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3 years ago

Consider the differential equation: dy/dx = (y-2)(x^2+1)

Mathematics

1 answer:

Klio2033 [76]3 years ago

3 0

Answer:

Step-by-step explanation:

Given,

$\dfrac{dy}{dx}=(y-2)(x^2+1)$ ...(i)

Differentiating w.r. to x.

$\dfrac{d^2y}{dx^2}= (y-2)(2x)+ (x^2+1)\dfrac{dy}{dx}$

From equation (1)

$\dfrac{d^2y}{dx^2}= (y-2)(2x)+ (x^2+1)^2(y-2)$

Now, at the point (1,3)

$\dfrac{d^2y}{dx^2}= (3-2)(2\times 1)+ (1^2+1)^2(3-2)$

$\dfrac{d^2y}{dx^2}=6$

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Alik [6]

Input each points. (x,y) for each equation to find out if the system of equations are equivalent.

Point (-3,4) is a solution of this system of equations.

Point (-2,-6) isn't a solution of this system of equations.

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3 years ago

Roland says the number of cups of iced tea t depends on the number of tea bags b. He says the equation represents the relationsh

nika2105 [10]

Answer:

I think Roland is correct in his statement.

Step-by-step explanation:

Roland says the number of cups of iced tea t depends on the number of tea bags b and he says the equation represents the relationship between the number of tea bags b and the cups of iced tea $t = \frac{b}{1.5}$ .

I think Roland is correct in his statement and this is because here t is a function of b i.e. t = f(b) and hence, the number of cups of iced tea t depends on the number of tea bags b. (Answer)

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3 years ago

A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

3 years ago

In quadrilateral ABCD, angle A is 75 degrees, angle B is 115 degrees, and angle D is 90 degrees. What is the measure of angle C?

galina1969 [7]

Answer:

Step-by-step explanation:

A quadrilateral measured 360. if you do not know that you can multiply 360 by 2 because there are 2 triangles in a quadrilateral. Then you subtract 360 by 75,115, and 90. And you will get 80 degrees

7 0

3 years ago

Order Of operation.

Nikolay [14]

Answer

18(2)+12(2)-4(5)

36+24-20

60-20

Step-by-step explanation:

since they had two-18 yard passes and two 12 yard runs, that's the first part of the expression, and then they had four penalties that cost them 5 yards, and that was the last term. When you simplify, you end up with 40 yards gained.

In math

Passes: 18(2)

Runs: 12(2)

Penalties:4(5)

equation

18(2)*12(2)-4(5)

Hope it helped

7 0

3 years ago

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