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3 years ago

How to you solve x2 -20x -17 = -53

Mathematics

1 answer:

Gennadij [26K]3 years ago

7 0

Answer:

solve for x

x=2

Step-by-step explanation:

x2-20x-17=-53

reorder like terms x2= 2x 2x=20x-17=-53

collect like terms 2x-20x=-18x -18x-17=-53

move constant to the right hand side and change its sign -18x=-53+17

calculate the sum -53+17= -36 -18x=-36

divide both sides by -18 -18x÷-18= x -36÷-18=2

x=2

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A tower is 234 meters tall. Jaylon is looking up at the top of the tower and thinking it would be cool to string a zip line from

gizmo_the_mogwai [7]

Answer:

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Step-by-step explanation:

The geometrical representation of the statement is summarized in the figure below attached. The length of the line is represented by hypotenuse of the right triangle, whose value is calculated by the help of trigonometrical relations:

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3 years ago

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Consider the following initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0, y(1) = 1 Let ∂f ∂x = (x + y)2 = x2 + 2xy + y2

IRISSAK [1]

$(x+y)^2\,\mathrm dx+(2xy+x^2-2)\,\mathrm dy=0$

Suppose the ODE has a solution of the form $F(x,y)=C$ , with total differential

$\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

This ODE is exact if the mixed partial derivatives are equal, i.e.

$\dfrac{\partial^2F}{\partial y\partial x}=\dfrac{\partial^2F}{\partial x\partial y}$

We have

$\dfrac{\partial F}{\partial x}=(x+y)^2\implies\dfrac{\partial^2F}{\partial y\partial x}=2(x+y)$

$\dfrac{\partial F}{\partial y}=2xy+x^2-2\implies\dfrac{\partial^2F}{\partial x\partial y}=2y+2x=2(x+y)$

so the ODE is indeed exact.

Integrating both sides of

$\dfrac{\partial F}{\partial x}=(x+y)^2$

with respect to $x$ gives

$F(x,y)=\dfrac{(x+y)^3}3+g(y)$

Differentiating both sides with respect to $y$ gives

$\dfrac{\partial F}{\partial y}=2xy+x^2-2=(x+y)^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies x^2+2xy-2=x^2+2xy+y^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=-y^2-2$

$\implies g(y)=-\dfrac{y^3}3-2y+C$

$\implies F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y+C$

so the general solution to the ODE is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=C$

Given that $y(1)=1$ , we find

$\dfrac{(1+1)^3}3-\dfrac{1^3}3-2=C\implies C=\dfrac13$

so that the solution to the IVP is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=\dfrac13$

$\implies\boxed{(x+y)^3-y^3-6y=1}$

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3 years ago

Given: p: 2x = 16 q: 3x – 4 = 20 which is the converse of p → q? if 2x ≠ 16, then 3x – 4 ≠ 20. if 3x – 4 ≠ 20, then 2x ≠ 16. if

exis [7]

If 3x – 4 = 20, then 2x = 16. Then the correct option is D.

<h3>What is the converse statement?</h3>

A converse claim is one that is derived by flipping the assumption and result of a predicate.

The condition will be

If p → q, then q → p.

The expressions are given below.

p: 2x = 16 q: 3x – 4 = 20

Then the converse of p → q will be

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Then the correct option is D.

More about the converse statement link is given below.

brainly.com/question/18152035

#SPJ1

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