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4 years ago

Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

1 answer:

4 0

1/2y^2=1/2x^2+8. The curve's slope at (x,y) is x/y, so dy/dx=x/y. To solve this differential equation, rearrange it to: y*dy=x*dx, and by integrating both sides, we get 1/2y^2=1/2x^2+C (some constant). Plug in (0,4) into this equation, 8=0+C, so C=8. The curve's equation is 1/2y^2=1/2x^2+8.

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A/ab-bsquare + b/ab-asquare?

lord [1]

Answer:

$\dfrac{(a+b)}{ab}$

Step-by-step explanation:

The given expression is :

$\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}$

It can be solved as follows :

$\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}=\dfrac{a}{b(a-b)}+\dfrac{b}{a(b-a)}\\\\=\dfrac{a}{b(a-b)}+\dfrac{b}{-a(-b+a)}\\\\=\dfrac{1}{a-b}(\dfrac{a}{b}-\dfrac{b}{a})\\\\=\dfrac{a^2-b^2}{ab(a-b)}\\\\=\dfrac{(a-b)(a+b)}{ab(a-b)}\\\\=\dfrac{(a+b)}{ab}$

So, the solution of the given expression is equal to $\dfrac{(a+b)}{ab}$ .

7 0

3 years ago

Geometry . Cosines / sines. Find a and round to the nearest 10th

Lorico [155]

This is the good part of Trigonometry, actually measuring triangles. It's much better than all the identities around sine and cosine and the rest, which actually have more to do with circles than triangles.

This part of trig has a short menu:

Law of Cosines. Three ways to write it, one is $c^2 =a^2+b^2-2ab \cos C$

Law of Sines: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Triangle angles: $A+B+C=180^\circ$

and two special cases of the Law of Cosines, the Pythagorean Theorem

$C=90^\circ, \quad \quad c^2=a^2+b^2$

and the Collinear Points Theorem:

$C=180^\circ, \quad \quad c^2=a^2+b^2 - 2 a b \cos 180^\circ = a^2+b^2+2ab=(a+b)^2$

$c = a+b$

Here we choose Triangle Angles followed by Law of Sines:

A = 180 - 105 -15 = 60 degrees

$\dfrac{a}{\sin 60^\circ}= \dfrac{2}{\sin 105^\circ}$

$a= \dfrac{2 \sin 60^\circ}{\sin 105^\circ} = 1.793...$

Answer: 1.8 cm

When I was a student we'd be expected to get $\sin 105^\circ$ exactly and get

$a = 3 \sqrt{2} - \sqrt 6$

But that was before online homework.

5 0

3 years ago

Background Layout Theme Transition 2 A hot air balloon travels up to 7500 feet. After exploring the sky for a few hours it desce

son4ous [18]

Answer:

No.

Step-by-step explanation:

This is incorrect because the hot air balloon traveled up to 7500 feet. The distance descended cannot be greater than 7500 feet. Joe's expression tells us that the hot air ballon descended 10500 feet. He is incorrect because 10500 > 7500.

5 0

3 years ago

Please help look at the pic and those are not the answers

Ivanshal [37]

2x²-2x-24 = 0

devide by 2

x²-x-12 = 0

(x+3) (x-4) = 0

x = -3
and
x = 4

5 0

3 years ago

Simplify the expresion 8w+5r-t+9r

Vilka [71]

To simplify an expression you need to combine like terms.

In the given equation, there are two like terms, 5r and 9r.

There is a plus sing in front of each one, so add those together: 5r + 9r = 14r

There are no ther like terms so the simplified expresssion becomes:

8w + 14r - t

7 0

3 years ago