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marshall27 [118]
3 years ago
15

The sum of three consecutive even integers is 36. Let x represent the least consecutive integer.

Mathematics
1 answer:
lubasha [3.4K]3 years ago
4 0
The integers are x, x + 2 and x + 4

x + x + 2 + x + 4 = 36
3x + 6 = 72
3x = 36 - 6 = 30
x = 30/3 = 10

The least numbers is 10
Therefore, the numbers are 10, 12 and 14
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What is the volume of the cylinder below?
Svetlanka [38]

now, let's recall Cavalieri's Principle, "solids with equal altitudes and cross-sectional areas at each height, have the same volume".

so, even though this cylinder is slanted, it has the same cross-sectional area as a cylinder that's straight-up, whose altitude is h = 5, and radius r = 4.


\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} h=5\\ r=4 \end{cases}\implies V=\pi (4)^2(5)\implies V=80\pi

6 0
3 years ago
stacy buys 3 cds in a set for $29.98. She save $6.44 by buying the set instead of buying the individual cds. if each cd costs th
Natalka [10]
29.98+ 6.44 = 36.42 (cost with out the discount)
36.42/3 = 12.14

Answer-
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4 0
3 years ago
Read 2 more answers
The line 5x – 5y = 2 intersects the curve x2y – 5x + y + 2 = 0 at
inna [77]

Answer:

(a) The coordinates of the points of intersection are (-2, -12/5), (2/5, 0), and (2, 8/5)

(b) The gradient of the curve at each point of intersection are;

Gradient at (-2, -12/5) = -0.92

Gradient at (2/5, 0) = 4.3

Gradient at (2, 8/5) = -0.28

Step-by-step explanation:

The equations of the lines are;

5·x - 5·y = 2......(1)

x²·y - 5·x + y + 2 = 0.......(2)

Making y the subject of equation (1) gives;

5·y = 5·x - 2

y = (5·x - 2)/5

Making y the subject of equation (2) gives;

y·(x² + 1) - 5·x + 2 = 0

y = (5·x - 2)/(x² + 1)

Therefore, at the point the two lines intersect their coordinates are equal thus we have;

y = (5·x - 2)/5 = y = (5·x - 2)/(x² + 1)

Which gives;

\dfrac{5 \cdot x - 2}{5} = \dfrac{5 \cdot x - 2}{x^2 + 1}

Therefore, 5 = x² + 1

x² = 5 - 1 = 4

x = √4 = 2

Which is an indication that the x-coordinate is equal to 2

The y-coordinate is therefore;

y = (5·x - 2)/5 = (5 × 2 - 2)/5 = 8/5

The coordinates of the points of intersection = (2, 8/5}

Cross multiplying the following equation

Substituting the value for y in equation (2) with (5·x - 2)/5 gives;

\dfrac{5 \cdot x^3 - 2 \cdot x^2 - 20 \cdot x + 8}{5} = 0

Therefore;

5·x³ - 2·x² - 20·x + 8 = 0

(x - 2)×(5·x² - b·x + c) = 5·x³ - 2·x² - 20·x + 8

Therefore, we have;

x²·b - 2·x·b -x·c + 2·c -5·x³ + 10·x²

5·x³ - 10·x² - x²·b + 2·x·b + x·c - 2·c = 5·x³ - 2·x² - 20·x + 8

∴ c = 8/(-2) = -4

2·b + c = - 20

b = -16/2 = -8

Therefore;

(x - 2)×(5·x² - b·x + c) = (x - 2)×(5·x² + 8·x - 4)

(x - 2)×(5·x² + 8·x - 4) = 0

5·x² + 8·x - 4 = 0

x² + 8/5·x - 4/5  = 0

(x + 4/5)² - (4/5)² - 4/5 = 0

(x + 4/5)² = 36/25

x + 4/5 = ±6/5

x = 6/5 - 4/5 = 2/5 or -6/5 - 4/5 = -2

Hence the three x-coordinates are

x = 2, x = - 2, and x = 2/5

The y-coordinates are derived from y = (5·x - 2)/5 as y = 8/5, y = -12/5, and y = y = 0

The coordinates of the points of intersection are (-2, -12/5), (2/5, 0), and (2, 8/5)

(b) The gradient of the curve, \dfrac{\mathrm{d} y}{\mathrm{d} x}, is given by the differentiation of the equation of the curve, x²·y - 5·x + y + 2 = 0 which is the same as y = (5·x - 2)/(x² + 1)

Therefore, we have;

\dfrac{\mathrm{d} y}{\mathrm{d} x}= \dfrac{\mathrm{d} \left (\dfrac{5 \cdot x - 2}{x^2 + 1}  \right )}{\mathrm{d} x} = \dfrac{5\cdot \left ( x^{2} +1\right )-\left ( 5\cdot x-2 \right )\cdot 2\cdot x}{\left (x^2 + 1 ^{2} \right )}.......(3)

Which gives by plugging in the value of x in the slope equation;

At x = -2, \dfrac{\mathrm{d} y}{\mathrm{d} x} = -0.92

At x = 2/5, \dfrac{\mathrm{d} y}{\mathrm{d} x} = 4.3

At x = 2, \dfrac{\mathrm{d} y}{\mathrm{d} x} = -0.28

Therefore;

Gradient at (-2, -12/5) = -0.92

Gradient at (2/5, 0) = 4.3

Gradient at (2, 8/5) = -0.28.

7 0
3 years ago
How would I solve for this radius?
Daniel [21]
The radius of a circleis part of the circumference formula: C = 2 pi r.
So we rearrange the formula: r = c/2 pi.
Now we have to figure out the circumference. If the outside of the circle is 12 cm for 17degrees, then17 degrees x what is 360 degrees? 360 divided by 17 is 21.2. So the 12 cm should be multiplied by 21.2, to give 254.1cm. This is our circumference.
Now we do r = 254/2 pi.
                   r = 40.46cm.
8 0
3 years ago
Find the area of the shaded region. Round to the nearest hundreth where necessary.
Jet001 [13]

Answer:

192.42 m²

Step-by-step explanation:

big circle

10.5 ² x   pi =346.3605

inner circle

 7 ² x pi = 153.9380

346.3605 -  153.9380 = 192.4225   (192.42)

3 0
3 years ago
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