Answer:
See attached
Step-by-step explanation:
The graph of both f(x) and g(x) attached
g(x) obtained from f(x) by x→ 3x - 1 and y → y/2 transformation rule
The transformation to get g(x) would be:
f(x) is the blue graph
g(x) is the red graph
The area of the top surface of the washer is: 160.14 square mm.
<h2>Step-by-step explanation:</h2>The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)
Now, we know that the area of the annulus region is given by:
where R is the outer radius and r is the inner radius.
Here we have:
Hence, we have:
Answer:
Step-by-step explanation:
(a)
Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.
Let assume the length of the rectangle is 50;
Then, the breath can be calculated as follows:
= 50 × 5 = 250 ( since the breath is divided into 5 parallel sides)
The fencing is said to be 950 ft
So, 950 - 250 = 700
Then divided by 2, we get:
= 700/2
= 350
So for the first diagram; the length = 50 and the breath = 350
The area = 50 × 350 = 17500 ft²
Now, let's go up a little bit.
If the length increase to 100;
Then 100 × 5 = 500
⇒ 950 - 500 = 450
⇒ 450/2 = 225
The area = 225 × 100 = 22500 ft²
Suppose the length increases to 150
Then 150 × 5 = 750
⇒ 950 - 750 = 200
⇒ 200/2 = 100
The area = 150 × 100 = 15000 ft²
The diagrams for each of the outline above can be seen in the image attached below.
(b) The diagram illustrating the general solution can be seen in the second image provided below.
(c) The expression for the total area A in terms of both x and y is:
Area A = x×y
(d) Recall that:
The fencing is said to be 950 ft.
And the length is divided inside into 5 parallel sides;
Then:
5x + 2y = 950 (from the illustration in the second image below)
2y = 950 - 5x
(e)
From (c); replace the value of y in (d) into (c)
Then:
Area A = x×y
Open brackets
(f)
By differentiating what we have in (e)
x = 475/5
x = 95
From (d):
∴
Area A = x × y
Area A = 95 × 237.5
Area A = 22562.5 ft²
so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.
Answer:
<h2>See the explanation.</h2>Step-by-step explanation:
a.
The initial length of the candle is 16 inch. It also given that, it burns with a constant rate of 0.8 inch per hour.
After one hour since the candle was lit, the length of the candle will be (16 - 0.8) = 15.2 inch.
After two hour since the candle was lit, the length of the candle will be (15.2 - 0.8) = 14.4 inch. The length of the candle after two hours can also be represented by {16 - 2(0.8)}.
Hence, the length of the candle after t hours when it was lit can be represented by the function, .
at t = 20.
b.
The domain of the function is 0 to 20.
c.
The range is 0 to 16.