Answer:
What is the question
Step-by-step explanation:
Answer:
1.
2.543.6
Step-by-step explanation:
We are given that
y(0)=200
Let y be the number of bacteria at any time
=Number of bacteria per unit time
Where k=Proportionality constant
2.
,y'(0)=100
Integrating on both sides then, we get
We have y(0)=200
Substitute the values then , we get
Substitute the value of C then we get
Differentiate w.r.t
Substitute the given condition then, we get
Substitute t=2
Then, we get 
e=2.718
Hence, the number of bacteria after 2 hours=543.6
Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
1. A quadratic equation has the following form: ax²+bx+c.
2. The leading coefficient is the number that is attached to the variable with the highest exponent. Then, the "a" is the leading coefficient of the quadratic equation.
3. The problem says that the leading coefficient is 1 (a=1) and the roots of the quadratic equation are 5 and -3. Then, you have:
(x-5)(x+3)=0
4. When you apply the distributive property, you obtain:
x²+3x-5x-15=0
x²-2x-15=0
5. Therefore, the answer is:
x²-2x-15=0
