Answer:
The value of cos Ф is ±
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
∵ sin Ф =
∴ sin²Ф =
∴ sin²Ф =
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 -
∴ cos²Ф =
→ Take square root for both sides
∴ cos Ф = ±
∴ The value of cos Ф is ±
Answer:
7
Step-by-step explanation:
First, plug-in f(-3) into t in the function:
Second, multiply -2 and -3 to get 6:
⇒
Third, add 6 and 1 to get your answer:
⇒
See the attached picture.
The resulting box has a volume
because the volume of a box is the product of its width , length
, and height
.
You know right away from the factored form of that the zeroes are
. (zero product property)
Easy to plot by hand. You know the zeroes, and you can check the sign of for any values of
between these zeros to get an idea of what the graph of
looks like. See the second attached picture.
Here's what I mean by "check the sign" in case you don't follow. We know when
and
. So we pick some value of
between them, say
, and find that
which is positive, so will be positive for any other
between 0 and 8. Similarly we would find that
for
between 8 and 12, and so on.
It's impossible to answer this without knowing the volume of each marble...
Thomas wants , so you solve
While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions
but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.
The box's dimensions are ( in) x (
in) x (
in).
If , then
and
.
If , then
and
.
