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3 years ago

Mr. Vance yearly taxable income is $35,675. What is the dollar amount taken out for taxes based on Mr. Vance’s taxable income?

Mathematics

1 answer:

steposvetlana [31]3 years ago

4 0

It would be $35,675 multiplied by 0.06.

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Of the 200 packages of bagels sold 15 of them were sesame seed bagels. What percent of the bagel packages sold are sesame seed b

Paladinen [302]

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2 years ago

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What is the value of p+9 when p=16

Tasya [4]

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25 :)

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2 years ago

So I’m not smart so like help meh pleasee<br><br> What is 49% of 200?

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Answer:98

Step-by-step explanation:

We assume, that the number 200 is 100%.if 200 is 100%, so we can write it down as 200=100%.We also know, that x is 49% of the output value, so we can write it down as x=49%.Now we have two simple equations:

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3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0

3 years ago