What is the radius of a hemisphere with a volume of 19160 ft', to the nearest tenth<br> of a foot?

Oil consumption in China grew exponentially from 8.938 million barrels per day in 2010 to 10.480 million barrels per day in 2013

Afina-wow [57]

Let the year represents x axis and consumption represents y axis.

Since 2010 is the initial year, x=0

and 2013 is third year , so x=3

Co-ordinates are (0,8.938)(3,10.480)

Exponential formula is $y=ab^{x}$

Putting the value of x in the above formula from 1st coordinate,

$8.938=ab^{0}$

As $b^{0}$ = 1

this gives a= 8.938

Now using the 2nd coordinate

$10.480=ab^{3}$

putting the value of a in it we have

$10.480=8.938b^{3}$

taking cube roots on both sides we get

b= 1.05448

Now putting the values of a and b in the exponential formula-

$y=8.938(1.05448)^{x}$

In the year 2028, x=28

so,

$y=8.938(1.05448)^{28}$

y= 39.474

Hence oil consumption per day in 2028 will be 39.474 million barrels.

5 0

3 years ago

Read 2 more answers

A circular swimming pool has a diameter of 40 meters. The depth of the pool is constant along west-east lines and increases line

Nataliya [291]

Answer:

Volume is $2000\pi\ m^{3}$

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

$c = \frac{1}{5}$

Therefore,

$h(y) = \frac{1}{5}y + 5$

Now, the Volume of the pool is given by:

$V = \int h(y)dA$

where

A = $r\theta$

$A = rdr\ d\theta$

Thus

$V = \int (\frac{1}{5}y + 5)dA$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}rsin\theta + 5) rdr\ d\theta$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}r^{2}sin\theta + 5r}) dr\ d\theta$

$V = \int_{0}^{2\pi} (\frac{1}{15}20^{3}sin\theta + 1000) d\theta$

$V = [- 533.33cos\theta + 1000\theta]_{0}^{2\pi}$

$V = 0 + 2\pi \times 1000 = 2000\pi\ m^{3}$

7 0

3 years ago

Needed Right now Worth 50 points

zimovet [89]

a = The cost of the pizza.

b = The cost of the pizza and sales tax.

f(a) = The cost of the pizza.

g(b) = The cost of the pizza and sales tax.

g(f(a)) = The cost of the pizza, sales tax, and delivery fee

5 0

2 years ago

A pizza restaurant starts the day with a certain amount of pizza dough. The length of time the dough will last varies inversely

nordsb [41]

Answer:

thats alot of people don't you think

Step-by-step explanation:

6 0

3 years ago

What’s the surface area of 5 inches and 7 inches

erik [133]

Answer:

Is the surface a rectangle?? If so, then the surface area would be 35

Step-by-step explanation:

5 * 7 = 35

Hope this helped!! :)

5 0

3 years ago

Read 2 more answers

What is the radius of a hemisphere with a volume of 19160 ft', to the nearest tenth of a foot?