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Mashutka [201]
3 years ago
15

✧・゚:Multiple Choice:・゚✧

Mathematics
2 answers:
muminat3 years ago
7 0

Answer:

-2

Step-by-step explanation:

Slope is rise over run  -2/1

Rom4ik [11]3 years ago
5 0

Answer:

-2

Step-by-step explanation:

slope is rise over run

-2/1

= -2

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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
Maria earned &amp;10.50 per hour working at an ice cream shop. She earned $147 each week before taxes. Write and solve an equati
Mekhanik [1.2K]
She worked 13 hours a week i think
5 0
3 years ago
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing
Stolb23 [73]
99+7.5 +3 +1.5 =111 that your awner 111

6 0
3 years ago
The equation d = 22.5n + 27.5 represents the amount of money, in dollars, that Kathryn earns for each sale she makes. The variab
egoroff_w [7]
The answer is c. I think not really sure
5 0
3 years ago
Read 2 more answers
One way to check on how representative a survey is of the population from which it was drawn is to compare various characteristi
weqwewe [10]

Answer:

a) See step by Step explanation

b) z(s) = 48.88

c) We reject H₀. The sample is not representative of American Adult Population

Step-by-step explanation:

From sample

sample mean .    x = 49.28

sample standard deviationn   s = 17.21

sample size  n₁  = 4857

Population mean according to Census data

μ  = 37.2

a) Test Hypothesis

Null Hypothesis .                  H₀ .                    x =  μ  = 37.2

Alternative Hypothesis        Hₐ .                    x ≠ μ

b) We have sample size (4857) we can use normal distribution

z (c) for    α = 0.01   α/2 . = 0.005  is from z-table . z(c) = 2.575

To calculate  z(s) =  ( x  - μ ) / s /√n

z(s) =  12.08 * √4857 / 17.21

z(s) = 12.08* 69.64 / 17.21

z(s) = 48.88

z(s) > z(c)

We should reject H₀. The sample is not representative of American Adult population

7 0
3 years ago
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