Ask question

Ask question

All categories

3 years ago

10

Type the correct answer in the box. Assume that I = 3.14, and round your answer to the nearest integer.

1 answer:

victus00 [196]3 years ago

8 0

Answer:

$648\ yd$

Step-by-step explanation:

step 1

Find the circumference of the complete circle

The circumference is equal to

$C=2\pi r$

we have

$r=35\ yd$

substitute

$C=2\pi(35)$

$C=70\pi\ yd$

step 2

Find the measure of the arc length for a central angle of 280 degrees

Remember that the circumference subtends a central angle of 360 degrees

so by proportion

$\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd$

step 3

Find the perimeter of the playground

$P=54.44\pi+45=54.44*3.14+45=215.96\ yd$

Multiply by 3

$215.96*(3)=647.87\ yd$

Round to the nearest integer

$647.87=648\ yd$

You might be interested in

Alex and Ben shares £520 in the ratio 1:3.<br> What fractions of the £520 does Ben receive?

Arisa [49]

Ben would receive £390 while Alex would only receive £130

4 0

3 years ago

Lines k and n intersect on the y-axis

avanturin [10]

a) The equation of line k is:

$y = -\frac{202}{167}x + \frac{598}{167}$

b) The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

The equation of a line, in <u>slope-intercept formula</u>, is given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change.
b is the y-intercept, which is the value of y when x = 0.

Item a:

Line k intersects line m with an angle of 109º, thus:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

In which $m_1$ and $m_2$ are the slopes of <u>k and m.</u>

Line k goes through points (-3,-1) and (5,2), thus, it's slope is:

$m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}$

The tangent of 109 degrees is $\tan{109^{\circ}} = -\frac{29}{10}$
Thus, the slope of line m is found solving the following equation:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

$-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}$

$m_2 - \frac{3}{8} = -\frac{29}{10} - \frac{87}{80}m_2$

$m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}$

$\frac{167m_2}{80} = \frac{-202}{80}$

$m_2 = -\frac{202}{167}$

Thus:

$y = -\frac{202}{167}x + b$

It goes through point (-2,6), that is, when $x = -2, y = 6$ , and this is used to find b.

$y = -\frac{202}{167}x + b$

$6 = -\frac{202}{167}(-2) + b$

$b = 6 - \frac{404}{167}$

$b = \frac{6(167)-404}{167}$

$b = \frac{598}{167}$

Thus. the equation of line k, in slope-intercept formula, is:

$y = -\frac{202}{167}x + \frac{598}{167}$

Item b:

Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

$-\frac{202}{167}m = -1$

$m = \frac{167}{202}$

Then

$y = \frac{167}{202}x + b$

Also goes through point (-2,6), thus:

$6 = \frac{167}{202}(-2) + b$

$b = \frac{(2)167 + 202(6)}{202}$

$b = \frac{1546}{202}$

The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

A similar problem is given at brainly.com/question/16302622

7 0

2 years ago

What is the value of c in the equation below? StartFraction 5 Superscript 5 Baseline Over 5 squared EndFraction = a Superscript

maw [93]

Answer:

125

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Two more than a certain number is 15 less than twice the number. Find the number

Svetllana [295]

2+x=2x-15
>> 2+15=2x-x
>> 17 = x

So the answer is <u>17</u>

6 0

3 years ago

Read 2 more answers

Find the side lengths ! help pls

sergeinik [125]

(a) the given triangle is a isosceles triangle, therefore the two leg sides will be congruent, as well as the two base angles. It is given that one of the base angles ∠XYW is 70°, therefore, due to the law of a isosceles triangle, the measurement of ∠XWY is also 70°. Remember, a triangle's interior angles add up to 180°, so:

180 - (70 + 70) = 180 - 140 = 40

40° is your answer.

m∠X = 40°

(b) All sides are congruent, making it a equilateral triangle. If it is a equilateral triangle, then all the angles also have the same measurement. The total of the interior angle's measurement is 180°. Divide by the amount of angles, 3:

180/3 = 60

60° is your answer.

m∠V = 60°

~

7 0

3 years ago