Answer:
We conclude that it would take 4.5 minutes to fill the full barrel.
Step-by-step explanation:
It is stated that it took 3/4 of a minute to fill a barrel 1/6 full of water.
- It means if it took 0.75 minutes to fill the 1 part out of 6 parts.
It is conditioned that the water continues at the same rate.
so
Total parts of a barrel = 6
It takes 0.75 minutes to fill the 1 part of a barrel
Thus, multiply 0.75 by 6 will determine the total time in minutes to fill all the 6 parts of a barrel (or a full barrel).
i.e.
0.75 × 6 = 4.5 minutes.
Therefore, we conclude that it would take 4.5 minutes to fill the full barrel.
Step-by-step explanation:
step 1. A geometric sequence is found by multiplying subsequent term by a number r.
step 2. 106.8/178 = 0.6. 64.08/106.8 = 0.6. a = 0.6. note that a geometric series must have the same number when dividing successive terms.
step 3. an = ar^(n - 1) = a(0.6)^(n - 1)
step 4. given a1 = 178. an = 178(0.6)^(n - 1)
step 5. therefore a11 is the 11th term!
step 6. a11 = 178(0.6)^10 = 1.0763 = 1.08.
Answer:
Rotated 180 degrees.
Step-by-step explanation:
Part A)<span>In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
we know that
</span>cos 45°=√2/2
[he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2
=22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) <span>What is the exact value of sin 45° ?
</span>
we know that
sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2
the answer part b) is √2/2
Part C)
<span>What is the area of a regular hexagon with a side length of 4 m?
we know that
</span>In case of a regular hexagon <span> each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m.
The area of this hexagon is six times greater than the area of such a triangle
</span>
In an equilateral triangle with a side d<span>
the altitude </span>h can be calculate from the Pythagorean Theorem as
h²=d²−(d/2)²=(3/4)d²
<span>Therefore,
</span><span>h=d<span>√3/2
</span></span><span>Area of such a triangle is
</span>A=d*h/2------------> d²*√3/4
From this the area of the regular hexagon with a side d<span> is
</span>S=6*A----------> d²3√3/2
for d=4 m
S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) <span>In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
</span>[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
the answer part D) is 10 cm
Answer:
816.514 greater than 86.684
Step-by-step explanation:
