Answer:
42.25 feet
Step-by-step explanation:
The height function is a parabola. The maximum value of a negative parabola is at the vertex, which can be found with:
x = -b/2a
where a and b are the coefficients in y = ax² + bx + c.
Here, we have y = -16t² + 52t. So a = -16 and b = 52. The vertex is at:
t = -52 / (2×-16)
t = 13/8
Evaluating the function:
h(13/8) = -16(13/8)² + 52(13/8)
h(13/8) = -169/4 + 169/2
h(13/8) = 169/4
h(13/8) = 42.25
After 30 minutes from the time recipe is kept in the oven, then the temperature of the oven is kept at 350 °F.
<h3>What is a function?</h3>
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
A pumpkin pie recipe says to bake the pie at 425°F for 15 minutes, and then to adjust the temperature down to 350°F for 45 additional minutes.
The function P(t) gives the oven temperature setting t, in degrees Fahrenheit, t minutes after the pie is placed in the oven.
Diego discovers that the temperature inside the oven is always 25 degrees warmer than the oven’s temperature setting.
The function B gives the actual temperature of Diego’s oven.
If P(30) = 350. Then the corresponding point on the function B will be
The temperature function can be written as
![P(t)=\begin{Bmatrix}425 & 0\leq t\leq 15 \\\\350 & 15 < t\leq 60 \\\end{Bmatrix}](https://tex.z-dn.net/?f=P%28t%29%3D%5Cbegin%7BBmatrix%7D425%20%26%200%5Cleq%20t%5Cleq%2015%20%5C%5C%5C%5C350%20%26%2015%20%3C%20t%5Cleq%2060%20%5C%5C%5Cend%7BBmatrix%7D)
The value of t = 30 lies in the interval of 15 < t ≤ 60.
After 30 minutes from the time recipe is kept in the oven, then the temperature of the oven is kept at 350 °F.
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Answer:
-
, 0
Step-by-step explanation:
8x⁴ + x = 0
factor out x:
x(8x³ + 1) = 0
The zero product property says that one of the terms needs to be equal to 0:
x = 0
8x³ + 1 = 0
Solve for x in the 2nd equation:
8x³ = -1
x³ = - ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
x = - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
When x is either 0 or -
, the product will be equal to zero.
The roots are 0 and - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
The probability that a college student will get to work in 30 mins or less is 0.4 or 40%.
What does uniformly distributed probability mean?
Uniform distribution refers to a type of probability distribution in which all outcomes are equally likely to occur.
According to the given question:
Since the time is uniformly distributed, every possible travel time has the same likelihood of occurring.
Lower boundary (L) = 20 minutes
Upper boundary (U) = 45 minutes
The probability that a student finishes her trip in 30 minutes or less is:
P (t ≤ 30) = (30 - L)/(U - L)
= (30 - 20)/(45 - 20)
= 10/25
= 0.4 or 40%
The probability that she will get to work in 30 mins or less is 0.4 or 40%
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