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xxTIMURxx [149]
3 years ago
7

10 + 3x < 4 or 2x + 5 > 11 in interval notation​

Mathematics
1 answer:
Stella [2.4K]3 years ago
6 0

Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

7 ≥ 2 x − 5

12 ≥ 2 x

6 ≥ x

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

be any number less than 6, but it could also be 6.

Let's try the second example:

3 x − 2 4 > 4

3 x − 2 > 16    3 x > 18 x > 6

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

( 6 , ∞ )  

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )

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Svetach [21]

Let , side lawn is a.

Area of boundary is :

A=4\times5\times a\\\\A=20a\ m^2

Now, total cost is given by :

T=20a\times 36.25\\\\90625=725a\\\\a=125\ m

Area left is :

A'=a^2-20a\\\\A'=125^2-20\times 125\ m^2\\\\A'=13125\ m^2

Price to empty space with turfs is :

P=A'\times 20\\\\P=13125\times 20\\\\P=262500

Therefore, the cost of covering the empty space with turfs at the rate of Rs 20 per sq. metre is Rs 262500.

Hence, this is the required solution.

3 0
3 years ago
On day t=0t=0t, equals, 0, the stock is at its average value of {\$}3.47$3.47dollar sign, 3, point, 47 per share, but 91.2591.25
Norma-Jean [14]

Answer:

S(t) = a.sin (b.t) + d

a = -1.5, b = (2π/365), d = 3.47

S(t) = -1.5 sin (2πt/365) + 3.47

Step-by-step explanation:

Complete Question is presented in the attached image to this solution.

- Dingane has been observing a certain stock for the last few years and he sees that it can be modeled as a function S(t) of time t (in days) using a sinusoidal expression of the form

S(t) = a.sin(b.t) + d.

On day t = 0, the stock is at its average value of $3.47 per share, but 91.25 days later, its value is down to its minimum of $1.97.

Find S(t). t should be in radians.

S(t) =

Solution

S(t) = a.sin(b.t) + d.

At t = 0, S(t) = $3.47

S(0) = a.sin(b×0) + d = a.sin 0 + d = 3.47

Sin 0 = 0,

S(t=0) = d = 3.47.

At t = 91.25 days, S(t) = $1.97

But, it is given that T has to be in radians, for t to be in radians, the constant b has to convert t in days to radians.

Hence, b = (2π/365)

S(91.25) = 1.97 = a.sin(b×91.25) + d

d = 3.47 from the first expression

S(t = 91.25) = a.sin (91.25b) + 3.47 = 1.97

1.97 = a.sin (2π×91.25/365) + 3.47

1.97 = a sin (0.5π) + 3.47

Sin 0.5π = 1

1.97 = a + 3.47

a = -1.5

Hence,

S(t) = a.sin (b.t) + d

a = -1.5, b = (2π/365), d = 3.47

S(t) = -1.5 sin (2πt/365) + 3.47

Hope this Helps!!!

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Answer:

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Step-by-step explanation:

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Answer:

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So, therefore, the answer is 2/3.

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