The expression (√90 *√40) - (√8*√18) simplifies to what

Which statement is true about whether Z and B are independent events

const2013 [10]

Independent Events are 2 events where the occurrence of the first doesn't affect the occurrence of the second and vice versa.
Example: rolling 2 simultaneously dies, the occurrence of the first, has no impact, no effect on the occurrence of the 2nd roll

6 0

3 years ago

If the acceleration of an object is given by dv/dt = −2v, Find the position function s(t) if v(0) = 7 and s(0) = 0.

kirill [66]

Answer:

Step-by-step explanation:

Given that acceleration of an object is

$\frac{dv}{dt} =-2v\\\frac{dv}{v} =-2dt\\ln v = -2t+C\\$

is the solution to the differential equation

Since v(0) =7

we get ln 7 = C

Hence $lnv = -2t+ln 7\\v=7e^{-2t}$

since velocity is rate of change of distance s we have

$v=\frac{ds}{dt} =7e^{-2t}\\s= [tex]s(t) =\frac{-7}{2} (e^{-2t})+C)[$

substitute t=0 and s=0

$C=7/2$

So solution for distance is

$s(t) =\frac{-7}{2} (e^{-2t}-1)$

4 0

3 years ago

A boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h.

docker41 [41]

Answer:

A)63miles per hour.

B)27 miles per hour

Step-by-step explanation:

HERE IS THE COMPLETE QUESTION

boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)??b) How fast does the current in the river flow?

Let the speed of boat in still water = V(boat)

speed of current=V(current)

To calculate speed of boat downstream, we add speed of boat in still water and speed of current. This can be expressed as

[V(boat) +V(current)]

It was stated that it takes 1hour for the

boat to travels between two points of 90 mi apart downstream.

To calculate speed of boat against current, we will substact speed of current from speed of boat in still water. This can be expressed as

[V(boat) - V(current)]

and it was stated that it takes 2 1/2 for return trip against the Current

But we know but Speed= distance/time

Then if we input the stated values we have

V(boat) + V(current)]= 90/1 ---------eqn(1)

V(boat) - V(current) = 90/2.5----------eqn(2)

Adding the equations we have

V(boat) + V(current) + [V(boat) - V(current)]= 90/2.5 + 90/1

V(boat) + V(current) + V(boat) - V(current)]=90+36

2V(boat)= 126

V(boat)=63miles per hour.

Hence, Therefore, the speed of boat in still water is 63 miles per hour.

?b) How fast does the current in the river flow?

the speed of the current in the river, we can be calculated if we input V(boat)=63miles per hour. Into eqn(1)

V(boat) + V(current)]= 90/1

63+V(current)=90

V(current)= 27 miles per hour

Hence,Therefore, the speed of current is 27 miles per hour.

7 0

3 years ago

Translate to an algebraic statement. "The quotient of twice a number and 7 is 20."

Genrish500 [490]

Answer:

Translation: 2x/7 = 20

Step-by-step explanation:

When we listen to the word "quotient", it means the solution to a division problem.
An unknown number that has been multiplied by 2 is in the numerator because it came before the 7 in the statement.
The number "7" is in the denominator because it came after the 2x in the statement.
The word "is" represents an equal sign.
The solution to the division problem (quotient) is 20.

If we put these clues together, we get 2x/7 = 20 as our translated equation.

Hence, our algebraic statement is 2x/7 = 20. The key is to listen to the statement. 

$BrainiacUser1357$

4 0

3 years ago

Please help meeee Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

Simora [160]

Answer:

<1=33, <2=90, <3=57

Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

5 0

3 years ago