What is the probability of rolling an even number and then an odd number when rolling two number cubes?
2 answers:
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9514 1404 393
Answer:
-10
Step-by-step explanation:
The first step is to write what you mean. We think you mean (-1000)^(1/3).
If you've been paying attention to place-value, and/or cubes of small integers, you already know that 10^3 = 1000. Since we're concerned with an odd power, we also know ...
-1000 = (-10)^3
Then your expression is ...
(-1000)^(1/3) = ((-10)^3)^(1/3) = (-10)^(3/3) = (-10)^1 = -10
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Some calculators can evaluate this for you (see attached).
Some calculators and spreadsheets use logarithms to compute roots or fractional powers, so will give you an error when you try to compute this. You should know that an odd-index root of a negative number (here, 3rd root of -1000) has the same sign as the number: negative. Then you can use your calculator to compute the positive root and add the sign yourself:
(-1000)^(1/3) = -(1000^(1/3)) = -(10) = -10
_____
Of course, a 1/3 power is the same as a cube root. Your calculator may have a cube root button that works just fine with negative numbers.
First set up equation
x times y=xy
so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so
if
ax+bx+c=0 then x=
that means x=
or x=
so
x^2-x-29
a=1
b=-1
c=-29
=![\frac{ +1-\sqrt{1^2-(-116)} }{2(1)}=\frac{ +1-\sqrt{1^2+116} }{2}=\frac{ +1-\sqrt{117} }{2}= \frac{1-10.816653826392}{2} = [tex] \frac{-9.816653826392}{2}= -4.908326913196](https://tex.z-dn.net/?f=%5Cfrac%7B%20%2B1-%5Csqrt%7B1%5E2-%28-116%29%7D%20%7D%7B2%281%29%7D%3D%5Cfrac%7B%20%2B1-%5Csqrt%7B1%5E2%2B116%7D%20%7D%7B2%7D%3D%5Cfrac%7B%20%2B1-%5Csqrt%7B117%7D%20%7D%7B2%7D%3D%20%5Cfrac%7B1-10.816653826392%7D%7B2%7D%20%3D%20%5Btex%5D%20%5Cfrac%7B-9.816653826392%7D%7B2%7D%3D%20-4.908326913196)
the second number is
the two numbers are
5.908326913196 and
-4.908326913196
x times y=xy
so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so
if
ax+bx+c=0 then x=
x^2-x-29
a=1
b=-1
c=-29
the second number is
the two numbers are
5.908326913196 and
-4.908326913196