What is the probability of rolling a 1 on a number cube And then a 4?

Jack crawled 4 ft and Christine crawled 3⁄4 the distance Jack crawled. If you add the distance they each crawled together, what

stepan [7]

Before going into the details of the problem, let us first write down the most important information required for solving this problem.
1 ft = 12 inches
The distance that was crawled by Jack = 4 ft
      = (4 * 12) inches
      = 48 inches
The distance crawled by Christine = 3/4 of the distance crawled by Jack
   = (3/4) * 48 inches
   = 3 * 12 inches
   = 36 inches
Then
The total distance crawled by the two children's = (48 + 36) inches
   = 84 inches
So Jack and Christine together crawled a distance of 84 inches.

8 0

3 years ago

Read 2 more answers

Binomial Theorem

Tatiana [17]

Answer:

$\frac{p^{4} x^{24}+6p^{2}q^{2}x^{12}+q^{4}+4p^{3}qx^{18}+4pq^{3}x^{6}}{x^{12} }$

Step-by-step explanation:

3 0

2 years ago

A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the

mezya [45]

Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring $\frac{8}{3}$ feet.

Mass= $m=\frac{W}{g}$

Mass= $m=\frac{16}{32}$

$g=32 ft/s^2$

Mass,m= $\frac{1}{2}$ Slug

By hook's law

$w=kx$

$16=\frac{8}{3} k$

$k=\frac{16\times 3}{8}=6 lb/ft$

$f(t)=10cos(3t)$

A damping force is numerically equal to 1/2 the instantaneous velocity

$\beta=\frac{1}{2}$

Equation of motion :

$m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)$

Using this equation

$\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)$

$\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)$

$\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)$

Auxillary equation

$m^2+m+12=0$

$m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}$

$m=\frac{-1\pmi\sqrt{47}}{2}$

$m_1=\frac{-1+i\sqrt{47}}{2}$

$m_2=\frac{-1-i\sqrt{47}}{2}$

Complementary function

$e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})$

To find the particular solution using undetermined coefficient method

$x_p(t)=Acos(3t)+Bsin(3t)$

$x'_p(t)=-3Asin(3t)+3Bcos(3t)$

$x''_p(t)=-9Acos(3t)-9sin(3t)$

This solution satisfied the equation therefore, substitute the values in the differential equation

$-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)$

$(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)$

Comparing on both sides

$3B+3A=20$

$3B-3A=0$

Adding both equation then, we get

$6B=20$

$B=\frac{20}{6}=\frac{10}{3}$

Substitute the value of B in any equation

$3A+10=20$

$3A=20-10=10$

$A=\frac{10}{3}$

Particular solution, $x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

Now, the general solution

$x(t)=e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

From initial condition

x(0)=2 ft

x'(0)=0

Substitute the values t=0 and x(0)=2

$2=c_1+\frac{10}{3}$

$2-\frac{10}{3}=c_1$

$c_1=\frac{-4}{3}$

$x'(t)=-\frac{1}{2}e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+e^{-\frac{t}{2}}(-c_1\frac{\sqrt{47}}{2}sin(\frac{\sqrt{47}t}{2})+\frac{\sqrt{47}}{2}c_2cos(\frac{\sqrt{47}t}{2})-10sin(3t)+10cos(3t)$

Substitute x'(0)=0

$0=-\frac{1}{2}\times c_1+10+\frac{\sqrt{47}}{2}c_2$

$\frac{\sqrt{47}}{2}c_2-\frac{1}{2}\times \frac{-4}{3}+10=0$

$\frac{\sqrt{47}}{2}c_2=-\frac{2}{3}-10=-\frac{32}{3}$

$c_2==-\frac{64}{3\sqrt{47}}$

Substitute the values then we get

$x(t)=e^{-\frac{t}{2}}(-\frac{4}{3}cos(\frac{\sqrt{47}t}{2})-\frac{64}{3\sqrt{47}}sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

8 0

3 years ago

How do you solve -3+r/3=-5

MAVERICK [17]

Answer:

r=-6

Step-by-step explanation:

Question: -3+r/3=-5

1) Multiply both sides of the equation by 3:

-9+r=-15

2) Add 9 to both sides:

r=-6

Footnotes:

1) In step 1 when I multiplied both sides of the equation by 3, don't forget you also have to multiply -3 by 3 because it is not part of the fraction (which is how I got -9)

7 0

2 years ago

F(x)=x^4-5x^2-6x-10 is divided by x-3

LiRa [457]

Answer:

Step-by-step explanation:

STEP

1

:

10

Simplify ——

x

Equation at the end of step

1

:

10

((((x4)-(5•(x2)))-6x)-——)-3

x

STEP

2

:

Equation at the end of step

2

:

10

((((x4) - 5x2) - 6x) - ——) - 3

x

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

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

x4 - 5x2 - 6x (x4 - 5x2 - 6x) • x

x4 - 5x2 - 6x = ————————————— = ———————————————————

1 x

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

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

x4 - 5x2 - 6x = x • (x3 - 5x - 6)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = x3 - 5x - 6

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 -6.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,3 ,6

Let us test ....

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

-1 1 -1.00 -2.00

-2 1 -2.00 -4.00

-3 1 -3.00 -18.00

-6 1 -6.00 -192.00

1 1 1.00 -10.00

2 1 2.00 -8.00

3 1 3.00 6.00

6 1 6.00 180.00

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3 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:

x • (x3-5x-6) • x - (10) x5 - 5x3 - 6x2 - 10

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

x x

Equation at the end of step

4

:

(x5 - 5x3 - 6x2 - 10)

————————————————————— - 3

x

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1 Subtracting a whole from a fraction

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

3 3 • x

3 = — = —————

1 x

Checking for a perfect cube :

5.2 x5 - 5x3 - 6x2 - 10 is not a perfect cube

Trying to factor by pulling out :

5.3 Factoring: x5 - 5x3 - 6x2 - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6x2 - 10

Group 2: x5 - 5x3

Pull out from each group separately :

Group 1: (3x2 + 5) • (-2)

Group 2: (x2 - 5) • (x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.4 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 10

See theory in step 4.2

In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Let us test ....

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

-1 1 -1.00 -12.00

-2 1 -2.00 -26.00

-5 1 -5.00 -2660.00

-10 1 -10.00 -95610.00

1 1 1.00 -20.00

2 1 2.00 -42.00

5 1 5.00 2340.00

10 1 10.00 94390.00

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.5 Adding up the two equivalent fractions

(x5-5x3-6x2-10) - (3 • x) x5 - 5x3 - 6x2 - 3x - 10

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

x x

Polynomial Roots Calculator :

5.6 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 3x - 10

See theory in step 4.2

In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,5 ,10

Let us test ....

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

-1 1 -1.00 -9.00

-2 1 -2.00 -20.00

-5 1 -5.00 -2645.00

-10 1 -10.00 -95580.00

1 1 1.00 -23.00

2 1 2.00 -48.00

5 1 5.00 2325.00

10 1 10.00 94360.00

Polynomial Roots Calculator found no rational roots

Final result :

x5 - 5x3 - 6x2 - 3x - 10

————————————————————————

x

3 0

3 years ago

What is the probability of rolling a 1 on a number cube And then a 4?​

What is the probability of rolling a 1 on a number cube And then a 4?