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4 years ago

At which of the given values is the graph discontinuous?

Mathematics

1 answer:

hammer [34]4 years ago

8 0

Answer: Option d.

Step-by-step explanation:

You can solve the problem shown above keeping on mind the facts shown below:

Observe that there is a point in the graph in which there is a jump or a discontinuity between both parts of the function.

The point mentioned is at x=5

By definition, this indicates that the function shown is not continuous at that point.

Therefore, you can conclude that the value in which the graph is discontinuous is the value of the option d: 5

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. 1 Find f for the function f. f(x) = 3x² + 3, x > 0 And find the domain

konstantin123 [22]

Answer:

y = $\sqrt{\frac{x-3}{3} }$

Domain = [3, infinity)

Step-by-step explanation:

x = 3y^2 + 3

3y^2 = x - 3

y^2 = (x-3)/3

y = $\sqrt{\frac{x-3}{3} }$

8 0

3 years ago

Find the area and perimeter of an isosceles trapezoid with legs 25cm and bases 16cm and 30cm

Varvara68 [4.7K]

A=1/2h(b1+b2)
= 1/2(h)(30+16)
>how to find h<
>30-16= 14/2 = 7<
>25²-7² = 625-49 = 576<
>√576 = 24 .. h=24<
= 1/2(24)(30+16)
= 12(46)
A = 552 cm²
P= b+b+l+l
= 30+16+25+25
P = 96 cm

4 0

4 years ago

Read 2 more answers

An arithmetic sequence is given below.

klasskru [66]

Answer:

$a_n=8+4n$

Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula:

$a_n=a+(n-1)d$

Where

a is the first term

d is the common difference

a is given as 12

To find d, we subtract any term from the term after it. So

d = 16 - 12 = 4

Now, the explicit formula for nth term is:

$a_n=a+(n-1)d\\a_n=12+(n-1)4\\a_n=12+4n-4\\a_n=8+4n$

3 0

3 years ago

Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(0, −8) and line

Musya8 [376]

Answer:

-1/32 × x

Step-by-step explanation:

let's define and identify the correct markers of the correct parabola.

so, we have the focus point F (0, -8).

we have the directrix y = 8.

that means the the vertex point (the middle between the focus and the directrix) is (0, 0).

a parabola is turning away from the directrix. the vertex here is below the directrix, so the parabola is opening downwards and has therefore a negative factor of x.

so, we can rule out the 2 positive answer options.

to decide between the other 2, let's use a value of x and see, if the point is equidistant to the focus and the directrix.

e.g. x = 1

so,

y = -1/8 × x²

gives us y = -1/8 for x = 1

that means the point is (1, -1/8).

the distance to the focus (0, -8) is

(1 - 0)² + (-1/8 - - 8)² = 1 + (7 7/8)² = 1 + (63/8)² =

= 64/64 + 3969/64 = 4033/64

the distance to the directrix is the distance to the point (1, 8) as the point on the directrix must have the same x value.

so, the distance (1, -1/8) to (1, 8) is

(1 - 1)² + (-1/8 - 8)² = 0 + (-65/8)² = 4225/64

that is not equal to the distance to the focus.

so, let's try

y = -1/32 × x

the point for x = 1 is (1, -1/32)

distance to focus

(1, -1/32) to (0, -8) = (1-0)² + (-1/32 - -8)² = 1 + (255/32)² =

= 1024/1024 + 65025/1024 = 66049/1024

distance to directrix

(1, -1/32) to (1, 8) = (1-1)² + (-257/32)² = 66049/1024

which is the same distance as to the focus.

so, y = -1/32 × x is the right answer.

FYI - for an actual distance I would have to create the square roots of the numbers used here.

but since we only needed to see, if distances are equal or not, it was sufficient to check if the squares of the distances are equal or not.

8 0

2 years ago

Perry acquired raw land as an investment 16 years ago. The land cost $50,000. In the current year, the land is sold for a total

Liula [17]

The cost of the land = $50000

The selling price of the land = $120000

Total profit gained on the land = $120000-50000=70000$

Total amount received in cash in current Year = $10000

As given , let us assume that Perry uses the installment method to recognize the gain

Profit to be recognized in current year using installment method =

(Total Profi *Cash Received) /Sales Consideration

= $\frac{70000*10000}{120000}$ =5833.33

Hence, Perry should recognize a gain of $5833.33

3 0

3 years ago