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
Ilya [14]
3 years ago
8

The hypotenuese of an isosceles right triangle is 16 inches. The midpoints of its sides are connected to form an inscribed trian

gle, and this process is repeated, creating a third triangle inscribed in the previous one. Find the sum of the areas of these triangles if this process is continued infinitely.
Mathematics
1 answer:
ser-zykov [4K]3 years ago
3 0

Answer:

  256/3 = 85 1/3 square inches

Step-by-step explanation:

The dimensions of the first inscribed triangle are 1/2 those of the original, so its area is (1/2)² = 1/4 of the original. The area of the original is ...

  A = (1/2)bh = (1/2)(16/√2)(16/√2) = 64 . . . . square inches

The sum of an infinite series with first term 64 and common ratio 1/4 is ...

  S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

  = 64/(1 -1/4) = 64(4/3) = 256/3 . . . . square inches

The sum of the areas of the triangles is 256/3 = 85 1/3 square inches.

You might be interested in
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 mill
abruzzese [7]

Answer:

V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year

Step-by-step explanation:

Given that oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 million barrels of oil in the well; six years later 1,500,000 barrels remain.

i.e. if V stands for volume of oil, then

V' =kV\\dv/V= kdt\\ln V = kt+C\\V = Ae^{kt}

To find A and k

V(0) = A = 3 million

Hence V = 3e^{kt}

V(6) = 1.5

i.e. 1.5 = 3e^{6k}\\ln 1.5 =ln 3 +6k\\k = -0.11552

V(t) = 3e^{-0.11552t}

a) Using the above value of k , we have

V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year.

4 0
3 years ago
A survey asked students whether they would like a drama club, a step team, both clubs, or neither club. The results are below:
Dmitry [639]

Hi, you've asked an incomplete question. Here are the remaining questions:

a) Describe what each region in the Venn diagram represents.

Region I: In drama club, not in step team.

Region II: In both clubs.

Region III: In step team not in drama.

Region IV: Not in either club.

b) How many students were in only one of the two clubs?

c) How many students were in the drama club or in the step team?

d) How many students were surveyed?

Attached is the Venn diagram depicting the regions.

Explanation:

b) By adding the number of students that like drama club and those that like step club we can derive the answer:  34 + 27 = 61.

c) By adding 34 + 27 + those that like both (14) = 75.

d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.

7 0
3 years ago
What two numbers add to 4 and multiply to 1
Arlecino [84]
There are no numbers for this, thus you will have to use the quadratic formula.
4 0
3 years ago
What is the length of 15,409,000 cubic yard in miles? (to<br> the nearest hundred)
cluponka [151]

Answer:

Step-by-step explanation:

The cube root of 15,409,000 = 248.84 yards.

There are 1760 yards in a mile

One edge of a cube = 248.84 / 1760 = .141386 miles.

So a cube would be .00283cubic miles. Your answer does not reach a hundredth place, I don't think.

4 0
3 years ago
A 12 ounce mixture of window cleaner is 4% alcohol. How many ounces of the mixture is alcohol
nekit [7.7K]
0.48 ounce is alcohol
Because you have to divide 100% from 12 ounces which is equivalent to 0.12 ounces for 1% now you will have to multiply 0.12 x 4% WHICH is 0.48 ounce
6 0
3 years ago
Other questions:
  • To get 20%percent what is it divide by
    12·2 answers
  • Help please ASAP don’t have much time ..
    5·2 answers
  • Selena brought 3.75 pounds of meat for $4.64 per round. what was the total cost of meat?
    13·1 answer
  • Can someone answer these two questions for me
    8·2 answers
  • What is 2.64 as a percent
    10·1 answer
  • Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
    9·1 answer
  • Please help me i need it ​
    8·1 answer
  • Find the value of x to the nearest tenth:
    5·1 answer
  • If g(x) = 3x + 7 what is the value of g(-2)? <br><br> 1- -1<br> 2- 1<br> 3- 8<br> 4- 12
    10·1 answer
  • How many millilitres are there in two point four litres?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!