Calculus

1 milliliter equals one cubic centimeter.

the volume of a trapezoidal prism is equal to the height times the base area of the trapezoid.

First you find the area of trapezoid h(a+b)/2

h is the height of the trapezoid, not the height of the prism

a is the length of the top

b is the length of the bottom

Then you find the volume of the trapezoidal prism with this formula H*h(a+b)/2

H is the height of the prism.

Multiply H by the area of the trapezoid that you found in step one.

2z - 5 = 11

Add 5 to both sides: 2z = 16

Divide both sides by 2: z = 8

x2 - 2x = x(x-2) and that cannot be simplified further.

If you count one number per second, and never stop to sleep or eat or anything, it will take over 31 years.

The taper angle is the angle where a thread is tapered as it is created. The formula to find it is to subtract the small diameter from the large diameter and multiply by 28, then divide by the length of the taper.

87,600,000

54,360,000,000.

(1-cosx)/sinx + sinx/(1- cosx)

= [(1 - cosx)*(1 - cosx) + sinx*sinx]/[sinx*(1-cosx)]

= [1 - 2cosx + cos2x + sin2x]/[sinx*(1-cosx)]

= [2 - 2cosx]/[sinx*(1-cosx)]

= [2*(1-cosx)]/[sinx*(1-cosx)]

= 2/sinx

= 2cosecx

2.5

3307.2

The question concerns a cubic (order 3) divided by a binomial (order 1) and so the quotient has order 3 - 1 = 2 and the remainder has order 0 (one less than the denominator).

That is

(2*x^3 + 5*x^2 - 14*x + 3)/(2*x - 3) = A*x^2 + B*x + C + D/(2*x - 3)

Multiplying both sides by 2x - 3 gives

2*x^3 + 5*x^2 - 14*x + 3 = 2A*x^3 - 3A*X^2 + 2B*x^2 - 3B*x + 2C*x - 3C + D

Compare coefficients of x^3: 2 = 2A => A = 1

Compare coefficients of x^2: 5 = -3A + 2B = -3 + 2B => 2B = 8 => B = 4

Compare coefficients of x^1: -14 = -3B + 2C = -12 + 2C => 2C = -2 => C = -1

Compare coefficients of x^0: 3 = -3C + 2D = 3 + 2D => 2D = 0 => D = 0

So, The quotient is (x^2 + 4 x - 1) and the remainder is 0.

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Alternatively you can do the long division by considering the coefficients of the largest power of x - ie dividing the largest power of x (left in the dividend) by 2x (the largest power of x in the divisor) and using that as the value to add into the quotient and to multiply the divisor by before subtracting it (as in a normal long division):

_______________ x² + _4x - 1

_______--------------------------

2x - 3 | 2x³ + 5x² - 14x + 3 ___ ← 2x³ ÷ 2x = x²; put "x²" in quotient

________ 2x³ - 3x² ______________ ←(2x - 3) × x² and subtract

________ ------------

______________ 8x² - 14x ________ ← bring down "- 14x"; 8x² ÷ 2x = 4x; put "+ 4x" in quotient

______________ 8x² - 12x ________ ← (2x - 3) × 4x and subtract

______________ ------------

____________________ -2x + 3 _____ ← bring down "+ 3"; -2x ÷ 2x = -1; put "- 1" in quotient

____________________ -2x + 3 _____ ← (2x - 3) × -1 and subtract

_____________________ ---------

__________________________ 0 _____ ← nothing to bring down, result is 0, so no remainder

(The underscores in the diagram are to help align the workings.)

→ (2x³ + 5x² - 14x + 3) ÷ (2x - 3) = x² + 4x - 1

The reading could be too high or too low.

4 x 12 - 45 + 8

= 48 - 45 + 8

= 3 + 8

= 11

-1

60-2x = 70-4x

60-2x+2x = 70-4x+2x

60 = 70 +2x

60-70 = 70 + 2x - 70

-10 = 2x

x = -10/2 = -5

1000

7.5% of $10 million = $750,000.00

We want to answer the equation 10x = 350

This can be done by dividing both sides by 10. That makes the equation x = 35.

Thus the value of x that makes 10x=350 is 35.

y = 1.5x.

y intercept = 0.

1545

negative four times two = ......

5.21564 feet

It is not possible to prove something that is not true. The square of 2 is rational, not irrational.