1. A circular coil (200 turn radius of 6. 0 cm) is rotated in a uniform magnetic field (B = 3. 6x10-4 T) At t = 0 the coil is perpendicular to the field and at t = 0. 015s the coil is parallel to the field what is the average emf induced in the coil

Answers

Answer 1

The average EMF induced in the coil is 2.714336 × 10⁻⁴

To calculate the average EMF induced in the coil, we need to determine the change in magnetic flux through the coil and divide it by the time interval over which the change occurs.

The magnetic flux (Φ) through a coil is given by the formula:

Φ = B * A * cos(θ),

where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil.

When the coil is perpendicular to the field at t = 0, the angle θ is 90 degrees, and the magnetic flux is:

Φ1 = B * A * cos(90) = 0,

since the cosine of 90 degrees is zero.

At t = 0.015s, the coil becomes parallel to the field, so the angle θ becomes 0 degrees. The magnetic flux at this moment is:

Φ2 = B * A * cos(0) = B * A.

The change in magnetic flux (ΔΦ) during this transition is given by:

ΔΦ = Φ2 - Φ1 = B * A.

To find the average emf (ε) induced in the coil, we divide the change in magnetic flux by the time interval (Δt) over which the change occurs:

ε = ΔΦ / Δt.

Given that the radius of the coil is 6.0 cm, the area (A) of the coil can be calculated using the formula for the area of a circle:

A = π * r²

where r is the radius of the coil. Substituting the values, we get:

A = π * (0.06 m)²

Substituting the values of B and A, and noting that the time interval Δt is 0.015s, we can calculate the average EMF induced in the coil:

ε = (B * A) / Δt.

By substituting the known values, the calculation becomes:

ε = (3.6x10⁻⁴ T) * (π * (0.06 m)²) / 0.015 s. =  2.714336 × 10⁻⁴

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Related Questions

which situation is most likley to show a constant rate of change

Answers

Option B. The situation that would be more likely to show a constant rate of change would be B. The distance traveled by a truck driving at a constant speed compared with time.

How to solve for the rate of change

This is the factor that is used to determine if there is a decrease or an increase in a given factor.

A good way to d this is by the use of time and speed to compare the distance that is being traveled.

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Complete question

Which situation is most likely to show a constant rate of change?

A. The weight of a child compared with its age in months

B. The distance traveled by a truck driving at a constant speed compared with time

C. The cost of a new car compared with the number of tires it has

D. The outside temperature compared with the time of day

True or False: Both equations have 'no solutions'.
15x +4-2x = 3(6x + 5)
(2x-8)=(8x+36)

Answers

Answer:

False

Step-by-step explanation:

They both have 1 solution

15x + 4 = 3(6x +5)

15x +4 = 18x + 15  Multiple everything in the parentheses by 3.

4 = 3x + 15  Subtract 15 x from both sides

-11 = 3x   Subtract 15 from both sides

-11/3 = x  Divide both sides by 3

There is only one solution for this equation.

2x -8 = 8x + 36

-8 = 6x + 36  Subtract 2x from both sides

--44 = 6x  Subtract 36 from both sides

-44/6 = x Divide both sides by 6.

There is only one solution for this equation.

Answer:

false

Step-by-step explanation:

They both have solutions

Can someone help me out on these geometry questions? ASAP!!!

Write formal proofs the LA Theorm.

Answers

Question 4

1) [tex]\angle B[/tex] and [tex]\angle E[/tex] are right angles, [tex]\overline{AB} \cong \overline{DE}[/tex], [tex]\angle A \cong \angle D[/tex] (given)

2) [tex]\triangle CBA[/tex] and [tex]\triangle FED[/tex] are right triangles (a triangle with a right angle is a right triangle)

3) [tex]\triangle CBA \cong \triangle FED[/tex] (LA)

Note: I wrote the names of the triangles in an alternate order because of the word filter.

Question 5

1) [tex]\overline{XY} \perp\overline{WZ}[/tex], [tex]\overline{UV} \perp \overline{WZ}[/tex], [tex]\overline{VW} \cong \overline{YZ}[/tex], and [tex]\angle Z \cong \angle W[/tex] (given)

2) [tex]\angle XYZ[/tex] and [tex]\angle UVW[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle XYZ[/tex] and [tex]\triangle UVW[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\triangle XYZ \cong \triangle UVW[/tex] (LA)

5) [tex]\overline{UW} \cong \overline{XZ}[/tex] (CPCTC)

Question 6

1) [tex]\overline{PQ} \perp \overline{QT}[/tex], [tex]\overline{ST} \perp \overline{QT}[/tex], [tex]\overline{PQ} \perp \overline{ST}[/tex] (given)

2) [tex]\angle PQR[/tex] and [tex]\angle RTS[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle PQR[/tex] and [tex]\triangle STR[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\angle PRQ \cong \angle SRT[/tex] (vertical angles are congruent)

5) [tex]\triangle PQR \cong \triangle STR[/tex] (LA)

6) [tex]\overline{QR} \cong \overline{TR}[/tex] (CPCTC)

Evaluate: 2^-4=

A. 1/8

B. -8

C. -16

D. 1/16

Answers

Answer:

D.

[tex] \frac{1}{16?} [/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{2^{-4}}[/tex]

[tex]\huge\textbf{Simplify it: }[/tex]

[tex]\mathbf{2^{-4}}[/tex]

[tex]\mathbf{\approx \dfrac{1}{2^4}}[/tex]

[tex]\mathbf{= \dfrac{1}{2\times2\times2\times2}}[/tex]

[tex]\mathbf{= \dfrac{1}{4\times4}}[/tex]

[tex]\mathbf{= \dfrac{1}{16}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ D. \ \dfrac{1}{16}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

If a line has a slope of 1/3 and passes through the point (1,-2) which ff points also lies on the line a) -2,-5 b) -2,1 c) 4,-1 d) 4,10

Answers

Answer: c

Step-by-step explanation:

The equation of the line is

[tex]y+2=\frac{1}{3}(x-1)\\\\y+2=\frac{1}{3}x-\frac{1}{3}\\\\y=\frac{1}{3}x-\frac{7}{3}[/tex]

To determine which point lies on the line, we can substitute in the x coordinate and see if the equation gives the same y-coordinate.

If x = 2, then the equation of the line gives that y = -5/3.If x = 4, then the equation of the line gives that y = -1.

Therefore, the answer is c.

Evaluate 2x for each value of x. Write your answers in simplest form. Show your work!
1. x = 1/4
2. x = 1/3
3. x = 1/2
4. x = 1/6
5. x = 1/7
6. x = 1/8
7. x = 2/3
8. x = 3/4

Answers

1. 1/2

2.2/3

3. 1

4. 1/3

5. 2/7

6. 1/4

7. 4/3

8. 3/2

How to evaluate the value

To find 2x of the vale of x, we have to multiply the value of 'x' by 2

1. x = 1/4

[tex]2x = 2 * \frac{1}{4}[/tex] ⇒ [tex]\frac{2}{4}[/tex] ⇒[tex]\frac{1}{2}[/tex]

2. x = 1/3

[tex]2x = 2 * \frac{1}{3}[/tex] ⇒[tex]\frac{2}{3}[/tex]

3. x = 1/2

[tex]2x = 2* \frac{1}{2}[/tex] ⇒ [tex]\frac{2}{2}[/tex] ⇒ [tex]1[/tex]

4. x= 1/6

[tex]2x = 2* \frac{1}{6}[/tex] ⇒ [tex]\frac{2}{6}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

5. x = 1/ 7

[tex]2x = 2 * \frac{1}{7}[/tex] ⇒ [tex]\frac{2}{7}[/tex]

6. x = 1/8

[tex]2x = 2 * \frac{1}{8}[/tex] ⇒ [tex]\frac{2}{8}[/tex] ⇒ [tex]\frac{1}{4}[/tex]

7. x = 2/3

[tex]2x = 2 * \frac{2}{3}[/tex] ⇒ [tex]\frac{4}{3}[/tex]

8. x = 3/4

[tex]2x = 2 * \frac{3}{4}[/tex] ⇒ [tex]\frac{6}{4}[/tex] ⇒ [tex]\frac{3}{2}[/tex]

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What is the slope of the equation y =5/4x-7/4?

Answers

Answer is 5/4The slope is the number next to the “x” in the y intercept formula

y= m (slope) x + b

Answer: m= 5/4

Step-by-step explanation:

La ecuación general de la recta es y=mx+by=mx+b, donde m es la pendiente y b es la intersección en y

y=mx+by=mx+b

Find RS.
A. 12
B. 5
C. 10
D. 9

Answers

Answer:

5

Step-by-step explanation:

(2x - 6) + 1 + (x - 4) = 18

3x - 9 = 18

3x = 27

x = 9


RS = x - 4 = 9 - 4 = 5

Answer:

B. 5

Step-by-step explanation:


Pls mark brainiest if helpful!!

PQ + QR + RS = 18

This statement is equivalent to the following:

(2x - 6) + 1 + (x - 4) = 18.

This is because we substitute the line segments with their values.

Now that we have an equation to work with, we will solve it. We start by removing the parenthesis as they are not necessary here.

2x - 6 + 1 + x - 4 = 18

Next, we will make it, so x is alone on the left. We will do this by adding 6 and 4 to both sides

2x - 6 (+6) + 1 + x - 4 (+4) = 18 (+6) (+4)


After doing this we are left with the following equation:

2x + 1 + x = 28

Now we will subtract 1 from both sides to make x alone of the left side of the equation.

2x + 1 (-1) + x = 28 (-1)

After we solve this, we get the following:

2x + x = 27

We can add 2x and x and get 3x because 2 + 1 = 3.

3x = 27

We now simplify this equation by dividing both sides by 3.

[tex]\frac{3x}{3}[/tex] = [tex]\frac{27}{3}[/tex]

We again simplify the equation to the following:

x = 9

BUT THATS NOT THE ANSWER!

Now that we know what x is, we can solve for the value of RS.

We input 9 for x in the equation x - 4.

When we do this, we get 9 - 4 which is 5.

And this is our final answer!!


I hope I could help! Have an amazing day and good luck on your homework!

"You can't predict the future, but you can create it"
            -Juliana Palazzolo, 2022

Pls mark brainiest if helpful!!


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in a school, the ratio of the number of boys to the number of girls is 2:3 and the ratio of the number of girls to the number of teachers is 7:3. what is the ratio of the number of students to the number of teachers

Answers

Answer:

  35:9

Step-by-step explanation:

The ratios can be combined by making the common element be represented by the same number.

Adjusted ratios

The common element in the two ratios is the number of girls. In the first ratio, girls are represented by 3 ratio units. In the second ratio, they are represented by 7 ratio units. Multiplying the first ratio by 7 and the second ratio by 3 will make the number of girls the same in both.

  boys : girls = 2 : 3 = 14 : 21

  girls : teachers = 7 : 3 = 21 : 9

Then the extended ratio can be written ...

  boys : girls : teachers = 14 : 21 : 9

The number of students is the total of the numbers of boys and girls, so we have ...

  students : teachers = (14 +21) : 9

  students : teachers = 35 : 9

1. Find the product using Suitable Property a) 55×99 ​

Answers

Answer:

5445

Step-by-step explanation:

We can use distributive property.  a*(b - c) = (a*b) - (a *c)

  99 = 100 - 1

55 * 99 = 55 * (100 - 1)

            = 55*100 - 55*1

            = 5500 - 55

            = 5445

Find the slope of the line passing through the vertex and the y-intercept of the quadratic function
[tex]f(x) = 5x{}^{2} + 20x - 7 [/tex]

Answers

Find y intercept

y=5(0)²+20(0)-7y=0-7y=-7

Point(0,-7)

Find vertex

x coordinate

-b/2a-20/10-2

y coordinate

y=5(4)-40-7y=-27

Vertex at (-2,-27)

Slope

m=(-27+7)/-2-0m=-20/-2m=10

Answer:

10

Step-by-step explanation:

Vertex

The x-coordinate of the vertex of a quadratic equation in the form

[tex]f(x)=ax^2+bx+c\quad \textsf{is} \quad -\dfrac{b}{2a}[/tex]

Given function:

[tex]f(x)=5x^2+20x-7[/tex]

[tex]\implies a=5, \quad b=20, \quad c=-7[/tex]

x-coordinate of the vertex

[tex]\implies -\dfrac{b}{2a}=-\dfrac{20}{2(5)}=-2[/tex]

To find the y-coordinate of the vertex, substitute the found value of x into the function:

[tex]\begin{aligned}\implies f(-2) & =5(-2)^2+20(-2)-7\\& = 5(4)-40-7\\& = 20-47\\& = -27\end{aligned}[/tex]

Therefore, the coordinates of the vertex are (-2, -27).

y-intercept

The y-intercept is when the curve crosses the y-axis, so when x = 0.

To find the y-coordinate of the y-intercept, substitute x = 0 into the function:

[tex]\begin{aligned}\implies f(0) & =5(0)^2+20(0)-7\\& = 0 + 0-7\\& = -7\end{aligned}[/tex]

Therefore, the coordinates of the y-intercept are (0, -7).

Slope

To find the slope of the line passing through the vertex and the y-intercept, simply substitute the found points into the slope formula:

[tex]\implies \sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-27-(-7)}{-2-0}=\dfrac{-20}{-2}=10[/tex]

Therefore, the slope of the line passing through the vertex and the y-intercept of the given quadratic function is 10.

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F(x)=4x^3+7x^2x-1. G(x)=4x-2 find (f-g)(x)

Answers

Answer:

4x^3 + 7x^2 - 3x + 1

Step-by-step explanation:

BTW your question, there is a sign misssing

what is the monthly interest payment for an account with a balance of $100 and an APR of 12%

Answers

Monthly interest payment is $100.

According to the statement

balance in account = $100

APR = 12%

we use the formula Balance formula to solve this problem.

So, BALANCE * [APR / 12 month] to find monthly interest payment

Here balance is the starting amount in the bank account

And APR is the type of interest rate applied on the amount

And 12 month is the time period for which APR is applicable.

So, substitute the values in it then

Monthly interest payment = 100 * [12/12]

After solving the equation become

Monthly interest payment = 100*1

Monthly interest payment = 100$

So, Monthly interest payment is $100.

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Ralph Warren purchased 27 shares of stock at 16 3/8 per share. He paid a $27.50 brokerage fee. He later sold all 27 shares at 17 5/8 and paid a $28.75 brokerage fee. (36) What was his total cost for the stock including his brokerage fee? (37) What did he receive from the sale of the stock after he paid the brokerage fee? (38) Did he have a capital gain or loss? (39) How much was the gain or loss? (40) What was the net change from 16 3/8 to 17 5/8?

Answers

Based on the number of shares that Ralph Warren purchased, the total cost of the stock was $469.63. The amount he received from sales was $447.13. The capital loss was $22.50.

What was the gain on the sale of the shares?

The cost of the stock was:

= (27 x 16³/₈) + 27.50

= $469.63

The amount received from sales:

= (27 x 17⁵/₈) - 28.75

= $447.13

This capital gain (loss):

= 447.13 - 469.63

= -$22.50

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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$

Answers

The measure of angle D in the convex pentagon ABCDE is 132°

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the measure of angle D, hence:

angle A = x - 40.

∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)

3(x - 40) + 2x = 540

x = 132°

The measure of angle D in the convex pentagon ABCDE is 132°

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One factor of the polynomial 3x3 + 20x2 - 21x + 88 is (x + 8). what is the other factor of the polynomial? (note: use long division.)
oa (3x2 - 4x+11)
b. (3x - 4x)
c. (3x2 +11)
d. (3x2 + 4x - 11)

Answers

The other factor of the polynomial is a. 3x2-4x+11

Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)

We need to find another factor using long division method

So,

We will divide the polynomial by the factor to find the another factor

Therefore,

[tex]\sqrt[x+8]{3x^3+20x^2-21x+88}[/tex]

Now calculating

First multiplying [tex]3x^2[/tex] with (x+8) so , [tex]3x^2[/tex] will be in the quotient

We get [tex]3x^3+24x^2[/tex]

simplifying the calculation for [tex]3x^3+20x^2[/tex] and [tex]3x^3+24x^2[/tex]

We get the remainder is [tex]-4x^2-21x+88[/tex]

Second we will multiply -4x with (x+8) Where -4x will be in the quotient

We get [tex]-4x^2-32x[/tex] and then we will simplify the equation

We get 11x +88 as a remainder

The quotient we get is [tex]3x^2-4x[/tex]

Third we will multiply +11 with (x+8) Where +11 will be in the quotient

we get 11x+88

Simplifying the equation we get the remainder 0

So the quotient we get is  (3x2 - 4x+11)

Hence the another factor of the polynomial is  (3x2 - 4x+11)

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Given cos(x)=1/2, what is the value of cos(x+pi)?

Answers

Answer:

-1/2

Step-by-step explanation:

cos(x+pi) = -cos(x), so the answer is -1/2.

A paragraph proof

uses inductive reasoning to prove a statement.
contains a table with a logical series of statements and reasons.
uses a visual chart of the logical flow of steps needed to reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.

Answers

A paragraph proof D. contains a set of sentences explaining the steps needed to reach a conclusion.

What is a paragraph proof?

It should be noted that a paragraph proof simply means a way of presenting a mathematical proof.

In this case, it contains a set of sentences explaining the steps needed to reach a conclusion.

In conclusion, the correct option is D.

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Answer:

D: contains a set of sentences explaining the steps needed to reach a conclusion.  

can someone please help me with this problem?

Answers

360degree =2pie
X =3/5pie
Than we cross multiplication
X=(3/5pie multiply 360) all divide be two pie
Than x=108

the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.

Answers

Answer: 2400

Step-by-step explanation:

3000 x 20/100 = 600

Discount = 600

Sale price of the article: 3000-600 = 2400

A circle is formed when a plane slices through a cone. Which of the following describes the relationship between the plane and the cone

Answers

The plane is parallel to the base of the cone describes the relationship between the plane and the cone

A circle is a spherical form without boundaries or edges or we can say that A circle is a closed, curved object with two dimensions in geometry.

The produced cross-section is a circle when a plane slices a cone such that the plane is parallel to the base of the cone.

Ellipse is the shape that is produced when a plane cuts a cone at an angle such that it misses the base or the vertex. (As shown in figure)

Hence A circle is formed when a plane slices through a cone and the plane is parallel to the base of the cone

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Find the center and radius of the circle with the equation: (x-5)^2 + (y+1)^2 = 4 a. center: (-5, 1) radius: 4 c. center: (-5, 1) radius: 2 b. center: (5, -1) radius: 4 d. center: (5, -1) radius: 2

Answers

Answer:

d

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

(x - 5 )² + (y + 1)² = 4 ← is in standard form

with centre (5, - 1 ) and r = [tex]\sqrt{4}[/tex] = 2

A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail. What is the standard deviation of the distribution

Answers

Using the binomial distribution, it is found that the standard deviation of the distribution is of 0.67.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The parameters are:

n = 5, p = 0.1.

Hence the standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5 \times 0.1 \times 0.9} = 0.67[/tex]

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A college's basketball team will play 33 games next winter. Each game can result in one of 2 outcomes: a win or a loss. Find the total possible number of outcomes for the season record.

Answers

The total possible number of outcomes for the season record is [tex]2^{33}[/tex].

What is an outcome?

An event that may be given a mathematical probability is known as an outcome in mathematics (an outcome of an experiment). The amount of potential outcomes for a particular experiment determines the probability assigned to each result.The result of an experiment is a number of outcomes.

According to the question,

The basketball team at a college will play 33 games next winter. There are only two possible outcomes for each game: a win or a loss.

So, the total number of possible outcomes for the season record=[tex]2^{33}[/tex].

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pls help >>> How many solutions does the quadratic
function represented on this graph have?

Answers

Answer:

Zero real number solutions

Step-by-step explanation:

Doesn't intercept the x-axis -> No real solutions

Zero would be your final answer

. A scale factor of 2 is applied to the dimensions of the prism. What effect will this have on the volume

Answers

The volume of the prism would be enlarged by a factor of 8

How to determine the effect?

The scale factor is given as:

k = 2

Let the initial volume be v and the final volume be V.

The relationship between both volumes is

V = k^3 * v

This gives

V = 2^3 * v

Evaluate

V = 8v

Hence, the volume of the prism would be enlarged by a factor of 8

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Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin

Answers

Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

According to the statement

We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.

So, According to the given diagram

Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation of rectangle at the origin.

Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.

The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.

According to the diagram In Rectangle ABCD:

Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).

Now consider rectangle EFGH:  

Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).

Hence the scale factor is becomes from these values is:

EF/AB = EH/AD = FG/BC = HG/DC = 4/3.

Hence the scale factor becomes 4/3.

Also

∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).

So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

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20 POINTS ILL MARK U BRAINLIEST PLS

Answers

Answer:

13 + [tex]\sqrt{89}[/tex]

or

22.43398... (depends on how you round it)

Step-by-step explanation:

1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.

2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.

--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length

3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.

We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.

--> OB^2 = 25 + 64

--> OB^2 = 89

--> OB = [tex]\sqrt{89}[/tex]

Now that we know the lengths of all three sides, we can add them up.

--> 5 + 8 + [tex]\sqrt{89}[/tex]

--> 13 + [tex]\sqrt{89}[/tex]

or

--> 22.43398113....

Find the maximum and minimum values of the curve y=2x³-3x²-12x+10​

Answers

[tex] \underline{ \orange{\huge \boxed{ \frak{Answer : }}}}[/tex]

Let ,

[tex] \sf \large \color{purple} y = 2 {x}^{3} - 3 {x}^{2} - 12x + 10 \: --( \: 1 \: )[/tex]

[tex] \: \: \: [/tex]

Now , Diff wrt ' x ' , we get :

[tex] \sf \: \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} - 3 {x}^{2} - 12x + 10) \\ \sf \: \sf \: \frac{dy}{dx} = \frac{d}{dx} \: 2(3 {x}^{2} ) - \frac{d}{dx} 3 {x}^{2} - \frac{d}{dx} 12x + \frac{d}{dx} 10 \\ \sf \: \frac{dy}{dx} =2(3 {x}^{2} ) - 3(2x) - 12(1) + 0 \\ \sf \: \frac{dy}{dx} =6 {x}^{2} - 6x - 12 + 0 \\ \: \sf \red{\frac{dy}{dx} = 6 {x}^{2} 6x - 12 -- (2)}[/tex]

[tex] \: \: \: [/tex]

For maxima or minima \frac{dy}{dx} = 0

[tex] \: \: \: [/tex]

[tex] \sf \: 6 {x}^{2} - 6x - 12 = 0[/tex]

[tex] \: \: \: [/tex]

Divided by 6 on both side , we get.

[tex] \: \: \: [/tex]

[tex] \sf \: {x}^{2} - x - 2 = 0 \\ \sf \: {x}^{2} - 2x + x - 2 = 0 \\ \sf \: x(x - 2) + 1(x - 2) = 0 \\ \sf \: (x - 2)(x + 1) = 0 \\ \sf \: x - 2 = 0 \: \: \bold or \: \: x + 1 = 0 \\ \sf \fbox{x = 2 \: } \: \bold or \: \fbox{ x = - 1}[/tex]

[tex] \: \: \: [/tex]

Again Diff wrt ‘ x ’ , we get.

[tex] \sf \: \frac{d}{dx} =(\frac{dy}{dx} ) = 6\frac{d}{dx} - 6\frac{d}{dx}x - \frac{d}{dx}12 \\ \sf \: \frac{ {d}^{2}y }{ {dx}^{2} } = 6(2x) - 6(1) - 0 \\ \sf \: \sf \bold{ \frac{ {d}^{2}y }{ {dx}^{2} } =12x - 6}[/tex]

[tex] \: \: \: [/tex]

At x = 2

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12(2) - 6 \\ \: \: \: \sf \: = 24 - 6 \\ \: \: \: \: \sf \red{ = 18 > 0}[/tex]

At x = -1

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12( - 1) - 6 \\ \: \: \: \sf \: = - 12 - 6 \\ \: \: \: \: \sf \red{ = - 18 < 0 }[/tex]

[tex] \: \: \: [/tex]

x = 2 gives minima value of function.

[tex] \: \: \: [/tex]

x = -1 gives maxima value of function.

[tex] \: \: \: [/tex]

Now, put x = 2 in eqⁿ ( 1 )

[tex] \: \: \: [/tex]

[tex] \sf \: y \: minima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( {2})^{3} - 3 ({2})^{2} - 12(2) + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: = 2(8) - 3(4) - 24 + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: = 16 - 12 - 24 + 10 \\\sf \: \: \: \: \: \: \: \: \: \: = - 20 + 10 \\\sf \color{red}{\boxed{ = - 10}}[/tex]

[tex] \: \: \: [/tex]

The Point of minima is ( 2 , -10 ).

[tex] \: \: \: [/tex]

Now , put x = -1 in eqⁿ ( 1 )

[tex]\sf \: y \: maxima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( { - 1})^{3} - 3 ({ - 1})^{2} - 12( - 1) + 10 \\\sf \color{red}{\boxed{ = 17}}[/tex]

[tex] \: \: \: [/tex]

The point of maxima value is ( -1 , 17 ).

[tex] \: \: \: [/tex]

[tex] \: \: [/tex]

Hope Helps! :)

Marina correctly simplified the expression StartFraction negative 4 a Superscript negative 2 Baseline b Superscript 4 Baseline Over 8 a Superscript negative 6 Baseline b Superscript negative 3 Baseline EndFraction, assuming that a not-equals 0, b not-equals 0. Her simplified expression is below.

Negative one-half a Superscript 4 Baseline b Superscript empty box

What exponent should Marina use for b?

Answers

The exponent Marina should use for b is: D. 7.

How to Divide Exponents with the same Base?

When dividing, you subtract the exponents. I.e. [tex]a^m \div a^n = a^{m - n}[/tex].

Using the rule, we would also subtract the exponents of b in the simplified expression. Thus:

[tex]b^4 \div b^{-3}[/tex]

Subtract the exponents

4 -(-3) = 4 + 3 = 7.

Therefore, the Maria should use the exponent b = 7.

Learn more about dividing exponents on:

https://brainly.com/question/2263967

#SPJ1

Answer:  D

Step-by-step explanation:

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