If the ratio is 5/8, or 8/5
Tobias picked five daisies and eight roses.
For every eight shots, Micah made five baskets.
If the ratio is 5/13, or 13/5
Sally found five green fruit loops in her cereal bowl, out of every thirteen pieces.
If the ratio is 8/3, or 3/8
Aly painted eight trees for every three birds.
Answer:
a = 1 b = -1.
Step-by-step explanation:
Suppose the quotient when you divide x^4+x^3+ax+b by x^2 + 1 is
x^2 + ax + b then expanding we have:
(x^2 + 1)(x^2 + ax + b)
= x^4 + ax^3 + bx^2 + x^2 + ax + b
= x^4 + ax^3 + (b + 1)x^2 + ax + b Comparing this with the original expression:
x^4 + x^3 + 0 x^2 + ax + b Comparing coefficients:
a = 1 and b+ 1 = 0 so b = -1.
Answer:
So we have 3 pounds of apples. 3 pounds= 6 dollars. This means for 1 pound, it costs 2 dollars. So since 1 pound is 2 dollars, take 10 pounds and multiply it by 2, you get 20 dollars. So the cost of 10 pounds is 20 dollars. If you wanna do it the short way, the cost is always twice the amount of the pounds.
Answer:
-1
Step-by-step explanation:
The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.
d(log(x))/dx = 1/(x·ln(10))
d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))
Then the ratio of these derivatives is ...
lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x
__
At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.
d(-sin(x)cos(x))/dx = -cos(2x)
dx/dx = 1
so the limit is ...
lim = -cos(2x)/1
lim = -1 when evaluated at x=0.
_____
I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.
Answer:
21 small dogs, 42 total dogs
Step-by-step explanation:
7×3=21
7+7=14
14×3=42
