Express x^4+1 ÷x ^3+9x in partial fraction

Shubham, Ashish, and Vinay participated in a long jump competition on their sports day. Shubham jumped 41 m 2 , while Ashish jum

9966 [12]

Answer:

Vinay jumped = 49m

Step-by-step explanation:

Given:

Shubham jumped = 41m

Ashish jumped = 3m less than Shubham

Vinay jumped = 11m more than Ashish

Find:

Length of Viney's jump

Computation:

Ashish jumped = Shubham jumped - 3m

Ashish jumped = 41m - 3m

Ashish jumped = 38m

Vinay jumped = Ashish jumped + 11m

Vinay jumped = 38m + 11m

Vinay jumped = 49m

6 0

3 years ago

Help its due in 15 mins

Anton [14]

Answer:

$\sqrt{44} = 2\sqrt{11}$

Step-by-step explanation:

Apply pythagorean theorem:

ABD is a right triangle with angle ADB = 90

hence AD = $\sqrt{AB^{2} - BD^{2} }$ where BD = 10 because it is half of BC

AD = $\sqrt{12^{2}-10^{2} }$ = $\sqrt{44} = 2\sqrt{11}$

8 0

2 years ago

Prove that root 7 is irrational by the method of contradiction

Alchen [17]

Let assume that $\sqrt7$ is a rational number. Therefore it can be expressed as a fraction $\dfrac{a}{b}$ where $a,b\in\mathbb{Z}$ and $\text{gcd}(a,b)=1$ .

$\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2$

This means that $a^2$ is divisible by 7, and therefore also $a$ is divisible by 7.

So, $a=7k$ where $k\in\mathbb{Z}$

$(7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2$

Analogically to $a^2=7b^2$ ------- $b^2$ is divisible by 7 and therefore so is $b$ .

But if both numbers $a$ and $b$ are divisible by 7, then $\text{gcd}(a,b)=7$ which contradicts our earlier assumption that $\text{gcd}(a,b)=1$ .

Therefore $\sqrt7$ is an irrational number.

8 0

3 years ago

4+(-7)-(-3) What will be the answer ?

viva [34]

=0 just need points tho lol

6 0

2 years ago

Please help me answer this question

avanturin [10]

By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ .

<h3>How to analyze a differential equation</h3>

Differential equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a differential equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that $z = \cos (2\cdot x + 3\cdot y)$ and $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ , then we conclude that:

$\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)$

$\frac{\partial^{2} t}{\partial x^{2}} = - 4 \cdot \cos (2\cdot x + 3\cdot y)$

$\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)$

$\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)$

$- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z$

By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ .

To learn more on differential equations: brainly.com/question/14620493

#SPJ1

3 0

2 years ago

Express x^4+1 ÷x ^3+9x in partial fraction​

Express x^4+1 ÷x ^3+9x in partial fraction