Solve x2 + 4x + 8 = 0. (2 points)

Statistics how do we determine a percentage

givi [52]

Percent simply means "per hundred" and the symbol used to express percentage is %. One percent (or 1%) is one hundredth of the total or whole and is thereforecalculated by dividing the total or whole number by 100. To calculate the percentagedifference between two numbers, the same basic calculations are used

7 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

I need help with this math problem!!

Vesnalui [34]

In order to find which one is or isn't, you need to solve for the value of 'x'.
2x + 15 = 35
2x = 20
x = 10

Substitute x =10, into equation. If each side are not the same (i.e. 0=2), then that's the equation that is not equivalent,

Answer is B
Double check this. Chur! :)

Hope this makes sense.

4 0

3 years ago

A mosquito accelerates at a rate of 0.4 m/s2 for an unknown amount of time. How long did the mosquito atcelerate if its velocity

cestrela7 [59]

Answer:

3.25 seconds.

Step-by-step explanation:

We can use the formula Final Velocity = Initial Velocity + Acceleration * Time to solve this problem.

First, we plug in the values we already know, and then we solve like normal:

1.5 = 0.2 + 0.4*t

1.3 = 0.4 * t

3.25 = t

Therefore, the mosquito accelerated for 3.25 seconds.

If this helped please consider giving me brainliest.

5 0

3 years ago

The value of y is inversely proportional to the value of x. When y=42, x=6.

NARA [144]

Because $x$ and $y$ are inversely proportional, there is some constant $k$ such that

$xy=k$

Given that $y=42$ and $x=6$ , we have

$k=6\times42=252$

So when $x=9$ , you have

$9y=252\implies y=\dfrac{252}9=28$

4 0

3 years ago