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erastovalidia [21]

1 year ago

14

Solve each of the quadratic equations 3x=0.5x2

1 answer:

aalyn [17]1 year ago

6 0

Answer:

$3x = 1 \\ x = \frac{1}{3}$

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Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch

enot [183]

Answer:

$y=\frac{-7t^2+22t-7}{7t-22}$

Step-by-step explanation:

We are given that

Initial value problem

$y'=(t+y)^2-1$ , y(3)=4

Substitute the value $z=t+y$

When t=3 and y=4 then

z=3+4=7

$y'=z^2-1$

Differentiate z w.r.t t

Then, we get

$\frac{dz}{dt}=1+y'$

$z'=1+z^2-1=z^2$

$z^{-2}dz=dt$

Integrate on both sides

$-\frac{1}{z}dz=t+C$

$z=-\frac{1}{t+C}$

Substitute t=3 and z=7

Then, we get

$7=-\frac{1}{3+C}$

$21+7C=-1$

$7C=-1-21=-22$

$C=-\frac{22}{7}$

Substitute the value of C then we get

$z=-\frac{1}{t-\frac{22}{7}}$

$z=\frac{-7}{7t-22}$

$y=z-t$

$y=\frac{-7}{7t-22}-t$

$y=\frac{-7-7t^2+22t}{7t-22}$

$y=\frac{-7t^2+22t-7}{7t-22}$

8 0

2 years ago

A rectangular prism is shown below 15mm 10mm 9mm

Verdich [7]

Area of cross section x height
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6 0

2 years ago

a certain triangle has a 30 degree angle and a 60 degree angle. which must be a true statement about the triangle

Oduvanchick [21]

The last angle is 90 degrees

6 0

2 years ago

Read 2 more answers

explain the relationship between multiplying and dividing by 10 100 1000 and moving decimals point to the right or to the left

ch4aika [34]

So basically a decimal is moved based on how many zeros are in the dividing number

Ex. 51,000/100

because there are 2 zeros in the number one hundred, the decimal in 51,000 gets moved 2 places to the left

So it goes from 51,000 to 510

Ex. 16 * 1000

There are three zeros in the number 1000. This means three zeros will be added onto the number 16

So the answer would be 16,000

Hope this helps!

6 0

2 years ago

After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum

Svetlanka [38]

Answer: 40000

Step-by-step explanation:

The formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$ , where p is the prior estimate of the population proportion.

Here we can see that the sample size is inversely proportion withe square of margin of error.

i.e. $n\ \alpha\ \dfrac{1}{E^2}$

By the equation inverse variation, we have

$n_1E_1^2=n_2E_2^2$

Given : $E_1=0.05$ $n_1=1000$

$E_2=0.025$

Then, we have

$(1000)(0.05)^2=n_2(0.025)^2\\\\\Rightarrow\ 2.5=0.000625n_2\\\\\Rightarrow\ n_2=\dfrac{2.5}{0.000625}=4000$

Hence, the sample size will now have to be 4000.

6 0

1 year ago