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2 years ago

An ice cream shop owner wishes to know what his best flavor is, so he

Mathematics

1 answer:

vredina [299]2 years ago

5 0

Answer:

C cluster

Step-by-step explanation:

just took it

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. Find the surface area of a sphere with diameter 30 m. Leave your answer in terms of

OlgaM077 [116]

The sphere has surface are of 900π m².

Step-by-step explanation:

Given,

Diameter = d = 30m

Radius = $\frac{d}{2} =\frac{30}{2} = 15m$

Surface area of sphere = $4\pi\ r^2$

$Surface\ area = 4*\pi *(15)^2\\Surface\ area = 4*\pi * 225\\Surface\ area= 990\pi$

The sphere has surface are of 900π m².

Keywords: Surface area, multiplication

Learn more about spheres at:

#LearnwithBrainly

3 0

3 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

Jason wants to plant 66 carrot seeds and 44 onion bulbs. He would like to plant them so

dexar [7]

The greatest number of plants he can have in each row is 22

He would have 3 rows of carrots

He would have 2 rows of onions

<h3>Greatest Common Factor</h3>

From the question, we are to determine the greatest number of plants he can have in each row

From the given information,

Jason wants to plant 66 carrot seeds and 44 onion bulbs

The greatest number of plants he can have in each row is the greatest common factor of 66 and 44

Factors of 66: 1, 2, 3, 6, 11, 22, 33, and 66

Factors of 44: 1, 2, 4, 11, 22 and 44

The greatest common factor of 66 and 44 is 22

Thus,

The greatest number of plants he can have in each row is 22

He would have 66/22 rows of carrots

66/22 = 3

Thus,

He would have 3 rows of carrots

He would have 44/22 rows of onions

44/22 = 2

Hence, he would have 2 rows of onions

Learn more on Greatest Common Factors here: brainly.com/question/5535901

#SPJ1

3 0

1 year ago

26. Higher Order Thinking Explain how<br>you know 437,160 is greater than 43,716.

aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

Locate the decimal point.

Count to the left of the decimal point.

The number with the most number of digits is larger than the number with fewer digits.

437160 has six digits.

It is 10 times bigger then

43716 which only has 5 digits.

5 0

2 years ago

What is 100+600 pls help me

liubo4ka [24]

700 is your answer........

5 0

3 years ago

Read 2 more answers