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3 years ago

Find the lateral surface area of the following cylinder

Mathematics

2 answers:

Tpy6a [65]3 years ago

6 0

Answer:

50 pi cm^2

Step-by-step explanation:

the lateral surface area of a cylinder = 2×pi×r×h

from the values given: 2×pi×5×5

=50pi

andriy [413]3 years ago

6 0

Answer:

Lateral surface area= 50π cm²

Step-by-step explanation:

The radius of the cylinder = r = 5 cm

The height of the cylinder = h = 5 cm

Lateral surface area of a cylinder is given by the formula: 2πrh

= $2\times\pi\times r\times h = 2\times\pi\times 5\times 5=50\pi cm^{2}$

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Simplify the given expression 8x^2-8/ x / 8(x^2 + 8)/26x^2 - 31x

notsponge [240]

Answer:

-x • (x2 - 208x + 814)

——————————————————————

Step-by-step explanation:

Step 1 :

x2 + 8

Simplify ——————

Polynomial Roots Calculator :

Find roots (zeroes) of : F(x) = x2 + 8

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is 8.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,4 ,8

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 9.00

-2 1 -2.00 12.00

-4 1 -4.00 24.00

-8 1 -8.00 72.00

1 1 1.00 9.00

2 1 2.00 12.00

4 1 4.00 24.00

8 1 8.00 72.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step 1 :

8 (x2+8)

((8•(x2))-((— ÷ 8•——————)•x2))-31x

x 26

Simplify —

Equation at the end of step 2 :

8 (x2+8)

((8•(x2))-((— ÷ 8•——————)•x2))-31x

x 26

Divide — by 8

1 (x2+8)

((8•(x2))-((—•——————)•x2))-31x

x 26

Equation at the end of step 4 :

(x2 + 8)

((8 • (x2)) - (———————— • x2)) - 31x

26x

Dividing exponential expressions :

x2 divided by x1 = x(2 - 1) = x1 = x

Equation at the end of step 5 :

x • (x2 + 8)

((8 • (x2)) - ————————————) - 31x

Equation at the end of step 6 :

x • (x2 + 8)

(23x2 - ————————————) - 31x

Rewriting the whole as an Equivalent Fraction :

Subtracting a fraction from a whole

Rewrite the whole as a fraction using 26 as the denominator :

23x2 23x2 • 26

23x2 = ———— = —————————

1 26

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

23x2 • 26 - (x • (x2+8)) -x3 + 208x2 - 8x

———————————————————————— = ————————————————

26 26

Equation at the end of step 7 :

(-x3 + 208x2 - 8x)

—————————————————— - 31x

Rewriting the whole as an Equivalent Fraction :

Subtracting a whole from a fraction

Rewrite the whole as a fraction using 26 as the denominator :

31x 31x • 26

31x = ——— = ————————

1 26

Pulling out like terms :

Pull out like factors :

-x3 + 208x2 - 8x = -x • (x2 - 208x + 8)

Trying to factor by splitting the middle term

Factoring x2 - 208x + 8

The first term is, x2 its coefficient is 1 .

The middle term is, -208x its coefficient is -208 .

The last term, "the constant", is +8

Multiply the coefficient of the first term by the constant 1 • 8 = 8

Find two factors of 8 whose sum equals the coefficient of the middle term, which is -208 .

-8 + -1 = -9

-4 + -2 = -6

-2 + -4 = -6

-1 + -8 = -9

1 + 8 = 9

2 + 4 = 6

4 + 2 = 6

8 + 1 = 9

Adding fractions that have a common denominator : Adding up the two equivalent fractions

-x • (x2-208x+8) - (31x • 26) -x3 + 208x2 - 814x

————————————————————————————— = ——————————————————

26 26

Pulling out like terms :

10.1 Pull out like factors :

-x3 + 208x2 - 814x = -x • (x2 - 208x + 814)

Trying to factor by splitting the middle term

10.2 Factoring x2 - 208x + 814

The first term is, x2 its coefficient is 1 .

The middle term is, -208x its coefficient is -208 .

The last term, "the constant", is +814

Multiply the coefficient of the first term by the constant 1 • 814 = 814

Find two factors of 814 whose sum equals the coefficient of the middle term, which is -208 .

-814 + -1 = -815

-407 + -2 = -409

-74 + -11 = -85

-37 + -22 = -59

-22 + -37 = -59

-11 + -74 = -85

-2 + -407 = -409

-1 + -814 = -815

1 + 814 = 815

2 + 407 = 409

11 + 74 = 85

22 + 37 = 59

37 + 22 = 59

74 + 11 = 85

407 + 2 = 409

814 + 1 = 815

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3 years ago

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Dima020 [189]

Is not a good one...because there is not enough people...it doesn't represent all of the customers

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4 years ago

Mrs burgoon put 3rd graders are tables in groups of 6 at the science conference.if there were 22 tables how many students were t

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7 0

3 years ago

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5x minus 4 equals x squared minus 4x plus 4. What is x

Sauron [17]

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((0 - 5x2) - 4x) - 4 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

-5x2 - 4x - 4 = -1 • (5x2 + 4x + 4)

Trying to factor by splitting the middle term

3.2 Factoring 5x2 + 4x + 4

The first term is, 5x2 its coefficient is 5 .

The middle term is, +4x its coefficient is 4 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 5 • 4 = 20

Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 4 .

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 3 :

-5x2 - 4x - 4 = 0

Step 4 :

Parabola, Finding the Vertex :

4.1 Find the Vertex of y = -5x2-4x-4

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -0.4000

Plugging into the parabola formula -0.4000 for x we can calculate the y -coordinate :

y = -5.0 * -0.40 * -0.40 - 4.0 * -0.40 - 4.0

or y = -3.200

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = -5x2-4x-4

Axis of Symmetry (dashed) {x}={-0.40}

Vertex at {x,y} = {-0.40,-3.20}

Function has no real roots

Solve Quadratic Equation by Completing The Square

4.2 Solving -5x2-4x-4 = 0 by Completing The Square .

Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:

5x2+4x+4 = 0 Divide both sides of the equation by 5 to have 1 as the coefficient of the first term :

x2+(4/5)x+(4/5) = 0

Subtract 4/5 from both side of the equation :

x2+(4/5)x = -4/5

Add 4/25 to both sides of the equation :

On the right hand side we have :

-4/5 + 4/25 The common denominator of the two fractions is 25 Adding (-20/25)+(4/25) gives -16/25

So adding to both sides we finally get :

x2+(4/5)x+(4/25) = -16/25

Adding 4/25 has completed the left hand side into a perfect square :

x2+(4/5)x+(4/25) =

(x+(2/5)) • (x+(2/5)) =

(x+(2/5))2

Things which are equal to the same thing are also equal to one another. Since

x2+(4/5)x+(4/25) = -16/25 and

x2+(4/5)x+(4/25) = (x+(2/5))2

then, according to the law of transitivity,

(x+(2/5))2 = -16/25

Note that the square root of

(x+(2/5))2 is

(x+(2/5))2/2 =

(x+(2/5))1 =

x+(2/5)

Now, applying the Square Root Principle to Eq. #4.2.1 we get:

x+(2/5) = √ -16/25

Subtract 2/5 from both sides to obtain:

x = -2/5 + √ -16/25

Since a square root has two values, one positive and the other negative

x2 + (4/5)x + (4/5) = 0

has two solutions:

x = -2/5 + √ 16/25 • i

x = -2/5 - √ 16/25 • i

Note that √ 16/25 can be written as

√ 16 / √ 25 which is 4 / 5

Solve Quadratic Equation using the Quadratic Formula

4.3 Solving -5x2-4x-4 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = -5

B = -4

C = -4

Accordingly, B2 - 4AC =

16 - 80 =

-64

Applying the quadratic formula :

4 ± √ -64

x = —————

-10

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)

Both i and -i are the square roots of minus 1

Accordingly,√ -64 =

√ 64 • (-1) =

√ 64 • √ -1 =

± √ 64 • i

Can √ 64 be simplified ?

Yes! The prime factorization of 64 is

2•2•2•2•2•2

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 64 = √ 2•2•2•2•2•2 =2•2•2•√ 1 =

± 8 • √ 1 =

± 8

So now we are looking at:

x = ( 4 ± 8i ) / -10

Two imaginary solutions :

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

or:

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

hope i helped

-Rin:)

6 0

3 years ago

Read 2 more answers

What is the mean? {38, 21, 64, 59, 21, 12, 13, 66, 55, 21}

pogonyaev

Answer:

Step-by-step explanation:

Add all the numbers up and you will get 370. How many numbers are there in total? 10 right so you divide 370 with 10 and get 37.

hope this help

5 0

3 years ago

Read 2 more answers