Part (i)
I'll use H in place of T to represent the heat of the object. That way there isn't a clash of variables lowercase t vs uppercase T.
The equation we're working with is updated to:
H(t) = 22 + a*2^(bt)
Plugging in t = 0 as the initial time value should lead to the temperature being H = 86 degrees Celsius.
So,
H(t) = 22 + a*2^(bt)
86 = 22 + a*2^(b*0)
86 = 22 + a*2^0
86 = 22 + a*1
86 = 22 + a
a+22 = 86
a = 86-22
a = 64
<h3>Answer: 64</h3>
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Part (ii)
We'll use the value of 'a' we found earlier. Plus we'll use the fact that H = 28 when t = 0.5 (since 30 min = 30/60 = 0.5 hr).
H(t) = 22 + a*2^(bt)
28 = 22 + 64*2^(b*0.5)
28-22 = 64*2^(0.5b)
64*2^(0.5b) = 6
2^6*2^(0.5b) = 6
2^(6+0.5b) = 6
log( 2^(6+0.5b) ) = log(6)
(6+0.5b)*log(2) = log(6)
6+0.5b = log(6)/log(2)
6+0.5b = 2.5849625
0.5b = 2.5849625-6
0.5b = -3.4150375
b = -3.4150375/(0.5)
b = -6.830075
<h3>Answer: Approximately -6.830075</h3>
Gradient = Change of y/ Change of x
= 14/10
= 1.4
You must divide the cost in 2011 by 1955 for each item and round your answer to the nearest hundredth after.
Hope that helps!
Answer:
14. 18 inches tall
Step-by-step explanation:
14. 24in wide = 12in wide
36in tall = 18in tall
So technically the relationship of 24 to 12 is dividing it by 2 so you would do the same for 36in tall wall.
Sorry I could only do one I’m lazy and in a rush but hope this helps!
Answer: 40
<u>Step-by-step explanation:</u>
Let x represent the original ratio and y represent the final ratio:
Egg : Tuna
2x 3x
<u> </u> <u> +15 </u> <em>15 tuna were added</em>
2x = y 3x + 15 = 3y <em>y and 3y are the final 1:3 ratio</em>
Now you have a system of equations. I am going to choose the substitution method. "2x" can be substituted for "y" in the second equation:
3x + 15 = 3y
3x + 15 = 3(2x)
3x + 15 = 6x
15 = 3x
5 = x
Egg (final): 2x = 2(5) = 10
Tuna (final): 3x + 15 = 3(5) + 15 = 15 + 15 = 30
Egg (final) + Tuna (final) = Total sandwiches
10 + 30 = 40
