Differentiating the function
... g(x) = 5^(1+x)
we get
... g'(x) = ln(5)·5^(1+x)
Then the linear approximation near x=0 is
... y = g'(0)(x - 0) + g(0)
... y = 5·ln(5)·x + 5
With numbers filled in, this is
... y ≈ 8.047x + 5 . . . . . linear approximation to g(x)
Using this to find approximate values for 5^0.95 and 5^1.1, we can fill in x=-0.05 and x=0.1 to get
... 5^0.95 ≈ 8.047·(-0.05) +5 ≈ 4.598 . . . . approximation to 5^0.95
... 5^1.1 ≈ 8.047·0.1 +5 ≈ 5.805 . . . . approximation to 5^1.1
Answer:
The area of the wall that she will paint in two rolls is <u>219.8 inches²</u>.
Step-by-step explanation:
Given:
Jenny uses a roller to paint a wall. The roller has a radius of 1.75 inches and a height of 10 inches.
Now, to find the area of the wall that she will paint in two rolls.
So, we find the lateral surface area of roller.
Radius (r) = 1.75 inches.
Height (h) = 10 inches.
So, to get the lateral surface area we put formula:
Thus, the lateral surface area of the roller = 109.9 inches².
Now, to get the area of wall that she will paint in two rolls we multiply 2 by the lateral surface area of the roller:
Therefore, the area of the wall that she will paint in two rolls is 219.8 inches².
Answer:
Height should be ≤ 9 inches.
Step-by-step explanation:
Given:
Frank is making a pennant in the shape of a triangle for his senior class photo.
Base of triangle = 6 in
Area of triangle ≤ 27
Let height of the triangle be h
Now we now that,
Area of triangle =
Hence the height of the triangle must be at most or ≤ 9 inches.