1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
barxatty [35]
2 years ago
7

Evaluate the summation of 3 n plus 2, from n equals 1 to 14. 39 49 340 343.

Mathematics
1 answer:
lord [1]2 years ago
5 0

The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

<h3>How to find the sum of consecutive integers?</h3>

1 + 2 + 3 + ... + n = \dfrac{n(n+1)}{2}

<h3>
What are the properties of summation?</h3>

\sum_{i=r}^s  (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b

where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).

For the given case, the considered summation can be written symbolically as:

\sum_{n=1}^{14}  (3n + 2)

It is evaluated as;

\sum_{n=1}^{14}  (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14}  (3n + 2) = 3 \times 105 + 28 = 343\\

Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

Learn more about summation here:

brainly.com/question/14322177

You might be interested in
There is a rectangular terrain with dimensions "x" and "y". If it is known that its area of ​​is 22m ^ 2 and that x ^ 2 + y ^ 2
Margaret [11]

9514 1404 393

Answer:

  24 m

Step-by-step explanation:

The area formula tells us ...

  22 = xy . . . . . square meters

Adding twice this to the quadratic constraint gives ...

  (x^2 +y^2) +2(xy) = (100) +2(22)

  (x +y)^2 = 144

  x +y = √144 = 12

The perimeter is double this amount, so is ...

  P = 2(x +y) = 2(12) = 24 . . . . meters

5 0
3 years ago
a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base s
slavikrds [6]

A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane  so that the two solids of equal weight will be formed.

<u>It is assumed that weight of pyramid is proportional to its volume.</u>

So,   w  = k V , where V is volume of original pyramid and v is volume of small pyramid and k is constant.

Let us consider that at h  distance,  pyramid is cut from its vertex. So a small pyramid is also formed.

Assume that base area of original pyramid is A and base of small pyramid is a.

Volume of original pyramid is,   V= \frac{1}{3}  *A* 5

So, weight of original pyramid,  W = k *(\frac{1}{3}  *A* 5) = 800

Volume of small pyramid is,  v = \frac{1}{3}* a* h

So, weight of small pyramid, w = k*(\frac{1}{3}* a* h)=400

<u>Since, base and height of small pyramid and original pyramid are in proportion.</u>

So,  \frac{a}{A}  = (\frac{h}{5}) ^{2}

       a = (\frac{h}{5} )^{2}A

Substituting value of a in  equation k*(\frac{1}{3}* a* h)=400

So, k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400

       (k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400

Since, (k *\frac{1}{3}  *A* 5) = 800, substitute in above equation.

    So, 800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet

Learn more:

brainly.com/question/17950304

6 0
2 years ago
Read 2 more answers
a family has five children The probability of having a gil is 1/2 What is the probability of having exactly 2 girls out of five
My name is Ann [436]
P(no girls in five births) = p(five boys) = (1/2)^5 = 1/32 = 0.0313
4 0
3 years ago
Wind farms are a source of renewable energy found around the world. If a turbine generates 500kW in a 10m/s wind, how much power
Annette [7]
<span>Wind farms are composed of tens of wind mills that us electric generator to harness the power of the wind. The power that comes out of the electric generators should be proportional with the force or the wind which is also proportional to the speed of the wind. Considering that a 10 m/s generates 500 kW, than a 12 m/s wind should generate somewhere around 600 kW.</span>
4 0
3 years ago
The Suarez family paid $15.75 for 3 movie tickets. How much would they have paid for 12 tickets?
Serjik [45]

Answer:

$63

Step-by-step explanation:

15.75 / 3 = 5.25

5.25 is what each ticket was worth

5.25 * 12 = 63

8 0
3 years ago
Read 2 more answers
Other questions:
  • Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S exten
    15·2 answers
  • What percent of 50 shirts is 35 shirts.. &gt;_
    9·2 answers
  • ​Felipe Rivera's savings account has a balance of $3159. After 4 years what will the amount of interest be at 1.6% compounded qu
    15·1 answer
  • Describe a real world problem you could solve with the help of a yardstick and a calculator.
    10·1 answer
  • A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 m
    10·1 answer
  • What is the measure of angle 1
    7·1 answer
  • Math help please help thanks
    9·1 answer
  • B) Find the value of a^2 + b^2 when a = 3 and b= -2
    14·2 answers
  • Sam makes $15 per hour mowing lawns. He makes an additional $16 each day because
    11·1 answer
  • What is 53232+10093200920 equal
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!