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svetlana [45]
2 years ago
6

Solve the inequality

Mathematics
1 answer:
aev [14]2 years ago
3 0

Answer:

x<3

Step-by-step explanation:

4x-7<5

4x<5+7

4x<12

x<3

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The region bounded by y=(3x)^(1/2), y=3x-6, y=0
Ganezh [65]

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is y = (3x)^{\frac{1}{2} }

⇒ y^{2} = 3x ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

y^{2} - y - 6 = 0

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = \int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx

= \sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}

= [\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} }  }{3}] - [13.5 - 18 - 6 + 12]

= 6 - 1.5

= 4.5 sq. units. (Answer)

7 0
3 years ago
Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x) be?
bekas [8.4K]

Using the concept of domain, the domain of (f.g)(x) is given by:

{x ∈ ℝ | x ≠ 3}

---------------------

  • The domain of a function is given by all possible input values, that is, <u>on a graph, all values that the x-axis assumes.</u>
  • In the graph, <u>function f assumes all real values.</u>
  • Function g is not defined for x = 3, thus, it's domain is all real values except 3.
  • Thus, the multiplication, as fg(x) = f(x) \times g(x), will also not be defined at x = 3, and the domain of the multiplication is:

{x ∈ ℝ | x ≠ 3}

A similar problem is given at brainly.com/question/4175434

4 0
3 years ago
A family spent $186 per week for food. This was 20% of its weekly income. What was the weekly income?
geniusboy [140]
It was $930.

To over check, multiply it by 20% , you will get $186.

Hope this helps !
5 0
3 years ago
Read 2 more answers
Brilliance for the right answer
maks197457 [2]
1cc means one cubic centimeter. I advise you to look at the letter units
4 0
3 years ago
Read 2 more answers
Graph this following function
Inessa05 [86]

Answer:

Please find attached the graph of the following function;

\left\{\begin{matrix}x - 1 & if & -2 \leq x < 0\\ 1 & if  & x = 0 \\ 3 & if & 0 < x \leq 2\end{matrix}\right.

Step-by-step explanation:

We note that the function is linear from x = 2 to just before x = 0

The linear relationship of the function f(x) with x changes just before x = 0

At x = 0, the value of f(x) is indicated as 1

From just after x = 0, the function is a straight horizontal line y = 3

The function also changes value immediately after x = 0 to the line y = 3

The areas where the function is defined are shown in continuous lines

8 0
3 years ago
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