Ask question

Ask question

All categories

2 years ago

11

The following curve passes through (3,1). Use the local linearization of the curve to find the approximate value of y at x=2.8.

...?

2 answers:

Vesnalui [34]2 years ago

6 0

ANSWER:

y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105

STEP-BY-STEP EXPLANATION:

y = (2x+13)/(2x^2+1)

y' = ((2x^2+1)*(2) - (2x+13)(4x)) / (2x^2+1)^2

at x=3, this is

y'(3) = (19*2 - 19*12)/19^2 = -10/19

So, your linearization is

y ≈ (-10/19)*(x-3) + 1

At x=2.8, this is

y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105

Artist 52 [7]2 years ago

3 0

d/dx (2 x^2 y + y = 2x + 13) 4xy + 2x^2 y' + y' = 2 4xy + y'(2x^2 + 1) = 2 y' = (2- 4xy)/(2x^2 +1)

<span>ow we can use this in a linear equation for a slope Ty = -5x/8 +5(3)/8 +8/8 = -5x/8 +(15+8)/8 = -5x/8 +23/8 this will gives us an approximation at x=2.8 now</span>

You might be interested in

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

Nataly_w [17]

Answer: 0.1289

Step-by-step explanation:

Given : The proportion of all students at a large university are absent on Mondays. : $p=0.15$

Sample size : $n=12$

Mean : $\mu=np=12\times0.15=1.8$

Standard deviation = $\sigma=\sqrt{np(1-p)}$

$\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369$

Let x be a binomial variable.

Using the standard normal distribution table ,

$P(x=4)=P(x\leq4)-P(x\leq3)$ (1)

Z score fro normal distribution:-

$z=\dfrac{x-\mu}{\sigma}$

For x=4

$z=\dfrac{4-1.8}{1.2369}\approx1.78$

For x=3

$z=\dfrac{3-1.8}{1.2369}\approx0.97$

Then , from (1)

$P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289$

Hence, the probability that four students are absent = $0.1289$

3 0

2 years ago

Jason places a mirror on the ground 40 feet from the base of a tree. He walks backwards until he can see the top of the tree in

MakcuM [25]

Given that the angle of incidence is equal to the angle of reflection, we can state tha the angle formed by the eyes of Jason with the mirror is equal to the angle formeb by the top of the three with the same mirror.

Then, you can write this similarity equation:

[height of the eyes of Jason] / [distance from the poistion of Jason to the image on the mirror] = [height of the tree / distance from the mirror to the base of the tree]

6feet / 8feet = x/40feet

x = 40feet *[6/8] = 30 feet.

Answer: 30 feet.

4 0

2 years ago

Read 2 more answers

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

Mrac [35]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have $DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute $A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

5 0

2 years ago

The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

Anit [1.1K]

Answer: The correct option is A.

Step-by-step explanation: We are given a polynomial which is a sum of other 2 polynomials.

We are given the resultant polynomial which is : $8d^5-3c^3d^2+5c^2d^3-4cd^4+9$

One of the polynomial which are added up is : $2d^5-c^3d^2+8cd^4+1$

Let the other polynomial be 'x'

According to the question:

$8d^5-3c^3d^2+5c^2d^3-4cd^4+9=x+(2d^5-c^3d^2+8cd^4+1)$

$x=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)$

Solving the like terms in above equation we get:

$x=(8d^5-2d^5)+(-3c^3d^2+c^3d^2)+(5c^2d^3)+(-4cd^4-8cd^4)+(9-1)$

$x=6d^5-2c^3d^2+5c^2d^3-12cd^4+8$

Hence, the correct option is A.

5 0

2 years ago

Read 2 more answers

The diagram shows a cube of side length 4 inches. A is a vertex of the cube, while B and C are located on opposite edges of the

Nikolay [14]

Answer:

we will get an isosceles triangle as a result.

Step-by-step explanation:

when the point A is joined to B and C we will get the side AB and AC of equal length.

length of AB and AC could be calculated easily with the help of pythagorean theorem where the base and perpendicular are of length 4in and 1in .

when we will cut a plane including the the points A,B and C we will get a triangle whose sides AB and AC are equal but BC would be of distinct length.

Hence, the resultant figure will be an isosceles triangle.

5 0

2 years ago

Read 2 more answers