Mr.Chang had 30 boxes each box has 10 erasers If he gave each student has 2 erasers how many students could he give erasers to

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

$\frac{dA}{A} = k\ dt$

Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

$t = 0\ when\ A =1\ million$ i.e. At initial

So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

To solve for k;

$6\ years\ later = 500,000$

i.e.

$t = 6\ A = 500000$

So:

$500000= 1000000e^{k*6}$

Divide both sides by 1000000

$0.5= e^{k*6}$

Take natural logarithm (ln) of both sides

$ln(0.5) = ln(e^{k*6})$

$ln(0.5) = k*6$

Solve for k

$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

$k = -0.1155$

Recall that:

$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

So, when

$A = 600000$

The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

Hence, the amount of oil was decreasing at 69300 barrels, yearly

7 0

2 years ago

Francisco is building a window seat below a bay window in the shape of an isosceles trapezoid. His blueprint for the window seat

Lera25 [3.4K]

Answer:

A

Step-by-step explanation:

I think it is a because if you mutiply and you will get your answer

6 0

3 years ago

Read 2 more answers

Solve 6(x + 1) > 2x - 1 x > -1/2 x > -7/4 x > 0

Bond [772]

Answer:

x > - $\frac{7}{4}$

Step-by-step explanation:

Given

6(x + 1) > 2x - 1 ← distribute parenthesis on left side

6x + 6 > 2x - 1 ( subtract 2x from both sides )

4x + 6 > - 1 ( subtract 6 from both sides )

4x > - 7 ( divide both sides by 4 )

x > - $\frac{7}{4}$

6 0

3 years ago

Read 2 more answers

use algebraic manipulation to find the minimum sum-of-products expression for the function x1x2'x3' + x1x2x4+x1x2'x3x4'

Dennis_Churaev [7]

Answer:

sum of products expression = x₁x₂x₃' + x₁x₂'x₄ + x₁x₂x₄

Step-by-step explanation:

Given function ( f ) = x₁x₂'x₃' + x₁x₂x₄ + x₁x₂'x₃x₄'

using algebraic manipulation

f = x₁ [ x₂'x₃' + x₂x₄ + x₂'x₃x₄' ]

= x₁ [ x₂'( x₃' + x₃x₄') + x₂x₄ ]

next apply Boolean rules

a + bc = ( a + b )(a + c )

a' + a =1

hence

minimum sum-of-products expression = x₁x₂x₃' + x₁x₂'x₄ + x₁x₂x₄

7 0

2 years ago

George and Carmen went on a Bicycle trip they took a bus to their starting point and then bike the rest they traveled 200 km in

Kipish [7]

Answer:

Step-by-step explanation:

240 km

8 0

3 years ago