Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.

Answers

Answer 1

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Answer:

The  generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is  [tex]y' = 4x +4[/tex]

The graph is shown on the first uploaded image

The  generally expression for the slope of [tex]y=2x^2+4[/tex] is   [tex]y' = 4x[/tex]

Step-by-step explanation:

From the question we are told that

  The  equation of the curve is [tex]y = 2x^2 + 4x[/tex]

First we differentiate the equation

So  

     [tex]y' = 4x +4[/tex]

Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is   [tex]y' = 4x +4[/tex]

The  next step is to substitute for x =  3 and  x =  0.5

So  for [tex]x_1 = 3 [/tex]

    [tex]y' = 4(3) +4[/tex]

     [tex]y' =m_1= 16[/tex]

And  for  [tex]x_2 = 0.5[/tex]

      [tex]y' = 4(0.5) +4[/tex]

       [tex]y' =m_2= 6[/tex]

Here m_1  and  m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So  at [tex]x_1 = 3 [/tex]

   [tex]y_1 = 2(3)^2 + 4(3)[/tex]

  [tex]y_1 = 21[/tex]

So the coordinate for the first tangent line is  

    [tex](x_1 , y_1 ) = (3 , 21)[/tex]

At  [tex]x_2 = 0.5 [/tex]      

    [tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]

=>  [tex]y_2 = 2.5[/tex]

So the coordinate for the second  tangent line is  

    [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]

Next we obtain the equation for the tangent lines

 So generally the slope is mathematically represented as

        [tex]m = \frac{y - y_1 }{x-x_1}[/tex]

For   [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and  [tex]y' =m_1= 16[/tex]

       [tex] 16 = \frac{y -21 }{x-3)}[/tex]

=>    [tex]y = 16x - 27[/tex]

For  [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and  [tex]y' =m_2= 6[/tex]

       [tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]

       [tex]y = 6x -0.5[/tex]

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating  y=2x^2+4 as follows

     [tex]y' = 4x[/tex]

     

Find The General Expression For The Slope Of A Line Tangent To The Curve Of Y=2x^2+4x At The Point P(x,y)

Related Questions

Can someone help me with 4?

Answers

Answer:

ok so the answer is 343

Step-by-step explanation:

so for 4) you first use PEMDAS(Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), and you do what's in the parenthesis first, so 7^4= 2401, that is inside the parenthesis, next you do the exponent outside the parenthesis, so is (2401)^2=5764801, and then you divide the 7^5=16807, so it looks like 5764801/16807=343

hope it helps

Answer:

The Answer is 343.

Step-by-step explanation:

First- We do the parenthesis first according to PEMDAS which is 7 x 7 x 7 x 7 equals 2401.

Next- We do 2401 x 2401 which equals 5764801.

Then- We do the bottom exponent which is 7 x 7 x 7 x 7 x 7 equals 16807.

Last- We divide 5764801 by 16807 and we get 343.

Hope this helps!

Which phrase should be inserted in the line to make a true statement? 2/3 is _____ 8/12 A. Is greater than B. Less than C. Cannot be compared.D.is equal to (HELP I NEED THIS HURRYY PLSSSS)

Answers

Answer:

the answer is equal because 8/12=2/3 so 2/3=8/12 (2/3)

Step-by-step explanation:

If the length of a box of Milk Duds box is tripled, how much longer will the box be?​

Answers

Answer:

3x

Step-by-step explanation:

x = original length of the box.

~theLocoCoco

Which expression is equivalent to –3 – 3x – 1 + x?
2x – 4
–2x + 4
–2x – 4?
4 – 2x

Answers

Answer:

-2x-4

Step-by-step explanation:

-3-1-3x+x

-4-2x

Answer:

-2x-4?

Step-by-step explanation:

Assignment on Edge 2021

⊂(®ω®)⊃  

someone please help me with #63! WILL MARK BRAINLIEST

Answers

Answer:

cos60=b/h

1/2= b/3

b=  3/2=1.5

again

sin60=p/h

[tex]\sqrt3[/tex]/2= p/3

p =3[tex]\sqrt3[/tex]/2

Step-by-step explanation:

Answer:

1.5 in. and [tex]\frac{3\sqrt{3} }{2}[/tex]in.

Step-by-step explanation:

easier method:

angle opp. to 30 degrees is 1/2 of hypotonuse:

3/2=1.5 inches

angle opp. to 60 degrees is [tex]\sqrt{3}[/tex] of 30 degree angle:

3/2*[tex]\sqrt{3}[/tex]=3[tex]\sqrt{3}[/tex]/2

Which are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”? Check all that apply. It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.” The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides. The hypothesis is: it is a trapezoid. The conclusion is: a quadrilateral having exactly one pair of parallel opposite sides. The conclusion is: it is a trapezoid.

Answers

Answer: A,B,E

Step-by-step explanation:

The statement is "The conclusion is: it is a trapezoid." the correct option is D.

What is a quadrilateral?

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We are given that;

The statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid”

Now,

The following statements are true regarding the statement "A quadrilateral having exactly one pair of parallel opposite sides is a trapezoid":

It is a conditional statement that can be written as “If a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid.”

The hypothesis is: a quadrilateral having exactly one pair of parallel opposite sides.

The conclusion is: it is a trapezoid.

Therefore, by quadrilaterals the answer will be "The conclusion is: it is a trapezoid."

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A serving of small frozen casserole is 1/3 of the pan. If you eat 1/4 of the pan, what fraction of a serving have you eaten

Answers

Answer:

If the portion of frozen casserole occupies 1/3 of the pan, it can be affirmed that it occupies 0.333 of it. Thus, if someone eats 1/4 of the pan, it could be stated that they are eating 0.25 of it.

Therefore, to determine the fraction of the portion that has been eaten, the following calculation must be performed:

33 = 100

25 = X

(25 x 100) / 33 = X

2500/33 = X

75.75 = X

25/33 = X

Therefore, the fraction of the serving that was eaten is 25/33, or 76% of the serving.

Where in real life do you work with radical expressions and functions? Give an example of your own.

Answers

Answer: Radical expressions are utilized in financial industries to calculate formulas for depreciation, home inflation and interest. Electrical engineers also use radical expressions for measurements and calculations.

Step-by-step explanation: Example: √x+y

√16

12+√x

√3*x²

the quotient of 15 and y

Answers

Answer:

Because we are working with a variable (y) and we don't know what number it represents, we can only write down what the calculation would be, but we can't get the actual number answer.

15/y

Step-by-step explanation:

A quotient is the answer to a division.

The statement "the quotient of 15 and y" can be written as 15/y

We have,

The statement "the quotient of 15 and y".

This can be written as,

15/y

The expression "15/y" represents the quotient of 15 and y.

When you divide 15 by y, you are calculating the quotient or the result of the division.

The numerator (15) represents the dividend, which is the number being divided, and the denominator (y) represents the divisor, which is the number by which you divide.

Thus,

The statement "the quotient of 15 and y" can be written as,

15/y

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MATH


Please heeeeeeeeeeeeeeelp​

Answers

Answer:
1. 5mn
2. -125p^3q^6

Step by Step:
1. 15m^2n^2/3mn
=5mn^2/n
=5mn

2. (-5q^2p)^3
=(-5pq^2)^3
=-125p^3q^6

I need help on. this question. (3x^6)^3 the answer must have one exponent

Answers

Answer:

[tex]27x^{18}[/tex]

Step-by-step explanation:

[tex]\left(3x^6\right)^3[/tex]

Separate [tex]3x^6[/tex]:

[tex]3^3\times\left(x^6\right)^3[/tex]

[tex]27\times\left(x^6\right)^3[/tex]

[tex]27x^{6\times3}[/tex]

[tex]27x^{18}[/tex]

What is the value of the expression 2.58 x - 53?​

Answers

Answer:

-136.74

Step-by-step explanation:

-136.74 is the answer because 2.58x53= 136.74 and then because one of the numbers is negative and in multiplication and devision if there is an odd number of negatives it’s negative and if there is an even amount it’s positive

If f(2) = 12 and f '(x) ≥ 3 for 2 ≤ x ≤ 5, how small can f(5) possibly be?

Answers

Answer:

21

Step-by-step explanation:

From our previous knowledge, if f'(x) = m ,

Then f(x) = mx+c

For a smaller value of f(5), m should be the smallest possible integer if m = 3

i.e. f(x) = 3x+c

replacing the value of x with 2 given from the question to get the value of c, we have:

f(x) = 3x+c

f(2) = (3×2)+c

where; f(2) = 12

12 = 6+c

- c = -12 + 6

- c = - 6

c = 6

Now, f(x) can now be;

f(x) = 3x + 6

f(5) = (3×5)+6

f(5) = 15 + 6

f(5) = 21

Therefore, smallest possible value of f(5) is 21

Please answer this question

Answers

Answer:

I think it would be B but im not completly sure.

Prasha has five blocks of wood The total weight of all five blocks of wood is 3 kilograms. 4 of the blocks of wood each have a weight of 650 grams. Work out the weight, in grams, of the other block of wood. Step by step please :).

Answers

Let’s convert 3 kilograms to 3000 grams just to make things easier.

650 * 4 = 2600 grams. This is the total weight of the 4 blocks.

To find the weight of the final block, 3000 - 2600 = 400 grams

The weight of the other block of wood is 400 grams.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Prasha has five blocks of wood the total weight of all five blocks of wood is 3 kilograms.

4 of the blocks of wood each have a weight of 650 grams.

∴ (4×650) = 2600 grams is the total weight.

So, the weight of the other block of wood is (3000 - 2600) grams.

= 400 grams.

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parallel to y = 3x – 1 and passes through the point ( – 4, – 11)

Answers

If the line is parallel, you know it’s going to have the same slope, which in this case is 3

Using the format y= mx + b, plug in your x and y values to find b (m is the slope)
-11 = 3(-4) + b
-11= -12 + b
b = 1

You now have all the needed values to write the equation in slope-intercept form:

y = 3x + 1



I need this right now please

Answers

I think this is the fraction -4/9
Yes i agree it is the first option

3.60 rounded to the nearest tenth

Answers

Answer:

3.6 its already rounded just take off the 0

The requried when rounding 3.60 to the nearest tenth is given as 3.60.

When rounding a number to the nearest tenth, we consider the digit immediately to the right of the tenth place. In this case, the number is 3.60.

The digit in the hundredth place is 0. Since it is less than 5, we do not need to round up. When rounding to the nearest tenth, if the digit in the hundredth place is 5 or greater, we would round up by increasing the digit in the tenth place by 1. However, if the digit in the hundredth place is less than 5, we leave the digit in the tenth place as it is.

In this case, since the digit in the hundredth place is 0, we simply keep the digit in the tenth place, which is 6. Therefore, rounding 3.60 to the nearest tenth results in 3.6.

Learn more about round-off here:

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What number is 7 unit to the leaft of -1

Answers

Answer:

-8

Step-by-step explanation:

Since its going left I’m assuming it means negative. So you’re adding -7 to -1.

That gives you -8.

2 lines intersect. Where the 2 lines intersect, 4 angles are created. Labeled clockwise, from uppercase right: angle 1 (3 x minus 1) degrees, angle 2 is blank, angle 3 (2 x + 9) degrees, and angle 4 is blank. What are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees.

Answers

Answer:angle 1 and 3 measure 29 degrees.

angle 2 and 4 measure 151 degrees.

Step-by-step explanation:

Answer:

29 and 151

Step-by-step explanation:

-5, -6, 0,6
Which pair of numbers has a sum of zero? (5 points)
-6,0
-5,6
6, -6
-5,0

Answers

Answer:

6,-6

Step-by-step explanation:

6+(-6)=6-6=0

The answer is 6,-6

Divide 2.9 x 107 by 6.9 x 103 by using scientific notation. Round your answer to one decimal place in scientific notation with no spaces

Answers

I think it’s 85 if I’m wrong Im really sorry

Please please help fast

Answers

Answer:

no I'm pretty sure. hope it helps

Answer: No

Step-by-step explanation:

First convert 10 feet to yards and also 20 inches to yards.

10 feet to yards is 3.3 and 20 inches to yards is  0.55

Now add them to see if they equal to 4 or greater than.

0.55 + 3.33= 3.88

3.88 is less than 4 so Anis will not be able to make a fence

Find the derivative of the function. g(x) = ∫5 x 4 x u2 − 1u2 +1 dug'(x) = g

Answers

Answer:

[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]

Step-by-step explanation:

The question can be better structured and represented as :

[tex]g(x) = \int ^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ du[/tex]

now the derivative of the function of g(x) is g'(x) which is equal to:

[tex]g'(x) = \dfrac{(5x)^2-1}{(5x)^2 +1 }\dfrac{d}{dx}(5x) - \dfrac{(4x)^2-1}{(4x)^2 +1 }\dfrac{d}{dx}(4x)[/tex]

[tex]\mathbf{g'(x) = 5 \times \dfrac{(25x^2-1)}{(25x^2+1)}- 4 \times \dfrac{(16x^2-1)}{(16x^2+1)}}[/tex]

PLEASE HELP A cylinder with radius 6 feet and height 6 feet has its radius doubled. How many times greater is the volume of the larger cylinder than the smaller​ cylinder? How many times greater is the volume of the larger cylinder than the smaller​ cylinder?

Answers

Answer:

16 Times Greater

Step-by-step explanation:

Smaller cylinder:

radius = 6 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)6^2(8)

radius = 24 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)24^2(8)

.

[(3.14)6^2(8)] / [(3.14)24^2(8)]

[6^2(8)] / [24^2(8)]

[6^2] / [24^2]

[36] / [576]

16 times greater

Answer:

Step-by-step explanation:

Smaller cylinder:

h = 6 ft

r = 6 ft

Volume of smaller cylinder = πr²h

                                             = π * 6 * 6 * 6 cubic ft

Bigger cylinder:

r = 6 * 2 = 12 ft

h = 6 ft

Volume of bigger cylinder = π * 12 * 12 * 6 cubic ft

Volume of bigger cylinder = π * 12 * 12 * 6

Volume of smaller cylinder    π * 6 * 6 * 6

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

                                           = 4 : 1

The volume of greater cylinder is 4 times than the smaller cylinder.

A student has some​ $1 and​ $5 bills in his wallet. He has a total of 14 bills that are worth ​50$. How many of each type of bill does he​ have?

Answers

Answer:

3.5$

Step-by-step explanation:

Nine 5's and five 1's. Nine five-dollar bills hit $45 dollars, and the remaining $5 can only be paid in 1's to reach 14 bills.

The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74. Find their ages

Answers

Noell is 17 and her father is 45
Noelle is 20. Her dad is 54.

23,500 rounded to the nearest thousand?

Answers

Answer:

24,000

Step-by-step explanation:

is simple just 3500 is closer to 4000 than 3000

Answer:

24,000

Step-by-step explanation:

A road map is drawn to the scale of 1 inch equals 20 miles. How far apart in miles are two towns which are 2 1/2 inches apart on the map?

Answers

50

Step-by-step explanation:

You set this up with a ratio,  1:20 or 1 equals 20 miles.   So i'm multiplying by 20 regardless.   Now I have 2 and a half inches or you can say 2.5.  Multiply 2.5 (on paper..) and 20 and there you go.    20 times 2 equals 40 and 20 times a half is 10, 40 + 10= 50.  

3. Jackie played the drums in the band. If he beat the drum at a rate of
110 beats per minute, how many beats would he play in 4 minutes

Answers

110x4=440 beats in 4 minutes

Answer:440 beats

Step-by-step explanation:

The minutes cancel when you multiply.

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