Answer:
A(t) = 300 -260e^(-t/50)
Step-by-step explanation:
The rate of change of A(t) is ...
A'(t) = 6 -6/300·A(t)
Rewriting, we have ...
A'(t) +(1/50)A(t) = 6
This has solution ...
A(t) = p + qe^-(t/50)
We need to find the values of p and q. Using the differential equation, we ahve ...
A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50
0 = 6 -p/50
p = 300
From the initial condition, ...
A(0) = 300 +q = 40
q = -260
So, the complete solution is ...
A(t) = 300 -260e^(-t/50)
___
The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.
Answer:
For tingle #1
We can find angle C using the triangle sum theorem: the three interior angles of any triangle add up to 180 degrees. Since we know the measures of angles A and B, we can find C.
We cannot find any of the sides. Since there is noting to show us size, there is simply just not enough information; we need at least one side to use the rule of sines and find the other ones. Also, since there is nothing showing us size, each side can have more than one value.
For triangle #2
In this one, we can find everything and there is one one value for each.
- We can find side c
Since we have a right triangle, we can find side c using the Pythagorean theorem
- We can find angle C using the cosine trig identity
- Now we can find angle A using the triangle sum theorem
For triangle #3
Again, we can find everything and there is one one value for each.
- We can find angle A using the triangle sum theorem
- We can find side a using the tangent trig identity
- Now we can find side b using the Pythagorean theorem
The zeroes of the given polynomial is 1 and -6.
<h3>What is Polynomials?</h3>
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here, given equation;
f(x) = (x - 1)(x + 6)
for finding the zeros of the equation we need to put.....f(x) = 0
0 = (x - 1)(x + 6)
x - 1 = 0 or x + 6 = 0
x = 1 or x = -6
Thus, The zeroes of the given polynomial is 1 and -6.
Learn more about Polynomials from:
brainly.com/question/17822016
#SPJ1
Answer:
B
Step-by-step explanation:
The domain is all possible values of x. Here, x is the number of $5 nontaxable items. So x must be an integer, and it can't be negative. It is possible for x to be 0. So x is all whole numbers.
Answer:
After 1 year, both the tress will be of the same height.
Step-by-step explanation:
Let us assume in x years, both trees have same height.
Type A is 7 feet tall and grows at a rate of 8 inches per year.
⇒The growth of tree A in x years = x times ( Height growth each year)
= 8 (x) = 8 x
⇒Actual height of tree A in x years = Initial Height + Growth in x years
= 7 + 8 x
or, the height of tree A after x years = 7 + 8x
Type B is 9 feet tall and grows at a rate of 6 inches per year.
⇒The growth of tree B in x years = x times ( Height growth each year)
= 6 (x) = 6 x
⇒Actual height of tree B in x years = Initial Height + Growth in x years
= 9 + 6 x
or, the height of tree B after x years = 9 + 6x
According to the question:
After x years, Height of tree A =Height of tree B
⇒7 + 8x = 9 + 6x
or, 8x - 6x = 9 - 7
or, 2 x = 2
or, x = 2/2 = 1 ⇒ x = 1
Hence, after 1 year, both the tress will be of the same height.
