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erik [133]
3 years ago
5

Solve 4 cos2x-3 = 0 for all real values of x.

Mathematics
1 answer:
vichka [17]3 years ago
3 0

4 cos² x - 3 = 0

4 cos² x = 3

cos² x = 3/4

cos x = ±(√3)/2

Fixing the squared cosine doesn't discriminate among quadrants.  There's one in every quadrant

cos x = ± cos(π/6)

Let's do plus first.  In general, cos x = cos a has solutions x = ±a + 2πk integer k

cos x = cos(π/6)

x = ±π/6 + 2πk

Minus next.

cos x = -cos(π/6)

cos x = cos(π - π/6)

cos x = cos(5π/6)

x = ±5π/6 + 2πk

We'll write all our solutions as

x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k

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Q # 7 please solve. the math
aleksandr82 [10.1K]
The first choice is the correct answer
12 in by 22 in by 4 in

the explanation is as shown in the figure
The dimension will be x , 20 - 2x , 30 -2x

the volume= v = x(20-2x)(30-2x) = 4x³ - 100x² + 600x
differentiating with respect to x and equating to zero
dv/dx = 12x² - 200x + 600 = 0
solve for x using calculator
x = 12.7 (unacceptable)   or x = 3.92 ≈ 4

∴ The dimension will be 4 , 12 , 22

7 0
4 years ago
Read 2 more answers
Write the quadratic function in standard form.<br> f(x) = -x2 + 2x + 4<br> f(x) =
goldenfox [79]

Answer:

f(x)=-1(x-2)^2+8

Step-by-step explanation:

Given:

The quadratic function is given as:

f(x)=-x^2+2x+4

The standard form of a quadratic function is given as:

f(x)=a(x-h)^2+k, where, 'a', 'h' and 'k' are real numbers.

Now, in order to convert the given function to standard form, we use completing by  square method.

-x^2+2x=-(x^2-2x)=-[(x-2)^2-2^2]=-[(x-2)^2-4]=-(x-2)^2+4

Now, f(x)=-x^2+2x+4 can be rewritten as:

f(x)=-(x-2)^2+4+4\\f(x)=-1(x-2)^2+8

Therefore, the standard form of the function is:

f(x)=-1(x-2)^2+8

7 0
3 years ago
Recall that rational numbers are numbers that can be represented as the ratio, or fraction, of two integers. When expressed as d
Alenkasestr [34]

Answer:

1)  \frac{5}{-14}=0.3571428571 2) Terminating

Step-by-step explanation:

1st. To answer this question let's divide with long division algorithm  5 and -14.

  <u> 0.3571428571</u>

-14)50

    42

     ---

     80

     -70

      --

    100

      98

      ---

     20

     14

    ----

      60

      -56

       ---

      40

       28

      --

     120

    -112

     ----

       80

       70

       --

      100

       -98

      --  

       2

5 (dividend) : -14 (divisor) \frac{5}{-14}

Long division (check below)

With the same two numbers -14 and 5 we can write in a Long Division

 

5) -14

<u>   - 2.8</u>

5) -14

    10

   40

So \frac{-14}{5}=-2.8

2nd. Both are terminating ones for they have finite quantities of numbers. -2.8 and 0.3571428571, as we can see that these are rational numbers for they can be written as a/b, and b≠ 0.

\frac{5}{-14} form.

\frac{-14}{5} form.

3 0
3 years ago
Read 2 more answers
The length of a planet's orbit around a star is approximately 29,870,000 km.
Sliva [168]

Answer:

745 k/hr

Step-by-step explanation:

mathematically, 1 day = 24 hours

1670 days = 1670 * 24 = 40,080 hours

The speed is thus;

(29,870,000)/40,080 = 745.259

= 745 km/h

5 0
3 years ago
Anita is 42 1/2 feet below jared. Steph is 67 3/7 feet above anita. What is stephs position compared to jared. Explain
Vilka [71]

Check the picture below.

let's firstly convert the mixed fractions to improper fractions and then subtract.

\stackrel{mixed}{42\frac{1}{2}}\implies \cfrac{42\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{85}{2}} ~\hfill \stackrel{mixed}{67\frac{3}{7}}\implies \cfrac{67\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{472}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{472}{7}~~ - ~~\cfrac{85}{2}\implies \cfrac{(2)472~~ - ~~(7)85}{\underset{\textit{using this LCD}}{14}}\implies \cfrac{944~~ - ~~595}{14}\implies \cfrac{349}{14}\implies 24\frac{13}{14}

3 0
3 years ago
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