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2 years ago

Solve differential equation dy(t) / dt = -2y(t) with initial condition y = 2 when t = 1

Mathematics

1 answer:

juin [17]2 years ago

6 0

Answer:

y = 2e^[2(1 - t)]

Step-by-step explanation:

1/y . dy = -2. dt

ln(y) = -2t + c

ln(2) = -2(1) + c

c = 2 + ln(2)

ln(y) = -2t + ln(2) + 2

ln(y) - ln(2) = 2 - 2t

ln(y/2) = 2 - 2t

y/2 = e^(2 - 2t)

y = 2e^[2(1 - t)]

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A customer desires to mix her own concrete. The clerk knows that the ratio of cement to sand to gravel is 1:3:4. If the customer

Aleks [24]

Answer:

The quantity of cement use is 125 pounds

The quantity of sand use is 375 pounds

The quantity of gravel use is 500 pounds

Step-by-step explanation:

Given as :

The ratio of cement to sand to gravel = 1 : 3 : 4

The total quantity of dry mix required = 1000 pounds

Let The quantity of cement required = 1 × x pounds

The quantity of sand required = 3 × x pounds

The quantity of gravel required = 4 × x pounds

So, According to question

The total quantity of dry mix required = The quantity of cement required + The quantity of sand required + The quantity of gravel required

Or, x + 3 x + 4 x = 1000 pounds

Or, 8 x = 1000 pounds

∴ x = $\frac{1000}{8}$

I.e x = 125

So , The quantity of cement required = 1 × 125 pounds = 125 pounds

The quantity of sand required = 3 × 125 pounds = 375 pounds

The quantity of gravel required = 4 × 125 pounds = 500 pounds

Hence The quantity of cement use is 125 pounds

The quantity of sand use is 375 pounds

The quantity of gravel use is 500 pounds

Answer

8 0

3 years ago

Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4 y=

stellarik [79]

Correct answer: y = $\frac{1}{3}$ x + 2

To find out the slope, you would need to remember this slope formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ . We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as $x_{1}$ and $y_{1}$ , and (0, 2) as $x_{2}$ and $y_{2}$ . Now we can plug these numbers into the slope formula to find out the slope:

m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ → $\frac{2-3}{0-3}$ → $\frac{-1}{-3}$ → $\frac{1}{3}$

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

y = mx + b

(3) = $\frac{1}{3}$ (3) + b

3 = 1 + b

2 = b

You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

Now we know that m = $\frac{1}{3}$ and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = $\frac{1}{3}$ x + 2.

Hope this helps you! Let me know if you have any more questions related to this problem.

3 0

3 years ago

Find the difference. (3- 2x + 2x2) - (4x -5 +3x2)

Gwar [14]

Answer:

6(1-x) is the answer your looking for if I'm right

6 0

3 years ago

Which of the following statements exemplifies a null hypothesis?

elixir [45]

Answer:

(A) there is no relationship between gender and jury verdicts

Step-by-step explanation:

The null hypothesis is the one in which we assume that there are no relationship between measures.

In this exercise, the only option that assume no relationship between measures(gender and jury verdicts) is

(A) there is no relationship between gender and jury verdicts

5 0

3 years ago

What is the gcf of 49 and 63

ValentinkaMS [17]

The greatest common factor for 49 and 63 would be 7 since you can divide 7 into both numbers perfectly

4 0

3 years ago

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