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Anit [1.1K]
3 years ago
8

A painter is asked to paint the exterior of a dome, excluding the bottom, which has a diameter of 9 ft. The painter already has

one gallon of paint which will cover 105 ft2.
How much more paint will the painter have to purchase to complete the job with the least amount of waste, calculated with a precision of 0.00?

Mathematics
1 answer:
astraxan [27]3 years ago
3 0
Area of the dome is given by:
A=1/2(4πr²)=2πr²
thus:
A=2×3.14×(9/2)²
A=127.17 ft²
Thus the remaining area to be painted will be:
127.17-105
=22.17 ft²

Amount of paint required will be:
22.17/105*1=0.211 gallons
Thus the best approximation is:

A] 1 quart covers 26.25 ft²
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What set of reflections and rotations would carry rectangle ABCD onto itself? Parallelogram formed by ordered pairs A at negativ
Hoochie [10]

Answer:

Option (4).

Step-by-step explanation:

Let's take the coordinates of point A for the set of reflections and rotations given in the options.

Option (1). Rotate 180° → A(-4, 1) becomes (4, -1)

                Reflect over x-axis → (4, -1) becomes (4, 1)

                Reflect over the line y = x → (4, 1) becomes A'(1, 4)

Therefore, point A will not overlap itself after the number of transformations given.

Option (2). Reflect across x-axis → A(-4, 1) will become (-4, -1)

                  Rotate 180° → (-4, -1) becomes (4, 1)

                  Reflect over the x-axis → (4, 1) becomes A'(4, -1)

Therefore, point A(-4, 1) doesn't overlap A'(4, -1).

Option (3). Rotate 180° → A(4, 1) becomes (-4, -1)

                  Reflect over the y-axis → (-4, -1) becomes (4, -1)

                  Reflected over y = x → (4, -1) becomes (-1, 4)

So the point A(4, 1) becomes A'(-1, 4) after the set of reflections,

Option (4). Reflect over the y axis → A(-4, 1) becomes (4, 1)

                 Reflect over the x-axis → (4, 1) becomes (4, -1)

                 Rotate 180° → (4, -1) becomes A'(-4, 1)

Therefore, point A will overlap itself following the set of transformations.

6 0
3 years ago
The equation of the line that contains diagonal HM is y = 2/3 x + 7.
nirvana33 [79]

Answer:

The slope of the line that contains diagonal OE will be = -3/2

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

Where m is the slope and b is the y-intercept

Given the equation of the line that contains diagonal HM is y = 2/3 x + 7

y = 2/3 x + 7

comparing the equation with the slope-intercept form of the line equation

y = mx+b

Thus, slope = m = 2/3

  • We know that the diagonals are perpendicular bisectors of each other.

As we have to determine the slope of the line that contains diagonal OE.

As the slope of the line that contains diagonal HM = 2/3

We also know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line that contains diagonal

OE will be = -1/m = -1/(2/3) = -3/2

Hence, the slope of the line that contains diagonal OE will be = -3/2

3 0
2 years ago
can someone explain it to me, i don't need the answer, i just need an detailed explanation of how they got the answer using the
zubka84 [21]

Answer:

Step-by-step explanation:

Good idea to review quadratic functions and the quadratic formula.

Quadratics have three coefficients:  ax² + bx + c, and the "discriminant" is defined as b²-4ac.  Please review these rules:

1) if the discriminant is +, the quadratic equation has two real, unequal roots.

2) if the disc. is 0, the equation has two real, equal root.

3) If the disc. is - , the equation has two complex roots.

Here a = 1, b  = -3 and c = 4.  Therefore the discriminant is (-3)²-4(1)(4), or

-7.  Rule 3) applies:  the equation has two complex roots, but no real ones.  Thus we know that the graph does not cross the x-axis.

Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful.  As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis.  Thus, y = x² - 3x + 4 is greater than 0 for all x.  The answer:  All real numbers.

4 0
3 years ago
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