Answer:
23.6 ft
Step-by-step explanation:
Sketch a right triangle representing this situation. The length of the hypotenuse is 26 ft and the angle of elevation from ground to top of ladder is 65°. The "opposite side" is the reach of the ladder, which we'll call x.
Then:
opp
- sin 65° = ----------
- 26 ft
or (26 ft)(sin 65°) = opp side = height off the ground of top of ladder.
Evaluating this, we get:
(26 ft)(0.906) = 23.56 ft, or, rounded off, 23.6 ft
The ladder reaches 23.6 ft up the side of the building.
Answer:
t=3.5 seconds
Step-by-step explanation:
Given
h(t) = −16t^2 + 111t + 0
h'(t)= -32t + 111
Maximum height occurs when h(t) = 0 and the ball begins to fall
h(t)= -32t + 111=0
-32t + 111=0
-32t=-111
Divide both sides by -32
t=3.46872
Approximately, t=3.5 seconds
Recall,
Maximum height occurs when h(t) = 0
h(t)= -32t + 111=0
= -32(3.46872)+111
= -110.99904+111
= 0.00096 ft
Categorical data may or may not have some logical order
while the values of a quantitative variable can be ordered and
measured.
Categorical data examples are: race, sex, age group, and
educational level
Quantitative data examples are: heights of players on a
football team; number of cars in each row of a parking lot
a) Colors of phone cover - quantitative
b) Weight of different phones - quantitative
c) Types of dogs - categorical
d) Temperatures in the U.S. cities - quantitative
We don't know which side your triangle is sitting on, so the 'height'
could be any one of three values.
Here are the two simple tools that tell you everything you want to
know about a 30°-60°-90° triangle. These are worth memorizing:
-- The side opposite the 30° angle is 1/2 of the hypotenuse.
-- The side opposite the 60° angle is 1/2 of the hypotenuse times √3 .
I memorized them exactly 60 years ago. They've been very useful,
and as far as I know, they haven't changed.
