Sketch the curve y = \sqrt{x+3} .
1 answer:
The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
<h3>How to determine the area bounded by the curve, x-axis and y-axis?</h3>The curve is given as:
y = √(x + 3)
The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0
When y = 0, we have:
0 = √(x + 3)
This gives
x = -3
So, we set up the following integral
A = ∫ f(x) d(x) (Interval a to b)
This gives
A = ∫ √(x + 3) d(x) (Interval -3 to 0)
When the above is integrated, we have:
A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)
Expand
A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]
This gives
A = 1/3 * 2(3)^3/2
Apply the law of indices
A = 2(3)^1/2
Rewrite as:
A = 2√3 or 3.46
Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
Read more about areas at:
#SPJ1
You might be interested in
Answer:
Length of the original rectangle is 2.75 cm
Step-by-step explanation:
The dimensions of the scale drawing of rectangle are 8 cm and 11 cm respectively.
This implies that the width of the rectangle is 8 cm while the length of the rectangle is 11 cm.
The scale factor is given as 4. This means that the dimensions of the original rectangle are 1/4 times the given dimensions.
So the length of the original rectangle =
=
Answer:
<h2>The ratios will be equal to the scale factor.</h2>Step-by-step explanation:
Dilation transforms an image to a different size.
In Dilation, the shape of the image remain same, but the size of the figure change as per the scale of the Dilation.
As per example, if the scale factor of Dilation is 2, then the area of the dilated figure = .
Similarly, the sides increase or decrease as per the scale factor.
.