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3 years ago

Find the exact circumference of a circle with diameter equal to 8 ft.

Mathematics

2 answers:

andreyandreev [35.5K]3 years ago

7 0

Answer: 25.12 ft.

Step-by-step explanation:

Given: The diameter of circle d= 8 ft.

We know that the circumference of a circle is given by the formula:-

$\text{Circumference}=\pi d\\\\\Rightarrow\text{Circumference}=(3.14)(8)\\\\\Rightarrow\text{Circumference}=25.12\ ft.$

Hence, the exact circumference of a circle with diameter equal to 8 ft is 25.12 ft.

mylen [45]3 years ago

3 0

The circumference of the circle is the linear length of the circle if the arcs are laid linearly. In this case, the formula that must be followed is C = pi D where C is the circumference and D is the diameter. The circumference then is equal to 8 pi ft

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Which shapes can be drawn with two opposite angles equal to 105°

sertanlavr [38]

Answer:

see the explanation

Step-by-step explanation:

we know that

A shape with two opposite angles equal to 105° could be a quadrilateral, a parallelogram, a rhombus or a trapezoid

Because

A quadrilateral: A quadrilateral is a four-sided polygon. The sum of the interior angles in any quadrilateral must be equal to 360 degrees

If the quadrilateral have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

A parallelogram: A Parallelogram is a flat shape with opposite sides parallel and equal in length. Opposite angles are congruent and consecutive angles are supplementary

If the parallelogram have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A rhombus: A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel. Opposite angles are congruent and consecutive angles are supplementary

If the Rhombus have two opposite angles equal to 105°, then the measure of each of the other two congruent interior angles must be equal to

$180^o-105^o=75^o$

A trapezoid: A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel

If the trapezoid have two opposite angles equal to 105°, then the sum of the other two interior angles must be equal to

$360^o-2(105^o)=150^o$

4 0

3 years ago

Ten students share 9 candy bars equally. what fraction of a candy bars does each student get

emmainna [20.7K]

Each person gets 9 tenths

6 0

3 years ago

Read 2 more answers

Please answer this asap!

777dan777 [17]

This is an exponential equation that can be represented by the following:

f(x) = a(b)^x

In this case...

25143 = a(0.66)^3

25143 is the population after 3 hours.

3 is the amount of time in hours.

0.66 represents the percent of the population remaining after each hour (66% as there is a 34% decline each hour).

We must solve for a, which is the initial population.

First, simplify (0.66)^3 to 0.2874.

25143 = 0.2874a

Now divide both sides by 0.2874 to isolate a.

a = 87455

There were initially 87,455 people within the city. I wouldn't want to be in that place!

7 0

3 years ago

A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How

Mazyrski [523]

Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:

In the year 1985 the worker earned $10,500.

In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

$10,500(1+0.06).

In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]= $$10,500(1.06)^2$ .

Similarly we can check that in the year 1987 the worker earned $$10,500(1.06)^3$ , which makes the pattern clear.

We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

$10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}$ .

Factorizing, we have

$=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]$

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

$\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r})$ (where a is the first term and r is the common ratio) we have:

$\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17$ .

Finally, multiplying 10,500 by 59.17 we have 621.285 ($).

The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating $(1.06)^{26}$ .

Answer: D

4 0

3 years ago

Work out the length of AB.

4vir4ik [10]

$\frac{AB}{BC}$ = $\frac{EB}{DC}$

$\frac{AB}{BC}$ = $\frac{1.75 m}{7 m}$

let AB = E

⇒ (AB) (7 m) = (1.75 m) ( BC + AB)
 (AB) (7 m) = (1.75 m) (1.5 m + AB)
 = 2.625 m² + (1.75 m ) (AB)
(AB) (7 m - 1.75 m) = 2.625 m²
 ∴ AB = 2.625 m² ÷ (5.25 m)

 ⇒ the length of AB is 0.5 m

7 0

3 years ago