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3 years ago

A right circular cylinder has a diameter of 16 mm and a height of 12 mm. what is the volume of the cylinder in terms of π?

2 answers:

8 0

Volume of the cylinder = hr²π

diameter = 2 × radius
16 = 2 × r
r = 16/2
r = 8 mm

V = hr²π
V = 12 × 8² × π
V = 12 × 64 × π
V = 768π mm³

Alina [70]3 years ago

4 0

V = π·r²·h
and D = 2·r => r = 16 : 2 = 8 mm

V = π·8²·12 = π·64·12 = 768 π mm³

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A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o

Drupady [299]

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

3 0

3 years ago

Please answer it now in two minutes

oksano4ka [1.4K]

Answer:

3.9

Step-by-step explanation:

Pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 1^2 = 4^2

a^2 + 1 = 16

a^2 = 15

a = sqrt(15)

a = 3.9

Answer a = 3.9 yards

3 0

2 years ago

Read 2 more answers

8090 [49]

Answer:

James bought 11 good tickets and 5 bad tickets.

Step-by-step explanation:

Given that:

Cost of each good ticket = $8

Cost of each bad ticket = $5

Total amount spent = $113

Total tickets bought = 16

Let,

x be the number of good tickets bought

y be the number of bad tickets bought

x+y=16 Eqn 1

8x+5y=113 Eqn 2

Multiplying Eqn 1 by 5

5(x+y=16)

5x+5y=80 Eqn 3

Subtracting Eqn 3 from Eqn 2

(8x+5y)-(5x+5y)=113-80

8x+5y-5x-5y=33

3x=33

Dividing both sides by 3

$\frac{3x}{3}=\frac{33}{3}\\x=11$

Putting x=11 in Eqn 1

11+y=16

y=16-11

y=5

Hence,

James bought 11 good tickets and 5 bad tickets.

3 0

2 years ago

Given the trinomial 2x*2 + 4x + 4, predict the type of solutions. a. Two rational solutions b. One rational solution c. Two irra

OverLord2011 [107]

Answer:

d. Two complex solutions

Step-by-step explanation:

We have been given a trinomial $2x^2+4x+4$ and we are supposed to predict the type of solutions of our given trinomial.

We will use discriminant formula to solve for our given problem.

$\text{Discriminant}=b^2-4ac$ , where,

$a =\text{Coefficient of }x^2$ ,

$b =\text{Coefficient of }x$ ,

$c =\text{Constant }$

Conclusion from the result of Discriminant are:

$D$

$D=0\text{ means one real zero with of multiplicity two}$

$D>0\text{ means two distinct zeroes}$

Upon substituting our given values in above formula we will get,

$\text{Discriminant}=4^2-4*2*4$

$\text{Discriminant}=16-32$

$\text{Discriminant}=-16$

Since our discriminant is less than zero, therefore, out given trinomial will have two complex solutions and option d is the correct choice.

3 0

3 years ago

Read 2 more answers

Solve x^3-7x^2+7x+15

ruslelena [56]

Step-by-step explanation:

\underline{\textsf{Given:}}

Given:

\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx

+7x

+7x−15

\underline{\textsf{To find:}}

To find:

\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx

+7x

+7x−15

\underline{\textsf{Solution:}}

Solution:

\textsf{Factor theorem:}Factor theorem:

\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}

(x−a)isafactorP(x)⟺P(a)=0

\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x

+7x

+7x−15

\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0

\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)

\mathsf{When\;x=-3}Whenx=−3

\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)

+7(−3)

+7(−3)−15

\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15

\mathsf{P(-3)=63-63}P(−3)=63−63

\mathsf{P(-3)=0}P(−3)=0

\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor

\mathsf{When\;x=-5}Whenx=−5

\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)

+7(−5)

+7(−5)−15

\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15

\mathsf{P(-5)=175-175}P(−5)=175−175

\mathsf{P(-5)=0}P(−5)=0

\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor

\underline{\textsf{Answer:}}

Answer:

\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x

+7x

+7x−15=(x−1)(x+3)(x+5)

\underline{\textsf{Find more:}}

Find more:

6 0

3 years ago