Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.
The relationship between the elapsed time, t, in days, since an ocean sunfish is born, and its mass, M(t), in milligrams, is modeled by the following function:
M(t)=3*(81/49)^t

The mass of the sunfish increases by a factor of 9/7 every days.

Half (1/2)

Step-by-step explanation:

The relation between the Mass, M(t), of the ocean sunfish and time t, in days, since it is born is given as:

This expression shows that the mass of sunfish increases by a factor of after each day. For example one day 1, the mass of sunfish would be:

And on day 2:

We can re-write the given equation as:

The exponent has changed from t to 2t. The term "2t" means 2 times in a unit time t. So this means, the mass of sunfish increases by a factor of 9/7 every 1/2(half) day.

On Day 1, the mass would be:

After 1.5 day, the mass would be:

This example shows that the mass of sunfish increases by a factor of 9/7 after every half of the day.

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).