Answer:
B
Step-by-step explanation:
Given
x² + 14x = 51
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = 51 + 49 , that is
(x + 7)² = 100 ( take the square root of both sides )
x + 7 = ± = ± 10 ( subtract 7 from both sides )
x = - 7 ± 10
Thus
x = - 7 - 10 = - 17
x = - 7 + 10 = 3
The area and the circumference of the circle are 530.93 square ft and 81.68 ft. If fertilizer will be applied to the lawn. Then the area is used. If the lawn will be surrounded by tape. Then the circumference is used.
<h3>What is a circle?</h3>It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
The figure below shows a circular lawn. Its diameter is 26 ft.
Then the area of the circle will be
Then the circumference of the circle will be
Circumference = π d
Circumference = π × 26
Circumference = 81.68 ft
If fertilizer will be applied to the lawn. Then the area is used.
If the lawn will be surrounded by tape. Then the circumference is used.
More about the circle link is given below.
#SPJ1
(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:
For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:
which reduces to
<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2
(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):