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bonufazy [111]
3 years ago
15

A rectangle is inscribed with its base on the x -axis and its upper corners on the parabola

Mathematics
1 answer:
ahrayia [7]3 years ago
7 0
The area of a rectangle is given by A = length * width.
width of the given rectangle is x
height is y = 2 - x^2
Area = x(2 - x^2) = 2x - x^3
For area to be maximum, dA/dx = 0
dA/dx = 2 - 3x^2 = 0
3x^2 = 2
x^2 = 2/3
x = √(2/3)
y = 2 - (√(2/3))² = 2 - 2/3 = 4/3

Therefore, the required rectangle has a width of 2√(2/3) ≈ 1.63 and a height of 4/3 ≈ 1.33
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In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?
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Answer:

There is only one distinct triangle possible, with m∠N ≈ 33°.   i hope this helps :)

Step-by-step explanation:

In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?

There are no triangles possible.

There is only one distinct triangle possible, with m∠N ≈ 33°.

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There are two distinct triangles possible, with m∠N ≈ 33° or m∠N ≈ 147°.

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3 years ago
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Find the volume.<br> 15 points
Anton [14]

Answer:

the volume is 196

Step-by-step explanation:

17x8=136

6x10=60

136+60=196

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4 years ago
Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the tab
expeople1 [14]

<span>
You can write the equation in point-slope form, which has the format <em>y-y</em>subscript1=<em>m</em>(<em>x-x</em>subscript1), with <em>y</em>subscript1 and <em>x</em>subscript1 being the y and x coordinates for a point on the line, and <em>m</em> being the slope. </span>

<span /><span>Substitute a y and x coordinate into the equation so you have <em>y</em>-6=<em>m</em>(<em>x</em>-2)</span>

<span /><span><span>Then find the slope so you can replace <em>m</em>. The slope formula is <em />(<em>y</em>subscript2-<em>y</em>subscript1)/(<em>x</em>subscript2-<em>x</em>subscript1). </span><span>Substitute the coordinates in so you have <em>m</em>=(16-6)/(4-2), which simplifies to 10/2 and then 5.</span></span>

<span><span /></span><span>Now the equation is <em>y</em>-6=5(<em>x</em>-2)</span>

<span />If you want a different form, for example slope-intercept form, you can change it to that:

<span><em>y</em>-6=5(<em>x</em>-2)</span>

<span><em>y</em>=5x-4</span>

6 0
4 years ago
Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value.
dimaraw [331]

Answer:

4

Step-by-step explanation:

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5 0
2 years ago
Find the slope of the line passing through the points given below or state that the slope is undefined. Then indicate whether th
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QUESTION A

The given points are

(x_1,y_1)=(8,3) and (x_2,y_2)=(9,8)

The slope can be found using the formula;

m=\frac{y_2-y_1}{x_2-x_1}

We substitute the point to obtain;

m=\frac{8-3}{9-8}

This simplifies to

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QUESTION 2

A positive slope indicates a rising line

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A zero slope means the line is horizontal.

An undefined slope means the line is vertical.

The correct answer is

A. The line rises from left to right.

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3 years ago
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