7

How long will it take 4000 to grow to 9000 if it is invested at 7% compounded monthly

NARA [144]

1.5 years, or 18 months.

4 0

3 years ago

13 A cylindrical iron rod 8 cm high and 6 cm in diameter stands in a cylindrical tin 12 cm in diameter. See Fig. 15.22. Water is

Eduardwww [97]

Answer:

2cm

Step-by-step explanation:

The volume of water displaced by the rod is

v = πr^2 h = π * 3^2 * 8 = 72π cm^3

The drop in water level is the rod volume divided by the cross-section area of the tin, or

72π/(π*6^2) = 2 cm

4 0

3 years ago

Read 2 more answers

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the populatio

Natalka [10]

Answer:

a) dy/dt = ky(1-y)

b) 3:36pm

Step-by-step explanation:

a) Let the number of people who have heard the rumor = p

Let those who have not heard the rumor= q

Total population = p+q

Fraction of those that heard the rumor = p/p+q = y

Fraction of those who did not hear the rumor = q/p+q = 1-y

The rate at which the rumor spreads = dy/dt

dy/dt varies directly to y(1-y)

dy/dt = ky(1-y) where k is a constant

b) Recall that dy/dt = ky(1-y)

y(t) = y/(y+(1-y) e^-kt)

At 8 am , t= 0

y = p/ p+q

y(0) = 280/3500

y(0) = 0.08

By noon(12pm), t = 4

At this time half of the population has heard the rumor

y(4) = 0.5

Recall that y(t) = y/(y+(1-y) e^-kt)

y(t) = y0/(y0+(1-y0) e^-kt)

y(t) = 0.08/(0.08+(1-0.08) e^-kt)

y(t) = 0.08/(0.08+0 92 e^-kt)

To find k, put y(4) = 0.5 into the equation

y(4) = y/(y+(1-y) e^-4k)

0.5 = 0.08/(0.08+0.92e^-4k)

0.08 + 0.92e^-4k = 0.08/0.5

0.92e^-4k = 0.16 - 0.08

0.92e^-4k = 0.08

e^-4k = 0.08/0.92

e^-4k = 0.087

-4k = ln(0.087)

-4k = -2.422

k = -2.422/ -4

k = 0.611

y(t) = 0.08/(0.08+ 0.92 e^-0.611t)

The time by which 90% of the population would have heard the rumor is

0.9 = 0.08/(0.08+0.92e^-0.611t)

0.08 + 0.92e^-0.611t = 0.08/0.9

0.92e^-0.611t= (0.08/0.9) - 0.08

e^-0.611t = [(0.08/0.9)-0.08] / 0.92

e^-0.611t = 0.00966

-0.611t = ln(0.00966)

-0.611t = -4.640

t = -4.640/ -0.611

t = 7.6hrs

t = 7 hrs + (0.6*60)mins

t= 7 hrs + 36mins

t = 7hrs 36 mins

Therefore 8 am + 7 hrs 36 mins = 3:36pm

The time by which 90% of the rumor spreads = 3:36pm

5 0

3 years ago

What is the surface area of the rectangular prism?

azamat

Answer:

its 288 if u search formula for surface area of a rectangular prism

Step-by-step explanation:

4 0

3 years ago

A. Find the common factors of 12 and 20.

Alchen [17]

Answer:

a. Common factors of 12 and 20 = 2, 2

2. Highest common factor of 12 and 20 = 4

3 packs of workbooks and 5 packs of text books to be purchased.

Step-by-step explanation:

a.) To find the common factors of 12 and 20:

First of all, let us find the factors of 12 and 20

12 = 2 $\times$ 2 $\times$ 3

20 = 2 $\times$ 2 $\times$ 5

The common factors are underlined above i.e. 2, 2.

2. The highest common factor between 12 and 20 is 2 $\times$ 2 = 4

-------------------------------------------

Workbooks are in packs of 25

Textbooks are in pack of 15

The school needs exactly same number of workbooks and textbooks.

And we have to find such least number.

This least number can simply be calculated by finding the LCM (Least Common Multiple).

LCM of two numbers p and q is the minimum number which is completely divisible by both the numbers p and q.

Let us find LCM of 25 and 15 using factorization method:

15 = 3 $\times$ 5

25 = 5 $\times$ 5

The common part is considered only once:

So LCM = 3 $\times$ 5 $\times$ 5 = 75

Hence, number of packs of workbooks to be bought = $\frac{75}{25} = 3$

number of packs of textbooks to be bought = $\frac{75}{15} = 5$

So, the answer are:

a. Common factors of 12 and 20 = 2, 2

2. Highest common factor of 12 and 20 = 4

3 packs of workbooks and 5 packs of text books to be purchased.

8 0

4 years ago