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spayn [35]
3 years ago
6

Find two values of c in (− π/ 4 , π /4) such that f(c) is equal to the average value of f(x) = 2 cos(2x) on ( − π/ 4 , π/ 4 ). R

ound your answers to three decimal places.
Mathematics
1 answer:
pentagon [3]3 years ago
4 0

Answer:

c₁ = 1/2 cos⁻¹ (2/π) = 0.44

c₂ = -1/2 cos⁻¹ (2/π) = -0.44

Step-by-step explanation:

the average value of f(x)=2 cos(2x) on ( − π/ 4 , π/ 4 ) is

av f(x) =∫[2*cos(2x)] dx /(∫dx) between limits of integration − π/ 4 and π/ 4

thus

av f(x) =∫[cos(2x)] dx /(∫dx) = [sin(2 * π/ 4 ) - sin(2 *(- π/ 4 )] /[ π/ 4 -  (-π/ 4)]

= 2*sin (π/2) /(π/2) = 4/π

then the average value of f(x) is 4/π . Thus the values of c such that f(c)= av f(x) are

 4/π = 2 cos(2c)  

2/π = cos(2c)

c = 1/2 cos⁻¹ (2/π) = 0.44

c= 0.44

since the cosine function is symmetrical  with respect to the y axis then also c= -0.44 satisfy the equation

thus

c₁ = 1/2 cos⁻¹ (2/π) = 0.44

c₂ = -1/2 cos⁻¹ (2/π) = -0.44

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ANEK [815]
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5 0
3 years ago
The "P" in 20p9 represents a:
Scorpion4ik [409]

Answer:

option (A) —Permutation.

Step-by-step explanation:

this is because permutation comes in this form and looks like that and I have learnt permutation in the past.

so yeah;

examples of permutations:

²⁰p9 ( 20 upper case, 9 lower case and p in-between)

we can solve it by

Formula: n!/(n-r)!

soooo

20!/(20-9)!

= 20!/(11)!

=20x19x18x17x16x15x14x13x12x11!/11!

we cancel out the 11!s (for easier solving)

and multiply or cancel out the remaining ( if you can't cancel out yet just multiply)

we get,

6.09493248 x 10¹⁰

~ 6 x 10¹⁰

there you go.( I know I did a little bit too much)

Hope this helps

Good luck.

7 0
3 years ago
A line that includes the points (4,j) and ( – 8, – 9) has a slope of 16 . What is the value of j?
Gnoma [55]
The answer is j= -8, if the slope is 16/1 then -8 goes up 16 to 4 and -9 goes over 1 to -8
3 0
3 years ago
Gabriella invested $73,000 in an account paying an interest rate of 3%
Ivanshal [37]

Answer:

Gabriella will make $61 more than Mila after 5 years

Step-by-step explanation:

Gabriella Data

Principal Amount P= $73,000

Rate r = 3% or 0.03

Compounded continuously

Time t = 5 years

The formula used is: A=Pe^{rt}

Putting values and finding A

A=Pe^{rt}\\A=73000e^{0.03*5}\\A=73000e^{015}\\A=84813.899\\A\approx84814

So, After 5 years Gabriella will have $84814

Mila Data:

Principal Amount P= $73,000

Rate r = 3% or 0.03

Compounded quarterly n = 4

Time t = 5 years

The formula used is:A=P(1+\frac{r}{n})^{nt}

Putting values and finding A

A=P(1+\frac{r}{n})^{nt}\\A=73000(1+\frac{0.03}{4})^{4*5}\\A= 73000(1+0.0075)^{20}\\A= 73000(1.0075)^{20}\\A=73000(1.161)\\A=84753

So, After 5 years Mila will have $84753

Now subtracting to find the difference 84814-84753 = 61

So, Gabriella will make $61 more than Mila after 5 years

4 0
3 years ago
Plz help I’ll give 20 points
Norma-Jean [14]
The first one is : y= -1/2x+3

The second one is : y=x-3
7 0
3 years ago
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