Answer:
1526.8 ft ^3
Step-by-step explanation:
the volume of a cylinder formula is V=π x r^2 x h
= pi x 9^2 x 6
= pi x 81 x 6
=1526.8 ft ^3
Answer:
1/6
Step-by-step explanation:
Given:
- Length of the trough: 9 ft
=> The volume of the trough: V =
* (b * h) (1)
- An isosceles right triangle with hypotenuse 2 feet
=> the other two sides of the triangle is:
= tan(45 degrees) = h/(b/2)
<=> b = 2h substitute in (1), we have:
V = *(2h *h) = 9
Take derivative of volume with respect to time to find equation for rate of filling the trough
dV/dt = 2 * 9 *h dh/dt = 18h dh/dt
<=> dh/dt = dV/dt /(18h)
As we know that, dV/dt = 2
So, dh/dt = 2 / 18h = 1/9h
<=> V = t * rate = 2 * 2 = 4
But V = 9
<=> 9 = 4
<=> h = 2/3
The rate is the height h feet of the water in the trough changing 2 minutes after the water begins to flow:
dh/dt = 1/(9h) = 1/(9 * 2/3) = 1/6
Answer:
Step-by-step explanation:
Two angles that are adjacent (share a leg) and supplementary (add up to 180°)
Given tan g = 5/12, find cos g:
5
tan g = ———
12
The tangent function is, by definition, the quotient between sine and cosine:
sin g 5
———— = ———
cos g 12
Product of them extremes = product of the means
12 · sin g = 5 · cos g
Square both sides:
(12 · sin g)² = (5 · cos g)²
12² · sin² g = 5² · cos² g
144 · sin² g = 25 · cos² g
But sin² g = 1 – cos² g. Substitute it for sin² g into the equation above, and you have
144 · (1 – cos² g) = 25 · cos² g
Multiply out the brackets, and then isolate cos² g:
144 – 144 · cos² g = 25 · cos² g
144 = 25 · cos² g + 144 · cos² g
144 = 169 · cos² g
Divide both sides by 169:
144
cos² g = ———
169
12²
cos² g = ———
13²
cos² g = (12/13)²
Now, take the square root of both sides:
cos g = ± √(12/13)²
12
cos g = ± ———
13
The sign of cos g depends on which quadrant the angle g lies. As tan g = 5/12, which is positive, then g lies either in the 1st or the 3rd quadrant:
• If g lies in the 1st quadrant, then
5
cos g > 0 ⇒ cos g = ——— ✔
13
• If g lies in the 3rd quadrant, then
5
cos g < 0 ⇒ cos g = – ——— ✔
13
I hope this helps. =)
Tags: <em>trigonometric relation tangent cosine sine tan cos sin trig trigonometry</em>
The two number that when added to the first number, give the second number, and when multiplied, give the second number are:
- a. 4 and 2
- b. 9 and -4
- c. -7 and 3
- d. 5 and 2
- e. -7 and -4
- f. 7 and 9
<h3>What numbers are required?</h3><h3 />
The question requires two numbers that can be added to get the first number and multiplied to get the second.
When 4 and 2 are multiplied, they get 8 and when added they get 6.
When 9 and -4 are added, they get 5 and when multiplied they get 36.
When -7 and 3 are multiplied, they get -21 and when added they get -4.
When 5 and 2 are added, they get 7 and when multiplied they get 10.
When -7 and -4 are multiplied, they get 28 and when added they get -11.
When 7 and 9 are added, they get 16 and when multiplied they get 63.
Find out more on number operations at brainly.com/question/1053492.
#SPJ1
