Answer:
Step-by-step explanation:(4+7)-(1)
Answer:
Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable
Step-by-step explanation:
We are given the Function
f(x) =
The two basic hypothesis of the mean valued theorem are
- The function should be continuous in [0,2]
- The function should be differentiable in (1,2)
upon checking the condition stated above on the given function
f(x) is continuous in the interval [0,2] as the functions is quadratic and we can conclude that from its graph
also the f(x) is differentiable in (0,2)
f'(x) = 6x - 2
Now the function satisfies both the conditions
so applying MVT
6x-2 = f(2) - f(0) / 2-0
6x-2 = 9 - 1 /2
6x-2 = 4
6x=6
x=1
so this is the tangent line for this given function.
Answer:
You didn't give the expression whose zero you want to find. From the options you wrote, the expression has two zeros, this means it is a quadratic expression.
I will however explain how to find the zero of a quadratic expression.
Step-by-step explanation:
An expression is called quadratic, if the highest degree of the variable is 2, no more, no less. It is of the form: ax² + bx + c, where a, b, and c are constants.
The zeros of a quadratic expression are the values that make the expression vanish, that is equal to zero.
Example: Find the zeros of 2x² - 6x + 4
First, equate the expression to zero
2x² - 6x + 4 = 0
Next, solve for x
2x² - 2x - 4x + 4 = 0
2x(x - 1) - 4(x - 1) = 0
(2x - 4)(x - 1) = 0
(2x - 4) = 0
Or
(x - 1) = 0
2x - 4 = 0
2x = 4
=> x = 4/2 = 2
Or
x - 1 = 0
x = 1
Therefore, the zeros of the polynomial are 1 and 2.
Answer:
84.13% probability a particular tire of this brand will last longer than 57,100 miles
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:

What is the probability a particular tire of this brand will last longer than 57,100 miles
This is 1 subtracted by the pvalue of Z when X = 57100. So



has a pvalue of 0.1587
1 - 0.1587 = 0.8413
84.13% probability a particular tire of this brand will last longer than 57,100 miles