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mestny [16]
3 years ago
14

HELP 40 POINTS

Mathematics
1 answer:
Tom [10]3 years ago
7 0
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

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Let f and g be the functions defined by f(x) = 10^ (x+2 / 3) and g(x) = log (x3 / 100) for all positive real numbers,
Vaselesa [24]

Answer:

F(x) and g(x) are not inverse functions.

Step-by-step explanation:

In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.

As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.

[tex]y=10^{(x+\frac{2}{3}) }\\\\log y=log 10^{(x+\frac{2}{3}) }\\log y = (x+\frac{2}{3}) . log10\\\frac{log Y}{log10} = (x+\frac{2}{3})\\\frac{log Y}{1} = (x+\frac{2}{3})\\log Y-\frac{2}{3}=x[/tex]

Now we change the variables.

F(x)=log x-\frac{2}{3}

F(x) and g(x) are not inverse functions.

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2 years ago
At the beginning of a snowstorm, Camden had 10 inches of snow on his lawn. The
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Answer:

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2 years ago
A Social welfare association decides to supply drinking water for the flood affected people. The drinking water is filled in a c
pickupchik [31]

Answer:

1,499 liter

Step-by-step explanation:

The rest of the question is:

each is in the shape of a cylinder of radius 21 cm and height is 50 cm.

==============================================================

The quantity of water left in the tanker after distribution

= Total quantity - Distributed quantity

Total quantity = Volume of the giving figure

                       = Volume of the cylinder + volume of 2 hemispheres

Volume of the cylinder of 4.2 m length and 1.2 m of a diameter.

L = 4.2 and radius = r = 0.5 * diameter = 0.5 * 1.2 = 0.6

Volume of cylinder = π r² L = (22/7) * 0.6² * 4.2 = 4.752 m³

Volume of 2 hemispheres = 2*0.5 * (4/3) π r³ = (4/3) * (22/7) * 0.6³

                                           =792/875 m³

Total volume = 4.752 + 792/875 = 198/35 ≈ 5.657 m³

Distributed quantity = 60 times the volume of a cylinder of radius 21 cm and height is 50 cm

Distributed quantity = 60 * π r² L = 60 * (22/7) * 21² * 50 = 4,158,000 cm³

Since 1 m³= 1,000,000 cm³

Distributed quantity = 4,158,000 cm³ = 4.158 m³

The quantity of water left in the tanker after distribution =

 = 198/35 - 4.158 ≈ 1.499 m³

Since 1 m³= 1,000 liter

The quantity of water left in the tanker after distribution =

  =  1.499 m³ = 1.499 * 1000 = 1,499 liter

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