A rectangle has a width of 5 inches and a length of 9 inches. What will be the new dimensions of the rectangle after it is dilat
ed by a scale factor of 3?
8 inches by 12 inches
15 inches by 9 inches
15 inches by 27 inches
45 inches by 81 inches
8 inches by 12 inches
15 inches by 9 inches
15 inches by 27 inches
45 inches by 81 inches
2 answers:
Answer:
Step-by-step explanation:
Alright, lets get started.
The given rectangle dimension is : 5 inches and 9 inches
Please refer the given diagram.
If the given rectangle is dilated with scale factor of 3, it means the sides of given rectangle if multiplied with given scale factor 3.
So, the width of rectangle is : inches
So, the length of rectangle is : inches
So the dimensions of new rectangle is : 15 inches by 27 inches : Answer
Hope it will help :)
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Answer:
The number of bacteria at initial = 187
Step-by-step explanation:
Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.
Integrating both side we get
㏑ N = k t + C ------- (1)
Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.
⇒ ㏑ 500 = 3 k + C -------- (2)
⇒ ㏑ 5000 = 10 k + C ------ (3)
⇒ ㏑ 5000 - ㏑ 500 = 7 k
⇒ ㏑ = 7 k
⇒ ㏑ 10 = 7 k
⇒ k = 0.329
Put this value of k in equation (2),
⇒ ㏑ 500 = 3 × 0.329 + C
⇒ C = 5.23
Put this value of C in equation 1 we get,
⇒ ㏑ N = k t + 5.23
Initially when t = 0 , then
⇒ ㏑ N = 5.23
⇒ N = 187
Thus the number of bacteria at initial = 187