What is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units

Which numbers below belong to the solution set of the equation 16x=224

Taya2010 [7]

x would equal 14 hope this helps

5 0

3 years ago

Each statement describes a transformation of the graph of y = x2. Which statement correctly describes the graph of y = (x + 4)2

alina1380 [7]

Vertex Form: $y=(x-h)^2+k$ , with (h,k) as the vertex.

So the new equation is in vertex form. And looking at this equation, we see the vertex as (-4,-7) (Remember that y = (x + 4)^2 - 7 can be also written as y = (x - (-4))^2 - 7).

Since negative x-coordinates go to the left on the x-axis and negative y-coordinates go down on the y-axis, your answer is going to be C. It is the graph of y = x^2 translated 7 units down and 4 units to the left.

6 0

3 years ago

Read 2 more answers

In which atmosphere layer do humans live most of their lives?

icang [17]

Answer:

Troposphere

Step-by-step explanation:

We humans live in the troposphere, and nearly all weather occurs in this lowest layer. Most clouds appear here, mainly because 99% of the water vapor in the atmosphere is found in the troposphere.

5 0

3 years ago

Identify the function that contains the data in the following table:Х-20o235f(x)531224O f(x) = x/ + 1O f(x) = x - 21O f(x) = lx

kirill [66]

To identify the function that contains the data in the table, we should first visualize the data.

A graph of the data is shown below:

From the plot above, we can identify that:

The graph above is a graph of f(x) = |x|, translated to the right 2 units and translated upwards 1 unit.

Hence, the function is:

$f(x)\text{ = |x-2| + 1}$

Answer:

Option D

3 0

1 year ago

I am having trouble with this relative minimum of this equation.

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$