A1000 gallon tank, initially full of water, develops a leak at the bottom. given that 300 gallons of water leak out in the first 30 minutes, find the amount of water, a(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present.

a. a(t)= 1000(1/3)^1/10t
b. a(t)= 1000(1/2)^-1/10t
c. a(t)= 1000(1001/2)^t
d. a(t)= 1000e ^-1/10t
e. a(t)= 1000(1/2)^1/10t
f. none of these

option F

Step-by-step explanation:

given,

capacity of tank = 1000 gallon

volume of water leak = 300 gallon

time = 30 min

water is leaking at the rate

formula used

At t = 0   A = 1000 gallons

B = 1000

at t = 30        A  = 700

taking ln both side

now,

hence, the correct answer is option F

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.

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).