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3 years ago

I really need help with this question

Mathematics

1 answer:

DerKrebs [107]3 years ago

6 0

I think its B ......

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(4x+5) (3x+1) -3 (x+1)

ollegr [7]

Answer:

-36x^3 - 69x^2 - 34x - 5

Step-by-step explanation:

(4x + 5) (3x + 1) -3 (x + 1)

(4x + 5) (3x + 1) ( -3x - 1)

12x^2 + 4x + 15x +5

Combine like terms

12x^2 + 19x + 5 (-3x - 1)

-36x^3 -57x^2 - 15x^2 -5

Combine like terms

-36x^3 - 69x^2 - 34x - 5

4 0

1 year ago

Let v be an eigenvector of a matrix A with a corresponding eigenvalue ?=2. Find one solution x of the system Ax=v.

Murljashka [212]

Answer with explanation:

For, a Matrix A , having eigenvector 'v' has eigenvalue =2

The order of matrix is not given.

It has one eigenvalue it means it is of order , 1×1.

→A=[a]

Determinant [a-k I]=0, where k is eigenvalue of the given matrix.

It is given that,

k=2

For, k=2, the matrix [a-2 I] will become singular,that is

→ Determinant |a-2 I|=0

→I=[1]

→a=2

Let , v be the corresponding eigenvector of the given eigenvalue.

→[a-I] v=0

→[2-1] v=[0]

→[v]=[0]

→v=0

Now, corresponding eigenvector(v), when eigenvalue is 2 =0

We have to find solution of the system

→Ax=v

→[2] x=0

→[2 x] =[0]

→x=0, is one solution of the system.

5 0

3 years ago

If <img src="https://tex.z-dn.net/?f=%5Cmathrm%20%7By%20%3D%20%28x%20%2B%20%5Csqrt%7B1%2Bx%5E%7B2%7D%7D%29%5E%7Bm%7D%7D" id="Tex

Harman [31]

Answer:

See below for proof.

Step-by-step explanation:

Given:

$y=\left(x+\sqrt{1+x^2}\right)^m$

First derivative

$\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $f(g(x))$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=f'(g(x))\:g'(x)$\\\end{minipage}}$

$\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}$

$\begin{aligned} y_1=\dfrac{\text{d}y}{\text{d}x} & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(1+\dfrac{2x}{2\sqrt{1+x^2}} \right)\\\\ & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(1+\dfrac{x}{\sqrt{1+x^2}} \right) \\\\ & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(\dfrac{x+\sqrt{1+x^2}}{\sqrt{1+x^2}} \right)\\\\ & = \dfrac{m}{\sqrt{1+x^2}} \cdot \left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(x+\sqrt{1+x^2}\right)\\\\ & = \dfrac{m}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m\end{aligned}$

Second derivative

$\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}$

$\textsf{Let }u=\dfrac{m}{\sqrt{1+x^2}}$

$\implies \dfrac{\text{d}u}{\text{d}x}=-\dfrac{mx}{\left(1+x^2\right)^\frac{3}{2}}$

$\textsf{Let }v=\left(x+\sqrt{1+x^2}\right)^m$

$\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{m}{\sqrt{1+x^2}} \cdot \left(x+\sqrt{1+x^2}\right)^m$

$\begin{aligned}y_2=\dfrac{\text{d}^2y}{\text{d}x^2}&=\dfrac{m}{\sqrt{1+x^2}}\cdot\dfrac{m}{\sqrt{1+x^2}}\cdot\left(x+\sqrt{1+x^2}\right)^m+\left(x+\sqrt{1+x^2}\right)^m\cdot-\dfrac{mx}{\left(1+x^2\right)^\frac{3}{2}}\\\\&=\dfrac{m^2}{1+x^2}\cdot\left(x+\sqrt{1+x^2}\right)^m+\left(x+\sqrt{1+x^2}\right)^m\cdot-\dfrac{mx}{\left(1+x^2\right)\sqrt{1+x^2}}\\\\ &=\left(x+\sqrt{1+x^2}\right)^m\left(\dfrac{m^2}{1+x^2}-\dfrac{mx}{\left(1+x^2\right)\sqrt{1+x^2}}\right)\\\\\end{aligned}$

$= \dfrac{\left(x+\sqrt{1+x^2}\right)^m}{1+x^2}\right)\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)$

Proof

$(x^2+1)y_2+xy_1-m^2y$

$= (x^2+1) \dfrac{\left(x+\sqrt{1+x^2}\right)^m}{1+x^2}\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)+\dfrac{mx}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m-m^2\left(x+\sqrt{1+x^2\right)^m$

$= \left(x+\sqrt{1+x^2}\right)^m\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)+\dfrac{mx}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m-m^2\left(x+\sqrt{1+x^2\right)^m$

$= \left(x+\sqrt{1+x^2}\right)^m\left[m^2-\dfrac{mx}{\sqrt{1+x^2}}+\dfrac{mx}{\sqrt{1+x^2}}-m^2\right]$

$= \left(x+\sqrt{1+x^2}\right)^m\left[0]$

$= 0$

8 0

1 year ago

F(x)=3x+2 what is f(5)

mario62 [17]

Answer:

Step-by-step explanation:

f(5)=3*5+2 where X is equal to 5

7 0

3 years ago

Help please

Len [333]

Answer:

Ques 1) 1440°

Ques 2) 4000

Ques 3) 33

Step-by-step explanation:

Ques 1)

The sum of the measures of the angles in degrees of a polygon with 'n' sides is given by: 180×(n - 2).

Now we have to find the sum of the measures the angles of a polygon with 10 sides.

i.e. n=10

Hence the value of the expression 180×(n-2) when n=10 is given by:

180×(10-2)=180×8=1440.

Hence, the sum of measure of the angles of a polygon with 10 sides is: 1440°.

Ques 2)

The Expression 500v gives the number of points a player earns for completing v voyages in video game.

We are asked to find the number of points earned for completing 8 voyages.

i.e. v=8 the value of 500v will be 500×8=4000.

Hence, 4000 points are earned for completing 8 voyages.

Ques 3)

we have to find the value of the question as given in the figure:

7x+y+16 for x=2 and y=3.

Hence, we find the value of the expression:

7×2+3+16=33.

Hence, the value of the expression is 33.

8 0

2 years ago