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aksik [14]
3 years ago
10

Find the diameter, approximate circumference and area of the circle below. (Use 3 for π)

Mathematics
2 answers:
vovikov84 [41]3 years ago
5 0

Answer:

Circumference = 42

Area = 147 to the power of 2

Step-by-step explanation:

7x2=14 diameter

3x14=42 circumference

Area = 7x7x3 =147 to the power of 2

seraphim [82]3 years ago
4 0
Diameter=14
Circumference =43.98
Area=153.94
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2 years ago
Does anyone know this
Arturiano [62]

Answer:

C

Step-by-step explanation:

Option C is the correct answer.

8 0
3 years ago
Find the volume of the wedge with vertices at points (0,0,0), (1,0,0), (0,1,0), (0,0,1) by integrating the area of cross-section
Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

V = \int\limits^b_a {S(x)} \, dx          (1)

V = volume of the solid bounded by x = a and x = b

S(x) = cross section area of the solid, perpendicular to the x axis

From the figure we have that S is the area of a triangle that has base Z and height Y

Area of the triangle = S(x)=\frac{y(x)*z(x)}{2}          (2)

Calculation of y(x) and z(x)

We apply the equation of the point-slope line (plane xy):

Slope = m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}          (3)

Equation of the line = y - y_{1} =m(x-x_{1} )          (4)

Replacing the points (1,0) and (0,1) in (3):

m=\frac{1-0}{0-1} =-1

Replacing the point (1,0) and m = -1 in (4):

y-0=(-1)(x-1)

y(x) = -x + 1 (Line A-B)          (5)

We apply the equation of the point-slope line (plane xz):

Slope = m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}          (6)

Equation of the line = z - z_{1} =m(x-x_{1} )          (7)

Replacing the points (1,0) and (0,1) in (6):

m=\frac{1-0}{0-1} =-1

Replacing the point (1,0) and m = -1 in (7):

z-0=(-1)(x-1)

z(x) = -x + 1 (Line A-C)        (8)

Replacing (5) and (8) in (2)

S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}          (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx

V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)  evaluated from x=0 to x=1

V= \frac{1}{2} (\frac{1}{3} -1 +1) = \frac{1}{6}

3 0
3 years ago
At what point on the parabola y = 3x^2 + 2x is the tangent line parallel to the line<br> y = 10x −2?
oksian1 [2.3K]

Answer:

( \frac{4}{3} , 8 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 10x - 2 ← is in slope- intercept form

with slope m = 10

Parallel lines have equal slopes

then the tangent to the parabola with a slope of 10 is required.

the slope of the tangent at any point on the parabola is \frac{dy}{dx}

differentiate each term using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1} , then

\frac{dy}{dx} = 6x + 2

equating this to 10 gives

6x + 2 = 10 ( subtract 2 from both sides )

6x = 8 ( divide both sides by 6 )

x = \frac{8}{6} = \frac{4}{3}

substitute this value into the equation of the parabola for corresponding y- coordinate.

y = 3(\frac{4}{3} )² + 2

   = (3 × \frac{16}{9} ) + 2

   = \frac{16}{3} + \frac{8}{3}

   = \frac{24}{3}

   = 8

the point on the parabola with tangent parallel to y = 10x - 2 is ( \frac{4}{3} , 8 )

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2 years ago
What is the relationship between 1.0 and 0.1
dexar [7]
1/10×1.0=0.1

answer: C
5 0
3 years ago
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