Solve this equation<br> y= 2x<br> x= -y + 6

2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA

professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

$A=45e^{-0.0045(t)}$

a) To find the initial amount of this substance

At t=0, we get

$A=45e^{-0.0045(0)}$ $A=45e^0$

We know that e^0=1 ( anything to the power zero is 1)

we get,

$A=45$

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

$\frac{45}{2}=45e^{-0.0045(t)}$

$\frac{1}{2}=e^{-0.0045(t)}$

Taking natural logarithm on both sides we get,

$\ln (\frac{1}{2})=-0.0045(t)^{}$ $(-1)\ln (\frac{1}{2})=0.0045(t)$ $\ln (\frac{1}{2})^{-1}=0.0045(t)$ $\ln (2)=0.0045(t)$ $0.6931=0.0045(t)$ $t=\frac{0.6931}{0.0045}$ $t=154.02$

Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

$A=45e^{-0.0045(2500)}$ $A=45e^{-11.25}$ $A=45\times0.000013=0.000585$ $A=0.000585$

The amount of substance will be present around in 2500 years is 0.000585 grams

4 0

5 months ago

Answers to fill in this table?????

Sladkaya [172]

The total of can counts - 397

The total of cannot counts - 110

Total number of boys - 263

Total number of girls - 244

The FULL total - 507

3 0

2 years ago

Answer asap ~~~~~~~~~~~~~~~~~~~~~V~~~~~~~~~~~~~~~~`

andriy [413]

6 units

12 is also a diameter because it goes through the whole circle.

Divide it by 2 to find 6.

6 0

2 years ago

Read 2 more answers

Determine the coordinator of the point<br>of intersection of lines<br>3x-2y=13 and 2y+x+1=0

finlep [7]

Answer:

(3,-2)

Step-by-step explanation:

Given equations of line

3x-2y=13

2y+x+1=0

=> x = -1 -2y

Point of intersection will coordinates where both equation have same value of (x,y)

top get that we have to solve the both equations by using method of substitution of simultaneous equation.

using this value of x in 3x-2y=13, we have

3(-1-2y) -2y = 13

=> -3 -6y-2y = 13

=> -8y = 13+3 = 16

=> y = 16/-8 = -2

x = -1 - 2y = -1 -2(-2) = -1+4= 3

Thus, point of intersection of line is (3,-2)

3 0

2 years ago

If a graph shows the function y=3x what are the coordinates of the intercepts

vladimir2022 [97]

Answer:

graph{3x+5 [-10, 10, -5, 5]}

x

intercept:

x

=

−

5

3

y

intercept:

y

=

5

Explanation:

For a linear graph, the quickest way to sketch the function is to determine the

x

and

y

intercepts and draw a line between the two: this line is our graph.

Let's calculate the

y

intercept first:

With any function,

y

intercepts where

x

=

0

.

Therefore, substituting

x

=

0

into the equation, we get:

y

=

3

⋅

0

+

5

y

=

5

Therefore, the

y

intercept cuts through the point (0,5)

Let's calculate the

x

intercept next:

Recall that with any function:

y

intercepts where

x

=

0

.

The opposite is also true: with any function

x

intercepts where

y

=

0

.

If we substitute

y

=

0

, we get:

0

=

3

x

+

5

Let's now rearrange and solve for

x

to calculate the

x

intercept.

−

5

=

3

x

−

5

3

=

x

Therefore, the

x

intercept cuts through the point

(

−

5

3

,

0

)

.

Now we have both the

x

and

y

intercepts, all we have to do is essentially plot both intercepts on a set of axis and draw a line between them

The graph of the function

y

=

3

x

+

5

:

graph{3x+5 [-10, 10, -5, 5]}

3 0

2 years ago

Solve this equation y= 2x x= -y + 6