Show that there is a root of the equation below between1 and 2.4x3 - 6x2 + 3x - 2 =0solution let f(x) = 4x3 - 6x2 + 3x - 2. we arelooking for a solution of the given equation, that is, a numberc between 1 and 2 such that f(c) = . therefore we take a = , b = , and n = in the intermediate value theorem. wehavef(1) =4 - 6 +3 - 2 = -1 < 0f(2) = 32 - 24 +6 - 2 = 12 > 0thus f(1) < 0 0a root must lie between and . a calculation gives, by trial anderror, f(1.22) =-0.007008 < 0f(1.23) = 0.056068 > 0so a root lies in the interval (1.22, 1.23).

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

cheater

step-by-step explanation: