Ask question

Ask question

All categories

sergij07 [2.7K]

3 years ago

13

A 100 foot rope is cut into 2 pieces (a and b). Piece a is 2ft less than 5 times the length of piece b.

1 answer:

kakasveta [241]3 years ago

3 0

Try this explanation/solution:

a) the system which describes this situation is:

$\left \{ {{a+b=100} \atop {a+2=5b}} \right.$

b) the solution of the system made up:

$\ => \ \left \{ {{a=83} \atop {b=15}} \right.$

You might be interested in

Convert 20 milligrams into grams.<br> Can somebody help ?

Fantom [35]

Answer:

0.02

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Rick buys 3 CDs and 5 video games. The cost of one video game is $12.00 more than the cost of one CD. If Rick spends $164.00, wh

Dmitry [639]

Step-by-step explanation:

x = price per video game

y = price per CD

164 = 5x + 3y

and then we know

x = y + 12

now we can use this as substitute in the first equation :

164 = 5(y + 12) + 3y = 5y + 60 + 3y = 8y + 60

104 = 8y

y = $13

x = y + 12 = 13 + 12 = $25

so, each CD costs $13.

4 0

3 years ago

250 in expanded form

11Alexandr11 [23.1K]

Answer:

(200)+(50)+(0)

Step-by-step explanation:

you just take all the numbers and break them up

8 0

2 years ago

a researcher in a personal submarine begins at the surface of thr ocean. The submarine descends 20.6 meters and the ascends 5 7/

Mumz [18]

Answer:

$Depth = 14.9\ metres$

Step-by-step explanation:

Given

$Desc = 20.6\ metres$

$Asc = 5\frac{7}{10}\ metres$

Required

Determine the depth

The depth is the distance between the two distances as follows'

$Depth = |Desc - Asc|$

Substitute values

$Depth = |20.6 - 5\frac{7}{10}|$

Convert fraction to decimal

$Depth = |20.6 - 5.70|$

$Depth = |14.9|$

$Depth = 14.9\ metres$

6 0

3 years ago

Find the work required to move an object in the force field F = e^x + y (1, 1, z) along the straight line from A(0, 0, 0) to B(-

DENIUS [597]

$\vec F(x,y,z)=(e^x+y)(1,1,z)$

is conservative if we can find a scalar function $f$ such that $\nabla f=\vec F$ . This would require

$f_x=e^x+y$

$f_y=e^x+y$

$f_z=(e^x+y)z$

Integrating both sides of the first equation wrt $x$ gives

$f(x,y,z)=e^x+xy+g(y,z)$

Differentiating both sides of this wrt $y$ gives

$f_y=x+g_y=1\implies g_y=1-x\implies g(y,z)=y-xy+h(z)$

but we assumed $g$ was a function of $y$ and $z$ , independent of $x$ . So there is no such $f$ and $\vec F$ is not conservative.

To find the work, first parameterize the path (call it $C$ ) by

$\vec r(t)=(1-t)(0,0,0)+t(-4,5,-5)=(-4t,5t,-5t)$

for $0\le t\le1$ . Then

$\vec r'(t)=(-4,5,-5)$

and the work is given by the line integral,

$W=\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1(e^{-4t}+5t,e^{-4t}+5t,-(e^{-4t}+5t)5t)\cdot(-4,5,-5)\,\mathrm dt$

$W=\displaystyle\int_0^1(125t^2+5t+(25t+1)e^{-4t})\,\mathrm dt=\boxed{\frac{2207}{48}-\frac{129}{16e^4}}$

8 0

3 years ago