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3 years ago

Rewrite the following equation in the center-radius form of the equation of a circle.

Mathematics

1 answer:

tekilochka [14]3 years ago

4 0

Answer:

Step-by-step explanation:

observe

x² + 12x + y² + 10y = –45

add 36 + 25 on both side

x² + 12x + 36 + y² + 10y + 25 = –45 + 36 + 25 = 16

(x + 6)² + (y + 5)² = 16

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Greater number832458or 83250

aksik [14]

832458 is the greater number

3 0

3 years ago

Read 2 more answers

mayelle earns $18000 a year. After a raise, she earns $19500. Find the percent change and if it’s a decrease or increase

Aneli [31]

Ok, it's all pretty much like the "$50 coat is on sale for $35".

If the regular price of the coat is $50 and now it is on sale for $35, then it will cost you $15 less, like this: 
$50 - $35 = $15 

You could also say the coat was discounted by $15, or the coat was reduced by $15, or you'll save $15 if you buy that coat ($50 - $15 = 35). 

You could also put it in terms of percentages. If the discount is $15, you can figure that $15 is what percent of the regular price, like this: 
$15 = X% of $50 
$15 = X% x $50 (divide both sides by 50 to isolate X) 
15/50 = X% 
.30 = X% (multiply by 100 to convert to a non-decimal) 
30% = X 

So, you can say all of the following and they all mean the same thing: 
1. the $50 coat is on sale for $35 
2. the $50 coat is discounted by $15 
3. the $50 coat is reduced by $15 
4. you'll save $15 if you buy this coat 
5. the $50 coat is on sale for 30% off 
6. the $50 coat is discounted by 30% 
7. you'll save 30% if you buy this coat 
8. 30% savings! 
9. Save 30%! 

So, how does that apply to the $18,000 a year? Ok, if Shelby earns $18,000 this year and then earns $19,500 next year, then she gets an additional $1,500 ($19,500 - $18,000 = $1,500). In the coat problem, everything was discounted, on sale, going down. In this problem, everything is going up, increasing. 

You know the dollar increase is $1,500. To figure the percent increase, you need to figure out that $1,500 is what % of $18,000. Remember, it's not the $19,500 that was increased; it was an increase on the $18,000: 
$1,500 = X% of $18,000 
1,500/18,000 = X% 
.083333 = X% 
8.3333% = X 

One more: If Shelby get a 10% increase in her salary at the end of one year, that's the same as saying that Shelby gets her salary plus she gets 10% more, like this: 

$18,000 + (10% of $18,000) = 
$18,000 + $1,800 = 
$19,800 end of first year 

For the second year, her salary begins at $19,800 and increases 10%, like this: 
$19,800 + (10% x $19,800) = 
$19,800 + $1,980 = 
$21,780 end of second year 

You can do it from here.

8 0

3 years ago

Read 2 more answers

Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

3 years ago

HELP MEEEEE........

Alex787 [66]

Answer:

Maybe Dependent

Step-by-step explanation:

3 0

3 years ago

Solve:7 +42-32-32 = 14.3-2a +7 A = -3 A= 0 A= 3 no solution

madreJ [45]

Answer:

a = 18.15

Step-by-step explanation:

$7+42-32-32=14.3-2a+7$

Combine like terms on the left side of the equation first. Add 7 and 42, then subtract 32 from the answer you get, then subtract 32 from that answer. This is going by order of PEMDAS.

Remember PEMDAS: (numbers 3 & 4 and numbers 5 & 6 are solved from left to right)