Which is equivalent to

In how many minutes will a heart beat in 140 times?

matrenka [14]

The answer is 5 minutes

7 0

3 years ago

Read 2 more answers

Calculate the total surface area of the give cuboid

notsponge [240]

320 centimeters squared

3 0

3 years ago

Read 2 more answers

Consider xưy" – 14xy' + 56y = 0. Find all values of r such that y=x" satisfies the differential equation for x > 0. Enter as

beks73 [17]

I bet the ODE is supposed to read

$x^2y''-14xy'+56y=0$

Then if $y=x^r$ , we have $y'=rx^{r-1}$ and $y''=r(r-1)x^{r-2}$ , and substituting these into the ODE gives

$r(r-1)x^r-14rx^r+56x^r=0\implies r(r-1)-14r+56=r^2-15r+56=0$

Solving for r, we find

$r^2-15r+56=(r-8)(r-7)=0\implies \boxed{r=8\text{ or }r=7}$

so that $y_1=x^8$ and $y_2=x^7$ are two fundamental solutions to the ODE. Thus the general solution is

$\boxed{y(x)=C_1x^8+C_2x^7}$

Given that $y(1)=4$ and $y'(1)=3$ , we get

$\begin{cases}4=C_1+C_2\\3=8C_1+7C_2\end{cases}\implies C_1=-25\text{ and }C_2=29$

So the particular solution is

$\boxed{y(x)=29x^7-25x^8}$

4 0

4 years ago

The Weiland Computer Corporation is trying to choose between the following mutually exclusive design projects, P1 and P2:

uranmaximum [27]

Answer:

a profitability index P1=1.27

profitability index P2= 1.41

b NPV P1 = $14145.01

NPV P2 = $6630.3

c YES ANSWERS ARE DIFFERENT due to fact that cash flows in P1 is higher than in P2

Step-by-step explanation:

profitability index or = present value of an investment cash flows=67145.01

benefit cost ratio initial cost 53000

For project 1 or P1

cost of capital 10 % = 1.27

initial investment = $53,000 since year 0

Year Cash flows (P1)$ present value of future cash flows PV

1 27,000 24545.46

2 27,000 22314.05

3 27,000 20285.50

Total = 67145.01

use the formula of present value of future cash flows = C/(1+i)ⁿ

C = cash = 27000

i = interest = 10% = 10/ 100 = 0.1

n = year = 1

year 1 = 27000/(1+0.1)¹ = 24545.46

year 2 = 27000/(1.1)² = 22314.05 note n = 2

year 3 = 27000(1.1)³ = 20285.50

Profitability index = 1.27 > 1 thus it should be accepted

profitability index or = present value of an investment cash flows=22630.30

benefit cost ratio initial cost 16000

For project 1 or P1

cost of capital 10 % = 1.41

initial investment = $16,000 since year 0

Year Cash flows (P2)$ present value of future cash flows PV

1 9,100 8272.73

2 9,100 7520.6

3 9,100 6836.97

Total = 22630.30

use the formula of present value of future cash flows = C/(1+i)ⁿ

C = cash = 9100

i = interest = 10% = 10/ 100 = 0.1

n = year = 1

year 1 = 9100/(1+0.1)¹ = 8272.73

year 2 = 9100/(1.1)² = 7520.6 note n = 2

year 3 = 9100(1.1)³ = 6836.97

Profitability index = 1.41 > 1 thus it should be accepted

Profitability index of P1 = 1.27 AND P2 1.41 SO Weiland Computer Corporation SHOULD TAKE P2

b Net Present Value (NPV) decision rule =∑ pv - initial investment required

P1 = 67145.01 - 53,000 = $14145.01

P2 = 22630.30 - 16000 = $6630.3

Weiland Computer should take P1 since P1 > P2 that is $14145.01 >$6630.3

C YES ANSWERS ARE DIFFERENT due to fact that cash flows in P1 is higher than in P2

6 0

3 years ago

Can someone help me with this and explain it?

Softa [21]

Answer:

4 pizzas

Step-by-step explanation:

Equation:

12x + 7 = 55

12x = 55 - 7

12x = 48

x = 4

4 0

3 years ago