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3 years ago

Which of the following is an even function need help quick

Mathematics

2 answers:

musickatia [10]3 years ago

8 0

Answer:

The correct option is D.

Step-by-step explanation:

If function f(x) is called an even function if f(-x)=f(x).

The first function is

$F(x)=2\sin(\frac{1}{2}x)$

Put x=-x,

$F(-x)=2\sin(\frac{1}{2}(-x))=-2\sin(\frac{1}{2}x)=-F(x)\neq F(x)$ $[\because \sin(-x)=-\sin x]$

So, this function is not an even function.

The second function is

$F(x)=2\cos(\frac{1}{2}x+\frac{\pi}{2})$

Put x=-x,

$F(-x)=2\cos(\frac{1}{2}(-x)+\frac{\pi}{2})\neq F(x)$

So, this function is not an even function.

The third function is

$F(x)=2\sin(\frac{1}{2}x+\pi)$

Put x=-x,

$F(-x)=2\sin(\frac{1}{2}(-x)+\pi)\neq F(x)$

So, this function is not an even function.

The fourth function is

$F(x)=2\cos(\frac{1}{2}x)$

Put x=-x,

$F(-x)=2\cos(\frac{1}{2}(-x))=2\sin(\frac{1}{2}x)=F(x)$ $[\because \cos(-x)=\cos x]$

So, this function is an even function.

Hence the correct option is D.

mrs_skeptik [129]3 years ago

4 0

Not sure but it is 3..

Thanks!

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A bucket that weighs 4lband a rope of negligible weight are used todraw water from a well that is 80ftdeep. The bucket is filled

liq [111]

Answer:

Workdone = 3200 lb.ft

Step-by-step explanation:

We are told that the bucket is filled with 40 lb of water but water leaks out of a hole in the bucket at a rate of 0.2lb/s

Thus,

Weight of water at any given time (t) would be;

w(t) = 40 - 0.2t - - - - (1)

We are told the bucket is pulled up at a rate of 2ft/s.

Thus, height at time (t); y = 0 + 2t = 2t

Since y = 2t,

Then,t = y/2

Put y/2 for t in eq 1

Thus; w(y) = 40 - 0.2(y/2)

w(y) = 40 - 0.1y

Now, at y = 80 ft, we have;

w(80) = 40 - 0.1(80)

w(80) = 40 - 8 = 32 lb

Since 32 lbs are left, it means there is always water in the bucket.

Thus, work done is;

W = 80,0[∫(Total weight).dy]

W = 80,0[∫[(weight of rope) + (weight of bucket) + (weight of water)]dy]

W = 80,0[∫[0 + 4 + 40 - 0.1y]dy]

Integrating, we have;

W = [44y - y²/20] at boundary of 80 and 0

So,

W = [44(80) - 80²/20] - [0 - 0²/20]

W = 3200 lb.ft

8 0

3 years ago

Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)

Rom4ik [11]

Answer:

Step-by-step explanation:

Given : $p(x)=x^{3} +6x^{2} -7x-60$

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, $\text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}$

Since constant term = -60

Leading coefficient = 1

$\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}$

$\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}$

Thus the possible roots are $\pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60$

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is $x^{2} +x-12$

And remainder is 0 .

So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting

$x^{2} +x-12=0$

$x^{2} +4x-3x-12=0$

$x(x+4)-3(x+4)=0$

$(x-3)(x+4)=0$

Thus x-3 and x+4 are the other two factors

So , p(x)=(x+5)(x-3)(x+4)

3 0

3 years ago

Read 2 more answers

What is the discriminant of f(x)=2x^2+8x+16 <br>and the number and type of roots

vfiekz [6]

Answer:

2 imaginary roots

Step-by-step explanation:

The discriminate is the portion of the quadratic equation under the square root

D = b^2 - 4ac

D = 8^2 - 4(2)(16)

D = 64 - 128

D = -64

Since the discriminate is negative the square root will be imaginary

and there will be 2 of them

2 imaginary roots

7 0

2 years ago

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How many times smaller is 2 × 10-3 than 4 × 10-2? PLEASE HELP

NNADVOKAT [17]

<h2>The required "option A) 20" is correct.</h2>

Step-by-step explanation:

Let x be the smaller than 4 × $10^{-2}$ .

To find, the number of times smaller is 2 × $10^{-3}$ than 4 × $10^{-2}$ = ?

∴ x = $\dfrac{4\times 10^{-2}}{2\times 10^{-3}}$

= 2 × $10^{-2}$ × $10^{3}$

Using the identity,

$a^{m}=\dfrac{1}{a^{-m}}$

= 2 × $10^{-2+3}$

Using the identity,

$a^{m} \timesa^{n}=a^{m+n}$

= 2 × $10^{1}$

= 2 × 10

= 20

Thus, the required "option A) 20" is correct.

6 0

3 years ago

How would I find x when there is a arrow pointing down instead of up<br><br> What does x equal to??

lys-0071 [83]

Since opposite exterior angles are congruent I would plug in numbers for X till you find a number that goes into both and gets you the same product.

7 0

3 years ago