What would 672,831 be rounded to the nearest hundred

What is the midline of this function? y=

Sergeeva-Olga [200]

Answers:

Midline: y = 0
Amplitude = 1.5
Function: g(x) = 1.5sin(0.5x + pi/4)

There are infinitely many possible ways to answer the third part.

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Explanation:

The midline is the horizontal line that goes through the center of the sine curve. Visually we can see that is y = 0. Another way we can see this is to note how y = 0 is the midpoint of y = 1.5 and y = -1.5, which are the max and min respectively.

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The amplitude is the vertical distance from y = 0 to y = 1.5, and it's also the vertical distance from y = 0 to y = -1.5; in short, it's the vertical distance from center to either the peak or valley.

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The general format of a sine curve is

y = A*sin(B(x-C)) + D

where,

|A| = amplitude
B = variable tied with the period T, specifically B = 2pi/T
C = handles the left and right phase shift
D = handles the vertical shifting, and y = D is the midline.

In this case, we found so far that

|A| = 1.5 which could lead to A = 1.5
B = 2pi/(4pi) = 0.5 since T = 4pi is the period
D = 0

The only thing we're missing is the value of C, which is the phase shift.

Note the point (pi/2, 1.5) is one of the max points on this curve. Also, recall that sin(x) maxes out at 1 when x = pi/2

This must mean that the stuff inside the sine, the B(x-C) portion, must be equal to pi/2 in order to lead sin(B(x-C)) = 1.

So,

B(x-C) = pi/2

0.5(pi/2-C) = pi/2

pi/4 - C/2 = pi/2

4*( pi/4 - C/2 ) = 4*(pi/2)

pi - 2C = 2pi

-2C = 2pi - pi

-2C = pi

C = pi/(-2)

C = -pi/2

This allows us to update the function to get g(x) = 1.5*sin(0.5(x+pi/2)) which is the same as g(x) = 1.5sin(0.5x + pi/4)

This is one possible answer because we could have infinitely many possible values for C, due to sin(x) = 1 having infinitely many solutions.

Also, you could use cosine instead of sine. Cosine is just a phase shifted version and of sine, and vice versa.

7 0

3 years ago

What is the next patter for 4.5,9,13.5,18

abruzzese [7]

22.5 because its counting by 4.5

4 0

3 years ago

14. Michelle simplified an expression for the perimeter of the rectangle below and got X + 35.

Zigmanuir [339]

Answer:

The correct expression for the perimeter is $P=(\frac{5}{3}x+70)\ units$

see the explanation

Step-by-step explanation:

The complete question in the attached figure

Let

L ----> the length of rectangle

W ---> the width of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

In this problem we have

$L=(\frac{5}{6}x+23)\ units$

$W=12\ units$

substitute the values

$P=2(\frac{5}{6}x+23+12)$

$P=2(\frac{5}{6}x+35)$

$P=(\frac{10}{6}x+70)\ units$

Simplify

$P=(\frac{5}{3}x+70)\ units$

so

Michelle didn't multiply the sum of length and width by 2

6 0

3 years ago

NEED HELP PLEASE IM BEGGING YOU PLEASE!!!!!<br> NEED HELP WITH BOTH PLEASE

UkoKoshka [18]

Answer:

14) F

15) D

Step-by-step explanation:

14

You have 80 minutes on a CD, minus the time you burned would equal the time you have left on the CD.

15

To find mark down, you multiply the percentage to the original price, and then subtract the answer to the original price.

8 0

4 years ago

An open box is made from a 20-cm by 50-cm piece of tin by cutting a square from each corner and folding up the edges. The area

kipiarov [429]

Answer:

Therefore,

The length of the sides of the squares is

$x=7\ cm$

Step-by-step explanation:

Let "x" be the length of Cut Square,

As the tin size(Dimension) is

20 cm × 50 cm

So the size(Dimension) of box will be

(20 - 2x) × (50 - 2x)

Length = 50 - 2x

Width = 20 - 2x

Area of base of box = 216 cm²

To Find:

x = ?

Solution:

Area of Rectangular field is given by

$(Area\ of\ Rectangle(Box)) = Length\times Width$

Substituting the values we get

$216=(50-2x)(20-2x)$

Applying Distributive property we get

$216=1000-100x-40x+4x^{2}$

$4x^{2}-140x+784=0$

Dividing throughout by 4 we get

$x^{2}-35x+196=0$

On Factorizing we get

$x^{2}-28x-7x+196=0\\\\(x-7)(x-28)=0\\\\x-7=0\ or\ x-28=0\\\\x=7\ or\ x = 28$

As x cannot be 28 because tin size is 20 cm × 50 cm i.e longer than 20

Therefore,

$x=7\ cm$

Therefore,

The length of the sides of the squares is

$x=7\ cm$

5 0

4 years ago

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