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3 years ago

Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.

Mathematics

1 answer:

Mariana [72]3 years ago

4 0

Answer:

Step-by-step explanation:

y4−

(y2−9)(y2+9)

Distribute:

=y4+

−1

y4+9

Combine Like Terms:

=y4+

−1

y4+9

=(y4+

−1

y4)+(9)

y4+9

Answer:

y4+9

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Need help on this problem

faust18 [17]

Using an exponential function, it is found that:

For Country A, the doubling time is of 43 years.

For Country B, the growth rate is of 1.9% per year.

<h3>What is the exponential function for population growth?</h3>

The exponential function for population growth is given as follows:

$P(t) = P(0)e^{kt}$

In which:

P(t) is the population after t years.

P(0) is the initial population.

k is the exponential growth rate, as a decimal.

t is the time in years.

For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:

$P(t) = P(0)e^{kt}$

$2P(0) = P(0)e^{0.016t}$

$e^{0.016t} = 2$

$\ln{e^{0.016t}} = \ln{2}$

$0.016t = \ln{2}$

$t = \frac{\ln{2}}{0.016}$

t = 43 years.

For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.

$P(t) = P(0)e^{kt}$

$2P(0) = P(0)e^{36k}$

$e^{36k} = 2$

$\ln{e^{36k}} = \ln{2}$

$36k = \ln{2}$

$k = \frac{\ln{2}}{36}$

k = 0.019.

For Country B, the growth rate is of 1.9% per year.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

3 0

1 year ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

777dan777 [17]

Answer: (C) 13,120

<u>Step-by-step explanation:</u>

Given the sequence {4, 12, 36, 108, ... , 8748} we know that the first term (a) is 4 and the ratio (r) is $\dfrac{12}{4}=3$

Input the values above into the Sum formula:

$S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_8=\dfrac{4(1-3^8)}{1-3}\\\\.\quad=\dfrac{4(1-6561)}{-2}\\\\.\quad=\dfrac{4(-6560)}{-2}\\\\.\quad=-2(-6560)\\\\.\quad=13,120$

5 0

3 years ago

Need help will give 15 points

Fantom [35]

Answer:

y = -2/3x + 6

Step-by-step explanation:

To find the slope, find how much y changes in proportion to x. Here, when x changes by 1, y changes by -2/3. So, the number before x is -2/3.

To find the y-intercept, we need to find what y will be when x is 0. Since we know that when x is 1, y is 16/3, and when x decreases by 1, y increases by 2/3. So, when x is 0, y is 16/3 + 2/3, which is 18/3, or 6.

5 0

3 years ago

Pepper jackie has 5.8

vesna_86 [32]

Answer:

Pepper Jackie still has 5.8

Step-by-step explanation:

If this is a english problem instead of a math problem to correct the sentence it would be Pepper Jackie has 5.8

4 0

3 years ago

joseph has a new rectangular aquarium. the aquarium has a length of four feet, width of two feet and height of two feet. What is

Darina [25.2K]

12 inches go into one foot, so we can calculate the volume of the tank in inches to make the calculations that follow easier. Therefore, to calculate the volume of the tank, we use length x breadth x height = 4 x 2 x 2 = 16 square feet x 12 for square inches = 192 square inches.
Every 12 square inches Joseph can fit a one inch fish. The fish that he has are 3 inches long, therefore he can only fit one fish every 36 square inches.
That means that if we take the total volume of the tank and divide it by the space that a 3 inch fish will take up, we are left with 192/36 = 5.3 fish.
You cannot have a third of a fish, so we round off to the nearest whole number, and we determine that Joseph can put 5 fish in his new aquarium.

3 0

3 years ago