Answer:
Step-by-step explanation:
The initial temperature difference of 72 -34 = 38 °F is reduced to a difference of 72 -41 = 31 °F after 35 minutes. The exponential term in the temperature expression could have the factor ...
(31/38)^(t/35) = e^(-kt)
Taking the natural log, we find ...
(t/35)ln(31/38) = -kt
k = ln(38/31)/35 ≈ 0.00581711
To the nearest thousandth, this is ...
k ≈ 0.006
Using this in the equation for temperature, we have ...
T = 72 -38e^(-0.006t)
Filling in the desired value for t (80), we find the turkey temperature after 80 minutes to be about
T = 72 -38e^(-.006×80) = 72 -38e^-.48 ≈ 48.49
T ≈ 48 °F
The value of k is about 0.006, and the turkey temperature is about 48 °F.
Answer:
The answer is D. Vertex at (-7,-9).
Step-by-step explanation:
The equation is in vertex form, so you take the opposite of x and the constant stays the same. So, the opposite of 7 is -7 and -9 stays the same.
Answer:
56 + 53pi
Step-by-step explanation:
<u><em>Area of small circles:</em></u>
diameter of small circle: 4cm
forumla to find area of circle: A = pir^2
r is radius = half of diameter -> d/2 = 4 / 2 = 2cm
A = pi (2cm)^2
A = pi (4cm)
A = 4pi
<u><em>Area of large circle:</em></u>
diameter of small circle: 4cm
forumla to find area of circle: A = pir^2
r is radius = half of diameter -> d/2 = 14 / 2 = 7cm
A = pi (7cm)^2
A = pi (49cm)
A = 49pi
<u><em>Area of rectangle:</em></u>
Area = width x length
Area = 14cm x 4cm
Area = 56cm
<u><em>Add all three areas:</em></u>
Area of rectangle + large circle + small circle
56cm + 49pi + 4pi = 56cm + 53pi
Answer: 14x^2 - 84x - 7
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Explanation:
The like terms 6x^2 and 8x^2 combine to 14x^2
The like terms -8x and -76x combine to -84x
Nothing pairs with the -7, so its stays as is.
Standard form is where we list the terms in decreasing exponent order. We can think of -84x as -84x^1 and the -7 as -7x^0. So 14x^2 - 84x - 7 would be the same as 14x^2 - 84x^1 - 7x^0. The exponents count down: 2,1,0.
The final answer is a trinomial since it has three terms. It is also a quadratic because the degree (highest exponent) is 2.
(4 2/3) / (4 1/5) = 1.111
