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Varvara68 [4.7K]
3 years ago
8

An amusement park has two merry-go-rounds. The first merry-go-round has a platform with a diameter of 13 meters and the second m

erry-go-round has a platform with a radius of 9.5 meters. How much larger is the area of the larger merry-go-round’s platform compared to the area of the smaller merry-go-round’s platform? Round to the nearest whole number. Show your work. (Use Pi = 3.14)
Mathematics
1 answer:
Zinaida [17]3 years ago
3 0

Answer:

  • <em>The larger merry-go-round's platform is </em><u>   151m²   </u><em> larger than the smaller merry-go-round's platform.</em>

Explanation:

The<em> area </em>of a round shape is equal to the area of a circle.

The formula for the area of a circle is:

  • Area = π × radius²

Then, use that formula for each merry-go-round.

<em><u>1. First merry-go-round</u></em>

<em />

  • diameter = 13m
  • radius = diameter / 2 = 13m / 2 = 6.5m
  • area = π (6.5m)² = 3.14 × (6.5m)² = 132.665m²

<em><u>2. Second merry-go-round</u></em>

  • radius =9.5m
  • area = π (9.5m)² = 3.14 × (9.5m)² = 283.385‬m²

<u />

<u>3. Difference of the areas</u>

<u />

  • Larger area - smaller area = 283.385m² - 132.665m² = 150.72m²

  • Round to the nearest whole number: 151m².

Hence, the larger merry-go-round's platform is 151m² larger than the smaller merry-go-round's platform.

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1.60. वात्सल्य के अन्तर्गत शिशु स्वरूप के सौंदर्य की अपनी महत्वपूर्ण भूमिका होती है । आपने भी जीवन में
Rus_ich [418]

Answer:

hope it helps

please mark me brainliest

Step-by-step explanation:

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संस्कृत के प्राचीन आचार्यों ने देवादिविषयक रति को केवल ‘भाव’ ठहराया है तथा वात्सल्य को इसी प्रकार की ‘रति’ माना है, जो स्थायी भाव के तुल्य, उनकी दृष्टि में चवर्णीय नहीं है[1]।

सोमेश्वर भक्ति एवं वात्सल्य को ‘रति’ के ही विशेष रूप मानते हैं - ‘स्नेहो भक्तिर्वात्सल्यमिति रतेरेव विशेष:’, लेकिन अपत्य-स्नेह की उत्कटता, आस्वादनीयता, पुरुषार्थोपयोगिता इत्यादि गुणों पर विचार करने से प्रतीत होता है कि वात्सल्य एक स्वतंत्र प्रधान भाव है, जो स्थायी ही समझा जाना चाहिए।

भोज इत्यादि कतिपय आचार्यों ने इसकी सत्ता का प्राधान्य स्वीकार किया है।

विश्वनाथ ने प्रस्फुट चमत्कार के कारण वत्सल रस का स्वतंत्र अस्तित्व निरूपित कर ‘वत्सलता-स्नेह’ [2] को इसका स्थायी भाव स्पष्ट रूप से माना है - ‘स्थायी वत्सलता-स्नेह: पुत्राथालम्बनं मतम्’।[3]

हर्ष, गर्व, आवेग, अनिष्ट की आशंका इत्यादि वात्सल्य के व्यभिचारी भाव हैं।

8 0
3 years ago
Prove that the point (2, 1) lies on the line with equation y = 3x – 5.
Oxana [17]

Answer:

3(2) - 5 = 1

Step-by-step explanation:

y = 3x - 5

(x, y)

plug x and y in

1 = 3(2) - 5

1 = 6 - 5

1 = 1

true

6 0
3 years ago
What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 s
IRISSAK [1]
The exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)

I assumed you meant 8y squared because you said 8 squared.

now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:

(15x^8 / 24y^5) * (8y^2 / 4x^4)

let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.

We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1

so:
(5x^8 / 8y^5) * (2y^2 / x^4)

multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)

now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3

now put together
5x^4 / 4y^3

so C
3 0
3 years ago
Consider the case of a triangle with sides 5, 12, and the angle between them 90°.
Daniel [21]

Answer:

a) Applying Pithagoras Theorem

b) Trigonometric relations

c) No we can not

d) No we can not

e) See step-by-step explanation

f) See step-by-step-explanation

Step-by-step explanation:

a) The easiest method for calculating the missing side is applying Pithagoras Theorem

c²  =  a²  +  b²

c²  =  (5)²  +  (12)²      ⇒  c²  = 25 + 144    ⇒ c²  =  169    ⇒  c  = 13

b) The easiest method to find the missing angles, is to calculate the sin∠ and then look for arcsin fuction in tables.

sin ∠α = 5/13    sin ∠α = 0.3846    ⇒      arcsin (0.3846 )   α  = 23⁰

Now we can either get the other angle subtracting 180 - 90 - 23 = 67⁰

Or calculating sinβ = 12 /13    sinβ = 0.9230  arcsin(0.9230)   β = 67⁰

c) The law of cosines should not be applied to right triangles, in fact for instance in our particular case we have:

Question a)

c²  = a² + b² - 2*a*b*cos90⁰   (law of cosines ) but cos 90⁰ = 0

then c²  = a² + b² which is the expression for theorem of Pithagoras

In case you look for calculating the missing angles

c²  = a²  +  b²  - 2*5*13*cos α

169 = 25  +  144 - 2*5*13* cos α

As you can see 169 - 25 - 144 = 0

Then we can not  apply law of cosine in right triangles, we shoul apply trigonometric relations and Pithagoras theorem, and as we saw you can get the expression of Pithagoras theorem from cosine law

c²  =  a²  +  b²  - 2*a*b*cos∠90°    cos ∠ 90°  = 0

Then     c²  =  a²  +  b²

3 0
3 years ago
What is the slope of a line that is perpendicular to the line 2y – 3x = 8
tensa zangetsu [6.8K]

Answer:

The slope is 3/2 and the y intercept is 4

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

2y -3x=8

Add 3x to each side

2y-3x+3x= 8+3x

2y = 3x+8

Divide by 2

2y/2 = 3/2x +8/2

y = 3/2x +4

The slope is 3/2 and the y intercept is 4

7 0
3 years ago
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