Hey i just wanted to try typing a question so whats 2+2?
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Finite approximation method of estimating the area under the curve of the
given function makes use of rectangular approximation of the area.
The correct responses are;
i) The estimated area using a lower sum with two rectangles of equal width is <u>1,715 square units</u>.
ii) The estimated area using a lower sum with four rectangles of equal width is <u>3,001.25 square units</u>.
iii) The estimated area using an upper sum with two rectangles of equal width is<u> 8,575 square units</u>.
iv) The estimated area using a upper sum with four rectangles of equal width is <u>6,431.25 square units</u>.
Reasons:
The given function is f(x) = 5·x²
The given domain is x₀ to x₁₄
i) Estimate using lower sum with two rectangles of equal width;
f(0) = 0
f(7) = 5 × 7² = 245
A = 0 × 7 + 245 × 7 = 1,715
The estimated area using a lower sum with two rectangles of equal width
is <u>1,715 square units</u>.
ii) Estimate using lower sum with four rectangles of equal width;
f(0) = 0
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
A = 0 × 3.5 + 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 = 3,001.25
The estimated area using a lower sum with four rectangles of equal width is <u>3,001.25 square units</u>.
iii) Estimate using an upper sum with two rectangles of equal width;
f(7) = 5 × 7² = 245
f(14) = 5 × 14² = 980
A = 245 × 7 + 980 × 7 = 8575
The estimated area using an upper sum with two rectangles of equal width
is <u>8,575 square units</u>.
iv) Estimate using an upper sum with four rectangles of equal width;
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
f(14) = 5 × 14² = 980
A = 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 + 980 × 3.5 = 6,431.25
The estimated area using a upper sum with four rectangles of equal width
is <u>6,431.25 square units</u>.
Learn more here:
The second-order equation as its equivalent system of first-order equations is
=
An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.
Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.
In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.
Taking v = u, we have:
u" + 4u' + 6u = 4sin(3t)
--> v' + 4v + 6u = 4sin(3t)
So the system of equations is:
u' = 0u + 1v
v' = -6u - 4v + 4sin(3t)
So we can write it as:
u(1) = 7.5
v(1) = u'(1) = 9
So the initial condition matrix is:
=
Learn more about the equivalent system here brainly.com/question/14878855
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