means that we can look at this as forming a kind of triangle where Tracking stations A & B will be

opposite ends of the base of the triangle while the satellite position will be the apex of the triangle.

We are given the angles of elevation at A and B to be 87.0° and 84.2° respectively.

Now, if we depict the satellite position as C. Then we have;

Angle at C = 180 - (87 + 84.2)

Angle at C = 8.8°

I've attached an image depicting this triangle.

A) To find the distance of the satellite from Station A, from the image attached, the distance will be AC.

Since AB is 90 mi.

Thus, using sine rule, we have;

AB/sin C = AC/sinB

Plugging in the relevant values;

90/(Sin 8.8) = AC/(sin 84.2)

AC = (90 × (sin 84.2))/(Sin 8.8)

AC = 585.27

To the nearest mile gives;

AC = 585 miles

B) To find out how high the satellite is above the ground, is the perpendicular distance from point C to line AB

Let's call the point at which the line touches AB as D.

It means angle D is 90° and it means triangle ADC it's a right angled triangle where AC is the hypotenuse = 585 miles.

Thus, using Trigonometric ratios we can find CD

Sin(87) = CD/585

CD = (Sin 87) x 585

CD = 584.198 miles

Approximating to the nearest mile gives;

CD = 584 miles

Answer:

Distance from A to Satellite: 1832.951 miles

Distance from satellite to ground: 1830.439 miles

Step-by-step explanation:

Answer: So unfortunately a lot of these answers for this question are not answering it correctly for the way that it is asked, which is not their fault because they cannot see the image in which it is referring to. Thats because in this question when it says the angle of elevation of A is 87° it is actually talking about the angle OUTSIDE of side A in the image, NOT THE INSIDE ANGLE. meaning that the inside angle across from angle B at 84.2 is actually 93° not 87°. (since it is the corresponding angle on a 180° line and we follow the geometric laws).

Now say we name the triangle ABC, we now have INNER ANGLE A at 93° and INNER ANGLE B at 84.2°.

To get INNER ANGLE C you subtract both ANGLE A & B added together from 180° to get ANGLE C since the all interior angles of a triangle = 180°

180°-(93°+84.2°)=2.8° so INNER ANGLE C =2.8°

Now we can use the LAW OF SINES to find the LENGHT OF SIDE "a"(lower case) (DISTANCE from A to C)(Which is Distance from Satellite to Station A)

DISTANCE FROM A TO C is referred to side "b" (lower case), as it is the side across from the INNER ANGLE B, same as side "c" (lower case) is DISTANCE FROM A TO B, as it is across from INNER ANGLE C.

LAW OF SIGNS EQUATION

b/sinB= c/sinC which means:

b/sin(84.2)=90/sin(2.8)

Which equates to c=90sin84.2/sin(2.8)

Which = 1832.951 (DISTANCE FROM SATELLITE TO A)

NOW to find the DISTANCE FROM THE SATELLITE TO GROUND: Draw a straight line down from satellite making a new RIGHT TRIANGLE.

Even though it is a RIGHT TRIANGLE (Call it XAC, X being the GROUND ANGLE) you can still use the Law of Sines to figure out the HEIGHT FROM GROUND TO SATELLITE.

This is where the 87° ANGLE comes in. With the new RIGHT TRIANGLE we have created, we know 2 of the interior angles: 87° and 90°. to find last interior angle just add together and subtract from 180.

180°-(87°+90°)=3°

Since we know side a SIDE "a" from previous Triangle, it now just becomes SIDE "x" (DISTANCE FROM A TO SATELLITE) which is 1832.9 miles.

Now use law of sines to find new side A (DISTANCE FROM X(GROUND) to SATELLITE(C)

The equation would be:

a/sinA=x/sinX which is

a/sin87=1832.951/sin90 which equates:

1832.951sin(87)/sin90=

1830.439 miles.

Very long and hard problem especially without image which I shall add. Good effort to everyone who tried to answer problem, it was correct if ANGLE A was inside the 2 SATELLITES, unfortunately it just wasn't the right way to find the answer that the actual question being asked (or I assume the actual question since I had it in my homework as well), which again was impossible to know without the image the problem gave.

I could never find the right answer for this problem so I made this to try and help others once I finally found the right answer (which I did finally get correct on the homework so I know this is correct, my problem simply had the distance from A to B as 80 Miles so I just reworked it for this problem with 90 miles instead. It is the same procedure no mater the values you are given, just replace them with the ones you're being asked)

HOPE THIS HELPS =]

Answer:

Let x and y be the two numbers. And x > y.

Then,

x + y = 80

Also,

x = 4y - 5

Solving the two equations,

80 - y = 4y - 5

75 = 5y

Therefore, y = 15.

Hope this helps you.

Answer:

45+35=80

Step-by-step explanation:

Answer:

112°

Hope it helps :)

Answer:

112 degrees

Step-by-step explanation:

since a circle is 360 degrees, we can subtract 472 and 360 to get an angle that is in the same position. the result is 112 degrees.

Answer:

-40

Step-by-step explanation:

We multiply both sides by 5:

x = -5 * 8

so x = -40