You need to find points where the line g(x) intercepts the quadratic function f(x) in one and only one point.
Then 3x^2 + 4x -2 = mx - 5
solve 3x^2 + 4x - mx -2 + 5 = 0
3x^2 + (4 - m)x + 3 = 0
In order to there be only one solution (one intersection point) the radicand of the quadratic formula must be 0 =>
b^2 - 4ac = (4 - m)^2 - 4(3)(3) = 0
(4 - m)^2 = 24
4 - m = +/- √(24)
m = 4 +/- √(24) = 4 +/- 2√(6)
Then m, the slope of the line, may be 4 + 2√6 and 4 - 2√6
The first you should have to do is calculate the volume so start by drawing a picture then just go on the math solutions website
Using z-scores, it is found that the value of z is z = 1.96.
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Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean
and standard deviation
, is given by:
- It measures how many standard deviations the measure is from the mean.
- Each z-score has an associated p-value, which is the percentile.
- The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
- The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
- The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
- Thus, the value of Z is 1.96.
A similar problem is given at brainly.com/question/16965597