3 digit largest number

Any help with this greatly appreciated.

Anestetic [448]

Put the equation in standard linear form.

$x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}$

Find the integrating factor.

$\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5$

Multiply both sides by $\mu$ .

$(t+5) x'(t) + x(t) = 5(t+5)e^{5t}$

Now the left side the derivative of a product,

$\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}$

Integrate both sides.

$(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt$

On the right side, integrate by parts.

$(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C$

Solve for $x(t)$ .

$\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}$

3 0

2 years ago

A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term

Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0

3 years ago

Which of the following is NOT true for a hypothesis test for correlation? Choose the correct answer below. A. If |r|less than

pantera1 [17]

Answer:

Answer explained

Step-by-step explanation:

From the information, the true statements for a hypothesis test for correlation is,

If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

If |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

<u>Explanation</u>

According to the decision rule of P-value approach, observe that if the P-value is less than or equal to the significance level, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

Similarly, if the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

According to the critical value approach, observe that if the test statistic value is greater than the critical value, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

- If |r| greater than critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

<u>Explanation </u>

Based on the decision rules of the hypothesis test, the false statement about the test for a correlation is, if |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

3 0

3 years ago

What is the distance between 4-i and -2+3i?

stepan [7]

If you're working with complex numbers, then I'm sure you're comfortable with plotting them on a complex-plane ... real part of the number along the x-axis, and imaginary part of the number along the y-axis.

When you look at it that way, your two points are simply two points on the x-y plane:

   4 - i    ===> (4, -1)

   -2 + 3i ===> (-2, 3) .

The distance between them is

   D = √ (difference in 'x')² + (difference in 'y')²

   = √ (6)² + (4)²

   = √ (36 + 16)

   = √ (52)

   =    7.211 (rounded)

4 0

3 years ago

Please show work and solve it! 100 points! n(n-7)=0

Dmitriy789 [7]

Step by step. :)

STEP
1
:
Equation at the end of step 1
0 - 7n • (n - 7) = 0
STEP
2
:
Equation at the end of step 2
-7n • (n - 7) = 0
STEP
3
:
Theory - Roots of a product
3.1    A product of several terms equals zero.    When a product of two or more terms equals zero, then at least one of the terms must be zero.    We shall now solve each term = 0 separately    In other words, we are going to solve as many equations as there are terms in the product    Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2      Solve  :    -7n = 0    Multiply both sides of the equation by (-1) : 7n = 0

Divide both sides of the equation by 7:
                     n = 0
Solving a Single Variable Equation:
3.3      Solve  :    n-7 = 0    Add 7 to both sides of the equation :                        n = 7

This is what i got! if i’m wrong i’m so sorry
but i tried. have a amazing day☺️☺️

5 0

3 years ago