the function f(x) =kx^4+8x^2 has three turning points, a maximum value of 8 and a root at x=2. determine the value of k as well as the other zeros

The Function F(x) =kx^4+8x^2 Has Three Turning Points, A Maximum Value Of 8 And A Root At X=2. Determine

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Answer 1

Given:

The function is f(x) =kx^4+8x^2.

The function has zero at x = 2.

Explanation:

The function has zero at x = 2, so f(2) = 0.

Determine the value of k by using f(2) = 0.

\(\begin{gathered} f(2)=k(2)^4+8(2)^2 \\ 16k=-32 \\ k=-\frac{32}{16} \\ =-2 \end{gathered}\)

So function is,

\(f(x)=-2x^4+8x^2\)

For the zeros of the function f(x) = 0. So,

\(\begin{gathered} -2x^4+8x^2=0 \\ -2x^2(x^2-4)=0 \\ -2x^2(x-2)(x+2)=0 \\ x=0,2,-2 \end{gathered}\)

So other roots of the function is 0 and -2.

Answer:

Value of k is -2

Other roots: 0 and -2


Related Questions

Jamall has 20 mo of planes and cars. He has three times as many cars in points. What is the

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But what is the question

what is 56+32 gcf and sum

Answers

Answer:

The GCF=8 The Sum=88

Aidan measure the perimeter of his classroom.He notices the classroom is 1m wider than it is long.Theperimeter of the classroom is between 20 and 35m.The length of each side is a whole number .
what could the dimensions of the room be?find four different possibilities

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Answer:

Step-by-step explanation:

The area of Mrs Brown’s classroom is

63 m2

. The area of Mr Black’s

classroom is 64 m2

. Mr Black’s

classroom is bigger.

Find the area of the parallelogram ABCD
А
B
12 cm
-10 cm-
C
D
-30 cm

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Answer:

I think it is 3600

Step-by-step explanation:

if a1 = 6 and an =5an-1 then find the value of a6

Answers

To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:

a1 = 6

a2 = 5a1 = 5(6) = 30

a3 = 5a2 = 5(30) = 150

a4 = 5a3 = 5(150) = 750

a5 = 5a4 = 5(750) = 3750

Now, we can find a6 using the recurrence relation:

a6 = 5a5 = 5(3750) = 18750

Therefore, the value of a6 is 18750.

help me with this PLEASE

help me with this PLEASE

Answers

Answer:

132°

Step-by-step explanation:

y°=7x+20° (vertically opposite angles)

3x°+7x°+20°=180° (interior angles, since M is parallel to N)

10x+20°=180°

10x=180°-20°

10x=160°

x=16°

y°=7(16°)+20°

y°=112°+20°

y°=132°

Your answer will be 132 degrees

Given a sphere with a diameter of 6.2cm, find its volume to the nearest whole

Answers

Answer:

the answer is 12

Step-by-step explanation:

d=2r=2*6.2=12.4

URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).

Answers

Answer:

\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)

\(7 = - \frac{8}{3} ( - 3) + b\)

\(7 = 8 + b\)

\(b = - 1\)

\(y = - \frac{8}{3} x - 1\)

The y-intercept is -1.

There are 120 boys in Morris middle school. What is the total number
students in Morris middle school?

Answers

Answer:

121

Step-by-step explanation:

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The total number of students

This cube has a volume of 1 millimeter.what is the side Length of the cube

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Answer:

1 milimiter

Step-by-step explanation:

that the answer

At a workshop , each of the 100 participants hugs each other participants once. Find the total number of hugs?​

Answers

Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

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Answer:

86 is the answer as it is the number after 85

85487
- 24315
= 61172

What is the slope of a horizontal line?

Answers

Answer:

Slope of a horizontal line. When two points have the same y-value, it means they lie on a horizontal line. The slope of such a line is 0, and you will also find this by using the slope formula.

Question provided in attachment.

Question provided in attachment.

Answers

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

How to calculate the value

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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What is the frequency of type A blood in this population? Enter your answer to two decimal places (example: 0.25 or 10.00).

Answers

The question is incomplete. Here is the complete question.

ABO blood type is examined in a Taiwanese population, nad the allele frequencies are determined. In the population, f(IA)=0.3, f(IB)=0.15 and f(i)=0.55.

Part A: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype IAIA? Enter your answer to two decimal places.

Part B: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype IBIB? Enter your answer to four decimal places.

Part C: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype IAIB? Enter your answer to two decimal places.

Part D: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype IAi? Enter your answer to two decimal places.

Part E: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype IBi? Enter your answer to three decimal places.

Part F: Assuming Hardy-Weinberg conditions apply, what is the frequency of genotype ii? Enter your answer to four decimal places.

Part G: What is the frequency of type A blood in this population? Enter your answer to two decimal places.

Part H: What is the frequency of type B blood in this population? Enter your answer to four decimal places.

Part I: What is the frequency of type AB blood in this population? Enter your answer to two decimal places.

Part J: What is the frequency of type O blood in this population? Enter your answer to four decimal places.

Answer: Part A: f(IAIA) = 0.09

              Part B: f(IBIB) = 0.0225

              Part C: f(IAIB) = 0.05

              Part D: f(IAi) = 0.16

              Part E: f(IBi) = 0.082

              Part F: f(ii) = 0.3025

              Part G: f(type A) = 0.25

              Part H: f(type B) = 0.1050

              Part I: f(type AB) = 0.05

              Part J: f(type O) = 0.3025

Step-by-step explanation: A population in Hardy-Weinberg equilibrium is a population with a constant value in the population's allele frequency.

In the population of Taiwan, frequencies are:

A: Frequency for genotype IAIA: Frequency of allele A is 0.3, then for genotype IAIA:

f(IAIA) = 0.3²

f(IAIA) = 0.09

B: Frequency of allele B is 0.15. Then, for genotype IBIB:

f(IBIB) = 0.15²

f(IBIB) = 0.0225

C: Frequency for genotype IAIB:

f(IAIB) = 0.3*0.15

f(IAIB) = 0.05

D: Frequency for genotype IAi:

f(IAi) = 0.3*0.55

f(IAi) = 0.16

E: frequency for genotype IBi:

f(IBi) = 0.15*0.55

f(IBi) = 0.082

F: frequency for allele i is 0.55. Then, for genotype ii:

f(ii) = 0.55²

f(ii) = 0.3025

Individuals with type A blood can be IAIA or IAi. Using probability's "OR" rule:

f(type A) = 0.09 + 0.165

f(type A) = 0.25

The same happens to individual with type B blood:

f(type B) = 0.0225 + 0.0825

f(type B) = 0.105

Since blood type is a codominance, i.e., allele A and allele B are expressed, frequency of type AB is equal to frequency of genotype AB:

f(type AB) = 0.3*0.15

f(type AB) = 0.05

Frequency for type O is:

f(type O) = 0.55²

f(type O) = 0.3025

What is the measure of x?
Angles are not necessarily drawn to scale.
B
40°
F
G
A
с
H
31°
D
E
x=

What is the measure of x?Angles are not necessarily drawn to scale.B40FGAH31DEx=

Answers

Answer:

x=71°

Step-by-step explanation:

x is 71 degrees because the unknown angle is the two known angle degrees added together.

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2. The Johnsons are planning a family reunion for 21 people. Each family is made up of
three people. Use a model or numbers to solve the equation 3x = 21. How many families
will attend the reunion?
Show your work

Answers

Answer: x=7

Step-by-step explanation:

3x=21

21 divided by 3 is 7

so x equals 7

Answer:

7 families

|||+|||+|||+|||+|||+|||+||| = 21

  7 families of 3 = 21

Step-by-step explanation:

3x=21

x=7 families

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Answers

Answer:

H. 3\(\frac{3}{4}\)feet

Step-by-step explanation:

Length of scale drawing = \(\frac{3}{12}\) × 15feet

                                        = 3\(\frac{3}{4}\)feet

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Find the area of a square with side length x when x is equal to the given value. Is the area of a square and the length of its side directly proportional? Justify your answer.

1. x=15 ft.
2. x=10 in.
3. x=3 in
so can you figure out the correct answers for 1,2 and 3? You have to figure out what the area of the square is for each value and you need to figure out if the area of the square and the length of its side is or is not directly proportional to quantities.

Answers

Answer:

1. 15*15

2. 10*10

3. 3*3

Step-by-step explanation:

Answer:

Square the given value

Step-by-step explanation:

1. 15^2=225

10^2=100

3^2=9

A square has sides of EQUAL length. area is length times width. So, if each side is the same, square the given value.

Given: tangent to Circle O.

If m = 140°, then A =

Answers

The measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Join the points B and O and then join points D and O

Angle A = (1/2)Angle BOD

Angle B = 140 degrees

Angle A = (1/2)140 degrees

Angle A = 70 degrees

Thus, the measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

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Given: tangent to Circle O.If m = 140, then A =

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.3 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to one decimal place.)

Answers

Answer:

  decreasing 0.5 m/s

Step-by-step explanation:

You want the rate at which the height of a shadow on a wall is decreasing as a 2 m tall man walks at 1.3 m/s toward the wall. The shadow is cast by a light 12 m from the wall, and the man is 4 m from the wall at the time of interest.

Similar triangles

In the attached diagram, triangles ABC and LMA are similar. This lets us write the proportion ...

  y/x = 2/(12 -x)

  y = 2x/(12 -x) . . . . . . multiply by x to get expression for y

Rate of change

Taking the derivative with respect to time gives ...

  y' = (2/(12 -x) +2x/(12-x)²)x'

At x = 4, this is ...

  y' = (2/8 +8/8²)x' = (3/8)x'

When x' = -1.3 m/s, the rate of change of the shadow height is ...

  y' = (3/8)(-1.3 m/s) = -0.4875 m/s

The length of the shadow is decreasing at about 0.5 m/s.

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A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward

which of the following is divisible by 90: 2,3,4,5,6,9,10

Answers

Answer: All of the numbers except for 4 is divisible by 90.

Step-by-step explanation: All the numbers beside 4 are divisible by 90 because they can all go into 90 equally.

Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7

Answers

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Find the perimeter of this shape

Find the perimeter of this shape

Answers

The perimeter of the given shape as represented in the task content is; 29 cm.

What is the perimeter of the given shape?

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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What is the meaning of "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un"?

What is the meaning of "all free variables of a formula (u1, . . . , un) are among u1, . . . , un"?

Answers

The phrase "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un" refers to a property of a logical formula ϕ with variables u1, u2, ..., un. In logic and formal systems, variables are used to represent unspecified elements or objects.

What does the phrase imply?

When a variable is considered "free" in a formula, it means that it is not bound by any quantifiers or other logical operators in the formula. In other words, it is a variable that is not restricted in any way within the formula.

The given statement implies that all the free variables in the formula ϕ(u1, . . . , un) are explicitly listed among the variables u1, u2, ..., un. In other words, the formula ϕ does not contain any additional free variables beyond the ones explicitly mentioned.

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evaluate 2(2)+-1 expression

Answers

Answer:

\(\boxed{\boxed{\sf 3}}\)

Step-by-step explanation:

\(\sf 2(2)+(-1)\)

Follow the PEMDAS order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

_________________________

\(\sf 2(2)+(-1)\)

1) Multiplication/Division:

\(\sf 2\left(2\right)\)

Multiply 2* 2= 4

\(\sf =4\)

2) Addition/Subtraction:

\(\sf 4+\left(-1\right)\)\(\sf +\left(-1\right)=-1\)

Subtract 1 - 4 = 3:

\(\boxed{\sf 3}\)

__________________________________

The height of a rectangular box is 7 ft. The length is 1 ft longer than thrice the width x. The volume is 798 ft³.
(a) Write an equation in terms of x that represents the given relationship.
The equation is

Answers

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Find the distance between the points (–7,–6) and (3,–6).

Answers

Answer:

(3+7)2+(-6+6)2

100+0

100

10

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Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions. Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.) Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.) Please help me outtt!

Answers

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Answer:

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WILL GIVE BRAINLIEST + MAX POINTS!!!Sara is working on a Geometry problem in her Algebra class. The problem

Two friends shop for fresh fruit. Elena buys a watermelon for ​$6.75 and 5 pounds of cherries. Taniy buys a pineapple for ​$3.55 and 4 pounds of cherries. Use the variable p to represent the​ price, in​ dollars, per pound of cherries. Write and simplify an expression to represent how much more Elena spent.

Answers

Answer:

The expression that represents how much more Elena spent is $3.2 + p

Step-by-step explanation:

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