Hi can some one please help me !!!

Alberto wants to keep their favorite tree from being uprooted by heavy winds. They plan to tie 3 sections of rope to a band on t

motikmotik

Answer:

39 ft

Step-by-step explanation:

Using the description as a guideline I have drawn out the situation (badly drawn) as seen in the picture below. From the picture, we see that we need to find x which is the length of one of the ropes. Once we have this length we simply multiply it by 3 to find out how much rope we need altogether. Since this is the diagonal of a triangle we can use the Pythagorean theorem to solve for x.

Pythagorean theorem: $a^{2} +b^{2} = c^{2}$ .... which a and b are the two sides while x is the diagonal.

$5^{2} +12^{2} = x^{2}$

$25 + 144 = x^{2}$

$169 = x^{2}$ ... now we square root both sides

$13 = x$

Now that we have the length of one of the ropes we simply multiply this by 3 to find the total amount of rope needed.

13 * 3 = 39 ft

6 0

3 years ago

Given V = 2πr2h, solve for h

Ipatiy [6.2K]

V=2*pi*r*2*h
V=(4*pi*r)*h
V/(4*pi*r)=h
so h=V/(4*pi*r)

8 0

3 years ago

A tank initially contains 60 gallons of brine, with 30 pounds of salt in solution. Pure water runs into the tank at 3 gallons pe

adoni [48]

Answer:

the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.

Step-by-step explanation:

The variation of the concentration of salt can be expressed as:

$\frac{dC}{dt}=Ci*Qi-Co*Qo$

being

C1: the concentration of salt in the inflow

Qi: the flow entering the tank

C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)

Qo: the flow going out of the tank.

With no salt in the inflow (C1=0), the equation can be reduced to

$\frac{dC}{dt}=-Co*Qo$

Rearranging the equation, it becomes

$\frac{dC}{C}=-Qo*dt$

Integrating both sides

$\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}$

It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.

$C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\$

The final equation for the concentration of salt at any given time is

$C=exp^{-3*t-0.693}$

To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:

$C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088$

5 0

3 years ago

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and

Sliva [168]

Answer:

( x+1)^2 + (y+2)^2 = 25

The center is (-1, -2) and the radius is 5

Step-by-step explanation:

x^2 + 2x + y^2 + 4y = 20

Complete the square

2/2 =1 1^2 =1 so add 1 for x 4/2 =2 2^2 = 4 so add 4 for y

x^2 +2x +1 +y^2 +4y+4 = 20 +1 +4

( x+1)^2 + (y+2)^2 = 25

(x+1) ^2 + (y+2)^2 = 5^2

(x - -1) ^2 + (y - -2)^2 = 5^2

This is in (x-h)^2 + (y-k)^2 = r^2 form where (h,k) is the center and r is the radius

The center is (-1, -2) and the radius is 5

4 0

3 years ago

(-13/4)(-12/5)(-7/3)

Juliette [100K]

Answer:

I got -18.2

Step-by-step explanation:

I just divide each parentheses then multiply all the answer and got my answer.

3 0

3 years ago