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3 years ago

10

Raina deposits $2000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in t

he first 3 years?

1 answer:

trasher [3.6K]3 years ago

8 0

I=prt
I=2,000×0.03×3
I=180

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Shelly ran 2 1/4 miles Lynne ran 3 1/8 Miles WhobRan Farther and by how much

ValentinkaMS [17]

Lynne ran farther and by 7/8 miles

You can tell Lynne ran further because she ran 3 whole miles while shelly only ran 2 whole miles. Now you have to subtract to see how much Lynne had ran more.

You found a common denominator between 8 and 4. 4 can turn into 8. so you multiply 4x2 and 1x2 to get a mixed number of 2 2/8

Now you have to turn 3 1/8 because you cannot subtract 2/8 from 1/8. You can turn the fraction into 2 9/8 because there are 8 pieces in a whole.

2 9/8 - 2 2/8 = 0 7/8

Hope this helps! :)

6 0

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

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

or

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

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

HEEEELP PLEASE<br> I dont understand

lesya [120]

Answer:

<h2>y = 0.5x</h2>

Step-by-step explanation:

$\dfrac{y}{x}=a\to y=ax\\\\\text{We have}\ x=1,\ y=0.5.\\\\\text{Substitute:}\\\\a=\dfrac{0.5}{1}=0.5\\\\\text{Therefore}\ y=0.5x$

7 0

3 years ago

Read 2 more answers

Henry decorates the top of each cupcake with 3 walnuts.If he has 56 walnuts,is that enough to decorate 2 dozen cupcakes?

Lesechka [4]

No, 56 is not enough to decorate 2 dozen cupcakes. If he was to top 2 dozen cupcakes with 3 walnuts then he would need 72 walnuts.

3•24(2dozen)=72

6 0

3 years ago

Alaina has $28 in her account. She wants to purchase a pair of shoes that cost $45. If Alaina makes the purchase, which integer

muminat

Answer:

-17

Step-by-step explanation:

You subtract $45 from $28 and get a negative number

4 0

3 years ago