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lorasvet [3.4K]
1 year ago
8

Need help with this fast

Mathematics
2 answers:
kramer1 year ago
8 0

Answer:

<u>C</u>

Step-by-step explanation:

Formula for the volume of a cone :

<u>Volume (cone) = 1/3πr²h</u>

<u />

===========================================================

Given :

⇒ r = 4 units

⇒ h = 21 units

============================================================

Solving :

⇒ Volume (cone) = 1/3 × π × (4)² × 21

⇒ Volume (cone) = 16 × 7 × π

⇒ Volume (cone) = <u>112π units²</u>

disa [49]1 year ago
4 0

Answer:

\sf C. \quad 112 \pi \:units^2

Step-by-step explanation:

\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

Given:

  • radius = 4 units
  • height = 21 units

Substituting the given values into the formula:

\implies \sf Volume=\dfrac{1}{3} \cdot \pi \cdot 4^2 \cdot 21

\implies \sf Volume=112 \pi \:units^2

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Ft?
VARVARA [1.3K]

Answer:

15 5/8 ft^3

Step-by-step explanation:

Volume of a cube = l x b x h

Given the Length of sides is

2 1/2

Change 2 1/2 to an improper fraction.

It becomes 5/2

Volume = 5/2 x 5/2 x 5/2

Multiply through

= 125/8

= 15 5/8 ft^3

5 0
3 years ago
Question 1<br> What is the solution of n² - 49 = 0?<br> 0 +7<br> 07<br> -7<br> O no solution
Sphinxa [80]
Hey there!

This can be written as n^{2}-(7)^{2}

This is in form of \fbox{a^{2}-b^{2}} , it can be expanded as \fbox{(a-b)(a+b)}

=> (n-7)(n+7)=0
=> n -7 = 0 or n + 7 = 0
=> n = 7 or n = -7

So option 7 , -7 are correct.

Hope this is clear :)
Have a good day:)
7 0
2 years ago
Read 2 more answers
1 3/4+1/6+____=7 1/2<br> Plz help
Mademuasel [1]

Answer:

7/4 +1/6 +X=15/2

1/6+X=15/2-7/4

1/6+X=30/4-7/4

X=23/4 - 1/6

X= 138-4/24

134/24

5.58333

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
An ice cream sells 4 drinks, in 5 sizes, and 7 flavors. How many ways can a customer order a drink?
tigry1 [53]

Answer:

140 ways

Step-by-step explanation:

4 x 5 x 7 = 140

3 0
3 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
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