a. Only a Hamiltonian path
One such path is
1 → 2 → 0 → 4 → 3
which satisfies the requirement that each vertex is visited exactly once.
There is no Hamiltonian circuit, however, since it is impossible for any Hamiltonian path on this graph to visit vertex 0 exactly once.
Answer. First option: t > 6.25
Solution:
Height (in feet): h=-16t^2+729
For which interval of time is h less than 104 feet above the ground?
h < 104
Replacing h for -16t^2+729
-16t^2+729 < 104
Solving for h: Subtracting 729 both sides of the inequality:
-16t^2+729-729 < 104-729
-16t^2 < -625
Multiplying the inequality by -1:
(-1)(-16t^2 < -625)
16t^2 > 625
Dividing both sides of the inequality by 16:
16t^2/16 > 625/16
t^2 > 39.0625
Replacing t^2 by [ Absolute value (t) ]^2:
[ Absolute value (t) ]^2 > 39.0625
Square root both sides of the inequality:
sqrt { [ Absolute value (t) ]^2 } > sqrt (39.0625)
Absolute value (t) > 6.25
t < -6.25 or t > 6.25, but t can not be negative, then the solution is:
t > 6.25
Equation in slope-intercept form is y = 2x - 6
Step-by-step explanation:
- Step 1: Given slope of the line, m = 2. Form an equation y = mx + b
⇒ y = 2x + b ---- (1)
- Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.
⇒ 2 = 2 × 4 + b = 8 + b
⇒ b = -6
- Step 3: Form the slope-intercept equation.
⇒ y = 2x - 6
Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.
Step-by-step explanation:
Given,
Chocolate used to make 200 ml of chocolate sauce = 30 grams
Ratio of chocolate to milliliters of chocolate sauce = 30:200
Let,
x be the milliliters of sauce made from 450 grams of chocolate
Ratio of chocolate to ml of sauce = x:450
Using proportion;
Ratio of chocolate to ml of sauce:: ratio of chocolate to ml of sauce
Product of extreme = Product of mean
Dividing both sides by 30
450 grams of chocolate will make 3000 milliliters of chocolate sauce.
We will convert this in liters.
1 liter = 1000 ml
3000 ml = 
= 3 liters
Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.
Keywords: ratio, proportion
Learn more about proportion at:
#LearnwithBrainly
(3*4)+(1*7)/7*4 = 12+7/28 = 19/28
your answer is 19/28
