Answer:
since output value is paried with input value teh relationship IS a function
Step-by-step explanation:
<span>Exponent
is a number used to express shorter equation; it is a number that says how many
times you are going to multiply the base number.
</span><span>
Exponents have several laws, here are
some:
=> x^1 = x
=> x^0 = 1
=> x^-1 = 1/x
=> x^m x^n = X^m+n
=> x^m/x^n = x^m-n
And since we were asked to write an
expression with a negative exponent that has a value between 0 and ½
=> 2^ -2 = ½
</span>
Answer:
n is a positive integer and here 90, 91, 92, 93, 94 and 95 is 9⁰ = 1
9¹ = 9
9² = 81
9³ = 729
9⁴ = 6561
9⁵ = 59049
so mathematical induction is prove given below.
Step-by-step explanation:
9⁰ = 1
9¹ = 9
9² = 81
9³ = 729
9⁴ = 6561
9⁵ = 59049
lets us consider by P (n) for the base case n = 0 then 9⁰ = 1 So P (1) is true
k ≥ 1so consider all integers
1≤l≤ k
There is a need to prove P (k+1)
if k is odd
=
.9.
is 9 so
= 9 +10m
then
= 9 ( 9 + 10m)
=81 + 10 (9m)
so digit is 1 and k +1 is even
Let x =lenght, y = width, and z =height
<span>The volume of the box is equal to V = xyz </span>
<span>Subject to the surface area </span>
<span>S = 2xy + 2xz + 2yz = 64 </span>
<span>= 2(xy + xz + yz) </span>
<span>= 2[xy + x(64/xy) + y(64/xy)] </span>
<span>S(x,y)= 2(xy + 64/y + 64/x) </span>
<span>Then </span>
<span>Mx(x, y) = y = 64/x^2 </span>
<span>My(x, y) = x = 64/y^2 </span>
<span>y^2 = 64/x </span>
<span>(64/x^2)^2 = 64 </span>
<span>4096/x^4 = 64/x </span>
<span>x^3 = 4096/64 </span>
<span>x^3 = 64 </span>
<span>x = 4 </span>
<span>y = 64/x^2 </span>
<span>y = 4 </span>
<span>z= 64/yx </span>
<span>z= 64/16 </span>
<span>z = 4 </span>
<span>Therefor the dimensions are cube 4.</span>
H=height
y=number of years.
we have the next expresion:
h(y)=my+b
m=the slope of the line, in this case, the slope is equal to "18"; (18 cm/ year).
b=the initial heigth, in this case, the initial heigth is equal to "5" (5 cm).
Therefore, our expression will be:
h(y)=18y +5
answer: h(y)=18y+5
