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Nutka1998 [239]

3 years ago

7

How to determine increase and decrease of a function without calc?

1 answer:

pashok25 [27]3 years ago

4 0

You grab a peice of paper and a pen and right a graph and try increase and decrease

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Write an expression that matches the phrase '7 more than the product of 2 and 15"

Vsevolod [243]

Answer:

2 x 15 +7

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A triangle has side lengths of x, x+11, and 3x+5.

horrorfan [7]

Answer:

The answer is 5X+16

Step-by-step explanation:

The formula for perimeter of a triangle is a+b+c.

meaning we are adding up everything.

That is

(x)+(x+11)+(3x+5).

collect like terms.

and u end up getting

5x+16

3 0

3 years ago

I am having trouble with this relative minimum of this equation.<br>

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.

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

$f'(x)=12x^2+26x-12$

$f''(x)=24x+26$

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here: x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

$24(-2.6)+25$

$-37.5$

So we have a maximum at x=-2.6.

$24(.4)+25$

$9.6+25$

$34.6$

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

$y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56$

I'm shoving this into a calculator:

$y=-58.4654411$

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

If you graph $y=4x^3+13x^2-12x-56$ you should see the graph taking a dip at this point.

3 0

3 years ago

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes

Nitella [24]

Answer:

P ( X < 4 ) = 0.1736706

Step-by-step explanation:

Given:

- A random variable X follows a binomial distribution as follows,

Where n = 8, and p = 0.6.

Find:

- P ( X < 4 )?

Solution:

- The random variable X follows a binomial distribution as follows:

X ~ B ( 8 , 0.6 )

- The probability mass function for a binomial distribution is given as:

pmf = n^C_r ( p )^r (1-p)^(n-r)

- We are asked to find P ( X < 4 ) which is the sum of following probabilities:

P ( X < 4 ) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 )

- Use the pmf to compute the individual probabilities:

P ( X < 4 ) = 0.4^8 + 8^C_1*(0.6)*(0.4)^7 + 8^C_2*(0.6)^2*(0.4)^6 + 8^C_3*(0.6)^3*(0.4)^5 .

P ( X < 4 ) = 6.5536*10^-4 + 7.86432*10^-3 + 0.04128768 +0.12386304

Answer: P ( X < 4 ) = 0.1736706

7 0

3 years ago

At the beginning of the summer,

Anastaziya [24]

She saved $548 just for $575 minus the $27

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2 years ago

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