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Aleks [24]
3 years ago
9

Consider the function below, which has a relative minimum located at (-3 , -18) and a relative maximum located at (1/3, 14/17).

f(x) = -x^3 - 4x^2 + 3x Select all ordered pairs in the table which are located where the graph of f(x) is decreasing. (-1,-6) (2,-18) (0,0) (1,-2) (-3,-18) (-4,-12)
Mathematics
1 answer:
leonid [27]3 years ago
8 0
First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27).  But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing.  The first derivative of the function is f'(x)=-3x^2-8x+3.  Set the derivative equal to 0 and factor to find the critical numbers. 0=-3x^2-8x+3, so x = -3 and x = 1/3.  We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing.  From there we will look at our points to determine which fall into the "decreasing" category.  Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞.  In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval.  In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval.  In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval.  In order to determine where our points in question fall, look to the x value.  The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12).  The point (-3, -18) is already a min value.
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8 goes in the place of thousands

5 goes in the place of hundred thousands

And 1 goes in the place of ten thousands

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Antonia picks one card from a set of three cards. The cards are a king (K), a queen (Q), and a jack (J). She then spins a spinne
Zielflug [23.3K]

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4 0
3 years ago
determine if each polygons are similar, if so, write the similarity statement and the similarity ratio. if not explain why.
Delicious77 [7]

Answer:

They are not similar

Step-by-step Explanation:

For two polygons to be considered similar, two conditions must be met:

1. The ratio of their corresponding sides must be equal, and must have the same scale factor.

2. Their corresponding angles must be the same. That is, the corresponding angles must be congruent.

Now let us examine the two polygons ( ∆AYP and ∆BOX) given to ascertain if they are similar.

First, we can observe that only two of their corresponding sides were given. The third corresponding side, "YP/OX" is not given. This makes it difficult for us to tell if the polygons are similar, if we are to base our conclusion on merely considering the ratio of their corresponding sides.

Although, the two given corresponding sides (AY/BO & AP/BX), both have equal ratio ⅖, i.e. AY/BO = AP/BX = ⅖. This is not enough to tell both polygons are similar, as we cannot tell if the third corresponding side would give us same ratio, since it wasn't given in the diagram.

==>Next is to examine the interior angles of the polygons, whether the measure of their corresponding angles are the same.

Thus, from the diagram, we can see that two angles of the each triangle were given. We can find the measure of the third angle not given since we know that sum of the interior angles of a triangle = 180°

Thus, <P in ∆AYP = 180 - (90+20) = 180 - 110

<P = 70°

Thus, <B in ∆BOX = 180 - (90+80) = 180 - 170

<B = 10°

From the above calculation, comparing both polygons having known the measures of their corresponding angles, we can conclude that both polygons given in the question are not similar.

This is because the measure of their corresponding angles are not congruent.

<A is not congruent to <B, so likewise with <P and <X.

4 0
3 years ago
An experiment was conducted to compare the wearing qualities of three types of paint (A, B, and C) when subjected to the abrasiv
MaRussiya [10]

Answer:

A) H0:  mean of A= mean of B= mean of C

   H1: all means are unequal

B) 3.48194

C) 0.04515

D) H0 is accepted. There is significant difference among mean hours after which visibile abrasion is observed for each type of paint

Step-by-step explanation:

A) Here Anova test will be used as we are comparing three groups

B) mean of A= 229.6, SD of A= 158.1962, SE of A= 50.026

   mean of B= 309.9 , SD of B= 147.8742, SE of B= 46.7619

   mean of C= 427.8, SD of C= 196.8179, SE of C= 62.2393

overall mean= 322.43

degrees of freedom between groups= 3-1=2

degrees of freeddom of error= total number of observations - number of groups= 30-3= 27

total degrees of freedom= total number of samples-1= 30-1 =29

Sum of squares between groups=∑ sample size of group×(individual group mean- over all mean)²

=198772.4667

mean of sum of squares between groups= sum of squares between groups/ (number of groups -1)

  = 198772.4667/2

sum of squares of error=∑∑ (individual observation of group- group mean)²

                                            = 770670.9223

mean sum of squares of erros= sum of squares of error/(total number of samples-number of groups)

                                                       = 770670.92/27

                                                         = 28543.38

F- stat= mean sum of squares between groups/ mean sum of squares of error

     F stat= 3.48194

C) p- value= 0.04515

D) since F-stat is greater than p- value, null hypothesis is rejected

from F distribution table

F(2,27)=

3 0
3 years ago
uhm pueden contestarme esto xfa- es para una amiga y tenemos que tener diferente respuestas si pueden claro :))
agasfer [191]

Answer:

hola

Step-by-step explanation:

t4eyyybkjdiwefvusknlabj dih

3 0
3 years ago
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