What is the relative maximum and minimum of the function?
f(x)=x^3+6x^2-36

The relative maximum is at (–6, 216) and the relative minimum is at (2, –40).

The relative maximum is at (–6, 40) and the relative minimum is at (2, –216).

The relative maximum is at (6, 216) and the relative minimum is at (–2, –40).

The relative maximum is at (6, 40) and the relative minimum is at (–2, –216).

Answer with explanation:

The given fourth degree polynomial is:

  [tex]f(x)=x^4+6 x^3-3 x^2+17 x-15[/tex]

By rational root theorem , the possible Zeroes of the polynomial are factors of 15 .

Factors of 15 are

  [tex]=\pm 1, \pm 3, \pm 5, \pm 15[/tex]

There are 8 possible Zeroes of the given Polynomial expression.

Answer:

Step-by-step explanation:

    Hence the size of the sample space is: [tex]7^4[/tex]

     since we have to fill in 4 places with the help of these 7 letters.

  so in first place we can select one out of any 7 letters, similarly for the second place as it is not mentioned that repetition is not allowed and the same can be done for third and fourth place.

Hence size of sample space is: [tex]7\times7\times7\times7=7^4[/tex]

 Probability=(Number of favourable outcomes)/(Total number of outcomes)

Hence here the total number of outcomes=[tex]7^4[/tex]

Total number of favourable outcomes=outcomes that the first three letters are vowels=[tex]3\times3\times3\times7[/tex] (since in the first place we have three choices for a vowel{A,I,0} similarly for second and third place and in the fourth place any one of the 7 letters could come)

Hence the probability(P) that the first three letters of the four-letter code are vowels is given by:

[tex]P=\dfrac{3\times3\times3\times7}{7\times7\times7\times7}=\dfrac{3\times3\times3}{7\times7\times7}=\dfrac{27}{343}[/tex]

Hence, the Probability is: [tex]\dfrac{27}{343}[/tex]

The function f(x) is a piecewise function. To find the limit as x approaches 2, you must consider it from the left and right. From the left, the limit is ln(2), from the right, it's 4ln(2). Since these are not equal, the limit does not exist.

The function f(x) is a piecewise function where the first range covers 0 < x <= 2 and the second ranging from 2 < x <= 4. To find the limit of f(x) as x approaches 2, we need to find the limit from both directions, as x approaches 2 from the left (<) and the right (>).

For x approaches 2 from the left (<), f(x) boils down to ln(x), so the limit as x approaches 2 would be ln(2).

 For x approaching 2 from the right (>), f(x) translates to x^2 * ln(2). Substituting x = 2 in this function gives us (2)^2 * ln(2) which is 4ln(2)

The limit does not exist since ln(2) not equal to 4ln(2).

https://brainly.com/question/28771967

#SPJ11

The limit of the function f(x) as x approaches 2 does not exist, because the values obtained when approaching from the left (ln2) and from the right (4ln2) do not match.

The question is asking us to find the limit of the function f(x) as x approaches 2. This is a well-known concept in calculus, called the limit of a function. It is easy to solve using the rule that if f(x) and g(x) are two functions that agree at every point of a certain interval, except perhaps at one single point 'a', then their limits as x approaches 'a' are the same.

So let's find the limit as x approaches 2 by looking at each side independently. For x less than or equal to 2, the function is defined as ln(x). So when x approaches 2 from the left, we get ln(2). For x greater than or equal to 2, the function is defined as x^2ln(2). So when x approaches 2 from the right, we get 4ln(2).

Since the values obtained when approaching 2 from the left (ln2) and from the right (4ln2) do not match, we can conclude that the limit of f(x) as x approaches 2 does not exist.

https://brainly.com/question/7446469

#SPJ12

Answer: Triangle ABC and Triangle ECD

Step-by-step explanation:

In Triangle ABC and Triangle ECD

BD=CD and AD=ED [given in the figure]

∠BDA=∠EDC  [Vertically opposite angles are equal]

⇒ΔABC ≅ ΔECD [By SAS postulate]

SAS postulate or Side Angle Side postulate tells that if two sides and their included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

P(at least one phobic)

= 1 - P(none phobic)

= 1 - 0.89^2

= 1-0.7921

= 0.2079

Step-by-step explanation:

Answer:

$1.90

Step-by-step explanation:

The correct answer is b. 8. 8 is the greatest age Brooke could be.

Let's denote Brooke's age as B and Mia's age as M. According to the information given:

M = 2B + 3 (since Mia is three years older than twice Brooke's age).

 We also know that the sum of their ages is less than 30:

M + B < 30.

 Substituting the expression for M into the inequality, we get:

2B + 3 + B < 30,

3B + 3 < 30,

3B < 27,

B < 9.

Since Brooke's age must be a whole number, the greatest integer less than 9 is 8. Therefore, the greatest age Brooke could be is 8 years old.

The fifth term in the binomial expansion of [tex](x+5)^{8}[/tex] is [tex]\boxed{43,750\ x^{4}}[/tex].

Further explanation:

Given:

The binomial term is [tex](x+5)^{8}[/tex].

The expansion of [tex](x+5)^{8}[/tex] is as follows:

[tex]\boxed{{\left({a+b}\right)^n}=\sum\limits_{k=0}^n{{}^n{{\text{C}}_k}{a^{n - k}}{b^k}}}[/tex]

There are [tex]n+1[/tex] terms in the expansion of [tex](a+b)^{n}[/tex].

The sum of indices of [tex]a[/tex] and [tex]b[/tex] is equal to [tex]n[/tex] in every term of the expansion.

The general term [tex]T_{r+1}[/tex] of the binomial term [tex](a+b)^{n}[/tex] is as follows:

[tex]\boxed{{{\text{T}}_{r + 1}}={}^n{{\text{C}}_r}{a^{n - r}}{b^r}}[/tex]

For [tex]5^{th}[/tex] term the value of [tex]r[/tex] is calculated as follows:

[tex]\begin{aligned}r+1&=5\\r&=5-1\\r&=4\end{aligned}[/tex]

Now, the [tex]5^{th}[/tex] term of [tex](x+5)^{8}[/tex] is calculated as follows:

[tex]\begin{aligned}T_{5}&=T_{4+1}\\&=^8C_{4}\cdot x^{8-4}\cdot 5^{4}\\&=\dfrac{8\cdot 7\cdot 6\cdot 5}{4\cdot 3\cdot 2\cdot 1}\cdot x^{4}\cdot 625\\&=625\cdot 70x^{4}\\&=43,750x^{4}\end{aligned}[/tex]

Therefore, the fifth term of the binomial expansion [tex](x+5)^{8}[/tex] is [tex]\boxed{43,750\ x^{4}}[/tex].

Learn more:

1. Learn more about the axis of symmetry for a function https://brainly.com/question/1286775

2. Learn more about the y-intercept of the quadratic function https://brainly.com/question/1332667

3. Learn more about has the equation of a line https://brainly.com/question/1473992

Answer details:

Grade: Senior school

Subject: Mathematics

Chapter: Binomial Theorem

Keywords: Binomial theorem, expansion, (x+5)^8, 175000x3, 43750x4, 3125x5, 7000x5, fifth term, binomial expansion, genral term, binomial, polynomial, indices.

The answer is:

[tex]\[\boxed{43750x^4}\][/tex]

To find the fifth term in the binomial expansion of [tex]\((x + 5)^8\)[/tex], we use the binomial theorem. The binomial theorem states that:

[tex]\[(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k\][/tex]

For the expansion of [tex]\((x + 5)^8\)[/tex], we identify:

[tex]\[a = x, \quad b = 5, \quad n = 8\][/tex]

The general term in the expansion is given by:

[tex]\[T_{k+1} = \binom{n}{k} a^{n-k} b^k\][/tex]

We need to find the fifth term, which corresponds to  k = 4  (since k  starts from 0):

[tex]\[T_5 = \binom{8}{4} x^{8-4} 5^4\][/tex]

First, calculate the binomial coefficient [tex]\(\binom{8}{4}\):[/tex]

[tex]\[\binom{8}{4} = \frac{8!}{4! \cdot 4!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70\][/tex]

Next, calculate [tex]\( x^{8-4} \)[/tex] and [tex]\( 5^4 \):[/tex]

[tex]\[x^{8-4} = x^4\]\[5^4 = 625\][/tex]

Now, combine these results:

[tex]\[T_5 = 70 \cdot x^4 \cdot 625\][/tex]

Finally, multiply the coefficients:

[tex]\[70 \times 625 = 43750\][/tex]

Thus, the fifth term is:

[tex]\[43750x^4\][/tex]

Therefore, the answer is:

[tex]\[\boxed{43750x^4}\][/tex]

Answer:

The answer is 5,5,5.

Step-by-step explanation:

Reflection mean same like a mirror, it says reflectional symmetry. So the sides are the same.

Answer: b)  the sum of six times a number and five

Step-by-step explanation:

The given expression is [tex]6b+5[/tex], where b represents any number.

The above expression has two terms combined by addition operation.

In the first term there is one variable b and 6 as coefficient of b and the second term is a constant term of 5.

Therefore, the correct description of the given expression [tex]6b+5[/tex] is " the sum of six times a number and five".

Option: b is the correct answer.

b) the sum of six times a number and five.

We are given an algebraic expression in term of a variable 'b' as:

                                  6b+5

As we could see that here there are two terms in an expression one is: 6b and the other is 5 which is separated by a summation sign.

  Hence, when 6 times of a number 'b' is added to 5 we get the given expression(i.e. 6b+5)

              Hence, the answer is:  Option: b

Answer:

First option is correct. The location of point A after the transformations is (-5,1).

Step-by-step explanation:

It is given that the coordinates of point A are (-5,1).

Rectangle ABCD is reflected over the x-axis. then x-coordinate remains the same but the sign of y-coordinate is changed.

[tex](x,y)\rightarrow (x,-y)[/tex]

Coordinates of point A are

[tex](-5,1)\rightarrow (-5,-1)[/tex]

After that ABCD is reflected over the y-axis, then y-coordinate remains the same but the sign of x-coordinate is changed.

[tex](x,y)\rightarrow (-x,y)[/tex]

Coordinates of point A are

[tex](-5,-1)\rightarrow (5,-1)[/tex]

After that ABCD rotated 180 degrees about the origin, then the sign of both coordinates are changed.

[tex](x,y)\rightarrow (-x,-y)[/tex]

[tex](5,-1)\rightarrow (-5,1)[/tex]

Therefore option 1 is correct.

Answer:

the wolf is 76 lbs.

Step-by-step explanation:

first you have to divide 32 by 8, which is 4. Then you know that 4 is the divider to the simplified ratio, 3:8. So you multiply 3 and 4 which is 12. so you add 32 and 12 which is 44. then you subtract 44 by 120 which is 76. So The weight of the wolf is 76 lbs.

Answer:

(<2 and <4 are vert angles)     reason:given

(lines m and n intersect at p)   reason: def of vertical angles

(<2 and <3 are a linear pair)      reason: def of a linear pair

(<2 and <3 are a linear pair)      reason: def of a linear pair

(m<2+m<3=180)                          reason:angle addition postulate

(m<3+m<4=180)                          reason:angle addition postulate

(m<2+m<3=m<3+m<4                  reason:substitution property

(m<2 = m<4)                                 reason:subtraction property

<2 ~<4                                            reason:definition of ~ angles

Step-by-step explanation:

edgenuity 2020

Measure of angle TRV is [tex]130^{0}[/tex].

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

According to the question

< TRS  + < TRV = [tex]180^{0}[/tex]

(x - 10) + (2x + 10) = [tex]180^{0}[/tex]

3x =  [tex]180^{0}[/tex]

x = [tex]\frac{180}{3}[/tex]

x = [tex]60^{0}[/tex]

< TRV = 2x + 10

= 2([tex]60^{0}[/tex])+10

= 120 + 10

= [tex]130^{0}[/tex]

Hence, measure of angle TRV is [tex]130^{0}[/tex].

Find out more information about angle here

https://brainly.com/question/2617159

#SPJ2