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Aliun [14]
3 years ago
7

Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim

||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Answer:

The corresponding definite integral may be written as

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x

The answer of the above definite integral is

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98

Step-by-step explanation:

The given limit interval is

\lim_{||\Delta|| \to 0}  \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i

[a, b] =  [-8, 6]

The corresponding definite integral may be written as

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x

\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x

Bonus:

The definite integral may be solved as

\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98

Therefore, the answer to the integral is

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x  = 98

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Answer:

C- 35 °

Step-by-step explanation:

Interior angle adjacent to 90° angle = 90° (supplementary angles of a line segment).

Interior angle adjacent to 125° angle = 55° (supplementary angles of a line segment).

Sum of two interior angles of the triangle = 55+90 = 145°

∠p = 180° - 145° = 35°

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3 years ago
How can you write 45.6 in words
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forty-five and six tenths

Step-by-step explanation:

45 = forty five

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Sara's telephone service costs $31 per month plus $0.25 for each local call. Long-distance calls are extra. Last month, Sara's b
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2 years ago
A car has mass 1500 kg and is traveling at a speed of 35 miles/hour. what is its kinetic energy in joules? (Be sure to convert m
photoshop1234 [79]

Answer:

Factor by which kinetic energy increase = 4 times

Step-by-step explanation:

Given,

  • Mass of the car, v1 = 1500 kg
  • initial speed of car = 35 miles/h

                               =\dfrac{35\times 1609.34}{3600}\ m/s

                               = 15.64 m/s

Initial kinetic energy of the car is given by,

k_1\ =\ \dfrac{1}{2}.m.v_1^2

       =\ \dfrac{1}{2}\times 1500\times (15.64)^2\ joule

       = 183606.46 J

  • Final velocity of car v2 = 70 miles/hour

                                      =\dfrac{70\times 1609.34}{3600}

                                      = 31.29 m/s

So, final kinetic energy of car is given by

k_2\ =\ \dfrac{1}{2}.m.v_2^2

        =\ \dfrac{1}{2}\times 1500\times (31.29)^2

        = 734425.84 J

Now, the ratio of final to initial kinetic energy can be given by,

\dfrac{k_2}{k_1}=\ \dfrac{734425.84}{183606.46}

=>\ k_2\ =\ 4k_1                      

Hence, the kinetic energy will increase by 4 times.

7 0
2 years ago
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