Mike read 1/4 of the newspaper in 1/3 of an

Reciprocals in mix fraction form

jok3333 [9.3K]

Answer: improper fractions

Step-by-step explanation:

5 0

3 years ago

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago

This table shows a linear relationship. x: 6 12 18 24 30 y: 252 504 756 1008 1260 Based on the information in this table, which

Anton [14]

Answer:

The difference between value of y at x=11 is 385, the correct option is third.

Step-by-step explanation:

The difference between value of y at x=11 is 385, the correct option is third.

The equation of a line which passing through two points is given below,

The two points from the table are (3,240) and (4,320), the equation is,

Put x=11

Therefore according to the table the value of y is 880 at x=11.

The two points from the table are (2,90) and (4,180), the equation is,

Put x=11,

Therefore according to the table the value of y is 495 at x=11.

The difference between the values of y at x=11 is,

Therefore third option is correct.

3 0

2 years ago

The local zoo is filling two water tanks for the elephant exhibit. One water tank contains 30 gal of water and is filled at a co

kakasveta [241]

You first have to set up the two equations. Y is equal to the total number of gallons in a tank and x is equal to the number of hours the tanks are filling.

Since the two equations both equal y I can make them equal each other. I then solved for x as you see and got -4.

Once I found my x value I now needed to find my y. You only needed to chose one equation to solve for y, so I decided to do the first one. I plugged in -4 where my x value currently was and solved for y. I got 2.

If you have any questions please comment!! Hope this helps!!

3 0

3 years ago

Can someone help me please

aleksklad [387]

9514 1404 393

Answer:

IS a parallelogram

Step-by-step explanation:

The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...

m = (y2 -y1)/(x2 -x1)

The distance formula for the length of that same line is ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.

The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)

_____

<em>Additional comments</em>

There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:

B +D = (-2+6, -9-3) = (4, -12)

C +E = (0+4, -5-7) = (4, -12)

These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.

__

If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)

7 0

2 years ago