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3 years ago

Scott correctly writes each fraction below as a decimal. Will the decimal Scott writes for each fraction terminate or repeat?

Mathematics

1 answer:

pickupchik [31]3 years ago

4 0

Answer:

It will terminate according to the rules of math

Step-by-step explanation:

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A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind

Lunna [17]

Given:

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.

Pilot's speed in still air is 315 miles per hour.

To find:

The speed of the wind.

Solution:

Let the speed of wind be x miles per hour.

Speed with wind = 315+x miles per hour

Speed against wind = 315-x miles per hour

We know that,

$Time=\dfrac{Distance}{Speed}$

According to the question,

$\dfrac{450}{315+x}=\dfrac{360}{315-x}$

Divide both sides by 90.

$\dfrac{5}{315+x}=\dfrac{4}{315-x}$

By cross multiplication, we get

$5(315-x)=4(315+x)$

$5(315)-5x=4(315)+4x$

$5(315)-4(315)=4x+5x$

$(5-4)315=9x$

Divide both sides by 9.

$\dfrac{(1)315}{9}=x$

$35=x$

Therefore, the speed of wind is 35 miles per hour.

4 0

3 years ago

CAN SOMEONE PLEASEEEE ANSERR THISSSSSSSS THANK YOU SO VERY MUCH

Lapatulllka [165]

Pyth. theorem
$\sqrt{20 { }^{2} - 8 {}^{2} }$

=18.33
=18.3 (corr. to the nearest tenth)

6 0

3 years ago

Read 2 more answers

Xét tính chẵn lẻ của hàm sô:<br> y=xmũ4+3x+5

e-lub [12.9K]

Answer:

i dont know what this language is

Step-by-step explanation:

please help me learn this language

7 0

2 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

Translate the phrase into an expression: 11 more than one third of a number

skelet666 [1.2K]

1/3x+11.
1/3 of a number can be shown as 1/3x, since the number is not identified.

We can represent 11 more as +11.
This, our expression is 1/3x+11

Hope this helps!

5 0

3 years ago