Complete Ratio table
2 answers:
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Answer:
Step-by-step explanation:
See attachment.
If both cyclists travel for the same time and speed, they will have travelled the same distance. Since one is headed north and the other east, we can see that the distance between them in one hour is the hypotenuse of a right triangle. Each leg has distance x. We can say x^2 + x^2 = (3)^2
2x^2 =1 8
x^2 = 9
x = 3
They both rode 3 miles.
Answer:
The number of bacteria in the dish after 9.9 minutes is 478
Step-by-step explanation:
The form of the function is , where a is the initial amount (value f(x) at x = 0)
To find a and b let us use two points from the graph and substitute their coordinates in the equation
∵ The graph passes through point (1 , 1)
∴ x = 1 and y = 1
- Substitute them in the equation
∵
∴ a.b = 1 ⇒ (1)
∵ The graph passes through point (1 , 1)
∴ x = 3 and y = 4
- Substitute them in the equation
∵
∴ a.b³ = 4 ⇒ (2)
Use equation (1) to find a in terms of b
∵ a.b = 1
- Divide both sides by b
∴ ⇒ (3)
- Substitute a in equation (2) by equation (3)
∴ . b³ = 4
- Remember the rule
∵ . b³ =
= b²
∴ b² = 4
- Take √ for both sides
∴ b = 2
Substitute the value of b in equation (3) to find a
∵ a =
∴ a = 0.5
∴
∵ f(x) represents the number of bacteria after x minutes
∵ x = 9.9 minutes
- Substitute x by 9.9 to find the number of bacteria
∵
∴ f(9.9) = 477.7128917
- Round it to the nearest whole number
∴ f(9.9) = 478
∴ The number of bacteria in the dish after 9.9 minutes is 478