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3 years ago

What is the difference in surface areas, in square feet, of the two boxes?

1 answer:

3 0

The difference is 3ft since the surface area for the prism is 57, and the surface area for the cube is 54.

You can use the surface area formula
2(wl+hl+hw) = Area
2·(3·4.5+2·4.5+2·3)=57

And a cubes surface area formula
6a^2 = Area
6·32=54

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3 years ago

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liq [111]

We can draw a unit circle as:

The sine is the vertical leg (or vertical projection) of the triangle formed by the angle.

The cosine will be the horizontal leg (or horizontal projection) of this same triangle.

The hypotenuse of this triangle will be the radius if the unit circle (r = 1).

a) The sine will be increasing from θ = 0° until it reaches its maximum at 90°.

Then it will be decreasing for angles between 90° and 270°.

Between 270° and 0° it will be increasing again.

b) The cosine has a maximum value for an angle of 0°.

It will decrease until 180°.

Then it will be increasing from angles between 180° and 360°.

c) We can see in the unit circle that the sine is 0 when the angle is one the horizontal axis, like when θ = 0° or θ = 180°.

The cosine will be equal to 0 when the angle is vertical: θ = 90° and θ = 270°.

Answer:

a) Increasing: (0°, 90°) and (270°, 360°)

Decreasing: (90°, 270°)

b) Increasing: (180°, 360°)

Decreasing: (0°,180°).

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1 year ago

What equation in slope-intercept form represents the line that passes through

gregori [183]

Answer:

So, equation in slope-intercept form that represents the line that passes through the points (1,3) and (2,5) is y=2x+1

Step-by-step explanation:

We need to write equation in slope intercept form that represents the line that passes through the points (1,3) and (2,5)

The standard equation of slope-intercept form is: y= mx+b

where m is the slope of the lines and b is the y-intercept.

To make the equation we need to find slope (m) and y-intercept (b)

Find Slope

The formula to find slope m is: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

We have $x_{1}=1, x_{2}=2, y_{1}=3\ and \ y_{2}=5$

Putting values in the formula to find slope

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{5-3}{2-1}\\m=\frac{2}{1}\\m=2$

So, value of slope m is m=2

Find y-intercept

Using formula of slope-intercept formula we can find b

y=mx+b

Using point (1,3) (where x=1 ,y=3) and slope m=2

$3=2(1)+b\\3=2+b\\b=3-2\\b=1$

So, value of y-intercept b is: b=1

Required equation in Slope Intercept Form

We have slope m = 2 and y-intercept b=1

$y=mx+b\\y=2x+1$

So, equation in slope-intercept form that represents the line that passes through the points (1,3) and (2,5) is y=2x+1

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3 years ago