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3 years ago

Functions f(x) and g(x) are shown below:

Mathematics

1 answer:

kondor19780726 [428]3 years ago

4 0

We look for the minimum of each function.
For f (x) = 3x2 + 12x + 16:
We derive the function:
f '(x) = 6x + 12
We match zero:
6x + 12 = 0
We clear the value of x:
x = -12/6
x = -2
We substitute the value of x in the equation:
f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16
f (-2) = 4
For g (x) = 2sin(x-pi):
From the graph we observe that the minimum value of the function is:
y = -2
Answer:
A function that has the smallest minimum y-value is:
y = -2

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2 years ago

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zmey [24]

Answer:

Part 22) The area is $A=15a^3b^6\ units^2($ and the perimeter is $P=10a^2b^4+6ab^2\ unit$

Part 24) The area is $A=16m^3n\ units^2$ and the perimeter is $P=24mn\ units$

Part 26) The area is equal to $A=9\pi x^6y^{2}\ units^2$

Step-by-step explanation:

Part 22) Find the perimeter and area

step 1

The area of a rectangle is equal to

$A=LW$

we have

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$W=3(a)(b^2)\ units$

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute in the formula

$A=(5(a^2)(b^4))(3(a)(b^2))$

$A=15a^3b^6\ units^2$

step 2

The perimeter of a rectangle is equal to

$P=2(L+W)$

we have

$L=5(a^2)(b^4)\ units$

$W=3(a)(b^2)\ units$

substitute in the formula

$P=2(5(a^2)(b^4)+3(a)(b^2))$

$P=10a^2b^4+6ab^2\ unit$

Part 24) Find the perimeter and area

step 1

The area of triangle is equal to

$A=\frac{1}{2}bh$

where

$b=8mn\ units$

$h=4m^2\ units$

Remember that

When multiply exponents with the same base, adds the exponents and maintain the base

substitute the given values

$A=\frac{1}{2}(8mn)(4m^2)$

$A=16m^3n\ units^2$

step 2

Find the perimeter

I will assume that is an equilateral triangle (has three equal length sides)

The perimeter of an equilateral triangle is

$P=3b$

where

$b=8mn\ units$

substitute

$P=3(8mn)$

$P=24mn\ units$

Part 26) Find the area

The area of a circle is equal to

$A=\pi r^{2}$

where

$r=3x^3y\ units$

Remember the property

$(a^{m})^{n}=a^{m*n}$

substitute in the formula the given value

$A=\pi (3x^3y)^{2}$

$A=9\pi x^6y^{2}\ units^2$

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2 years ago

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pashok25 [27]

Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

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3 years ago

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Step-by-step explanation:

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