#45 How many solutions exist for the equation (cos^2x/x)-(1/5)=0

Mathematics

2 answers:

marissa [1.9K]2 years ago

7 0

45. A graphing calculator shows there to be 3 solutions. (There is no algebraic way to find them.)

_____

Rewriting the equation to

... f(x) = cos(x)² -x/5

We note sign changes in this function between 0 and π/2, between π/2 and π, and between π and 3π/2. Outside the range 0 to 3π/2, there are no more sign changes, hence no more solutions.

inn [45]2 years ago

4 0

check the picture below.

notice, you're asked to use a graphing calculator to get them.

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Step-by-step explanation:

The angle measure of a straight line is (180) degrees As given in the picture, line (AC) is a straight line, thus its angle measure is (180) degrees. Angles (ABD) and (DBC) make up line (AC). Therefore, one can conclude that the sum of angles (ABD) and (DBC) is (180) degrees. Form an equation, simplify and use inverse operations to solve for the unknown parameter (q).

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Substitute for the angle measures,

$(7q-46)+(3q+6)=180$

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Inverse operations,

$10q-40=180\\\\10q = 220\\\\q = 22$

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