which of the following is a solution of 2cos^2x-cost-1=0 a. 0 degrees b. 150 degrees c. 180 degrees d. 210 degrees

Mathematics

1 answer:

Luba_88 [7]3 years ago

3 0

Answer:

{0, 150} degrees

Step-by-step explanation:

Given 2cos^2x-cost-1=0, let's simplify this problem by temporarily replacing cos x with y:

2y^2 - y -1 = 0

This can be solved by factoring: (2y + 1)(y - 1) = 0. From this we get two solutions: y = -1/2 and y = 1.

Remembering that we let y = cos x, we now solve:

cos x = -1/2 and cos x = 1.

Note that cos x = 1 when x = 0 and the "adjacent side" coincides with the hypotenuse.

cos x = -1/2 when the hypotenuse is 2 and the "adjacent side" is -1. This has two solutions between 0 and 360 degrees: 150 degrees and 270 degrees.

Four answer choices are given. Both (a) (0 degrees) and (b) (150 degrees) satisfy the original equation. Thus, the solution set is {0, 150} (degrees).

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2. The mean birth weight of a full term boy born in the US is 7.7 lbs, with standard deviation of 1.1 lbs. A. Find the probabili

Fed [463]

Answer:

The value is $P( X < 7 ) =0.26226$

The value is $P( X < 7 ) = 0.00073$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 7.7 lbs$

The standard deviation is $\sigma = 1.1 \ lbs$

The sample size is n = 25

Generally the probability that a boy born full term in the US weighs less than 7 lbs is mathematically represented as

$P( X < 7 ) = P( \frac{X - \mu }{\sigma} < \frac{7 - 7.7 }{1.1 } )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

=> $P( X < 7 ) = P(Z$

From the z table the area under the normal curve to the left corresponding to -0.6364 is

$P(Z$

=> $P( X < 7 ) =0.26226$

Generally the standard error of mean is mathematically represented as

$\sigma_{x} = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 1.1 }{\sqrt{25} }$

=> $\sigma_{x} = 0.22$

Generally the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs is mathematically represented as

$P( \= X < 7 ) = P( \frac{\= X - \mu }{\sigma_{x}} < \frac{7 - 7.7 }{ 0.22 } )$