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3 years ago

The difference between total surface area and curved surface area of a hemisphere is 154 cm^2, find it's volume.

Mathematics

1 answer:

OLga [1]3 years ago

4 0

Answer:

Surface area of a sphere=4πr

=154cm

⇒4×

=154cm

⇒r

154

⇒r

⇒r=

∴r=

=3.5cm

Volume of the sphere=

πr

×(3.5)

×42.875‬=179.67cm

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4 years ago

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number o

Zielflug [23.3K]

To be clear, the given relation between time and female population is an integral:
 $t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,
dP$

The problem says that r = 1.2 and S = 400, therefore substituting:
 $t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]}
} \, dP$ 

= $
\int { \frac{P+400}{P(0.2P - 400)} } \, dP$

In order to evaluate this integral, we need to write this rational function in a simpler way:
 $\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} +
\frac{B}{(0.2P - 400)}$ 

where we need to evaluate A and B. In order to do so, let's calculate the LCD:
 $\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P -
400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)}$ 

the denominators cancel out and we get:
P + 400 = 0.2AP - 400A + BP
 = P(0.2A + B) - 400A

The two sides must be equal to each other, bringing the system:
 $\left \{ {{0.2A + B = 1} \atop {-400A =
400}} \right.$ 

Which can be easily solved:
 $\left \{ {{B=1.2} \atop {A=-1}} \right.$ 

Therefore, our integral can be written as:
 $t = \int { \frac{P+400}{P(0.2P - 400)} } \,
dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP$ 
= $- \int { \frac{1}{P} \, dP +
1.2\int { \frac{1}{0.2P-400} } \, dP$ 
= $- \int { \frac{1}{P} \, dP +
6\int { \frac{0.2}{0.2P-400} } \, dP$ 
= - ln |P| + 6 ln |0.2P - 400| + C

Now, let’s evaluate C by considering that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5) 
 Therefore, the equation relating female population with time requested is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)

8 0

3 years ago

A pound of apples costs $1.98 how much will 0.75 pounds cost ?

PolarNik [594]

Given:

Cost of one pound of apples = $1.98

To find:

The cost of 0.75 pound of apples.

Solution:

We have,

Cost of one pound = $1.98

So, cost of 0.75 pound of apples = 0.75 × cost of one pound of apples

$\text{Cost of 0.75 pound of apples}=0.75\times 1.98$

$\text{Cost of 0.75 pound of apples}=1.485$

Therefore, the cost of 0.75 pound of apples is $1.485.

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4 years ago

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She is now in debt of $2.00
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i hope this helped

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3 years ago

The difference between total surface area and curved surface area of a hemisphere is 154 cm^2, find it's volume.​

The difference between total surface area and curved surface area of a hemisphere is 154 cm^2, find it's volume.