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3 years ago

Write 375 as the product of prime factors write the prime factors in ascending order

Mathematics

1 answer:

Eddi Din [679]3 years ago

8 0

Answer:

The prime factors are: 3 x 5 x 5 x 5

or also written as ( 3, 5, 5, 5 )

Step-by-step explanation:

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What has a slope of 2/3

Angelina_Jolie [31]

Answer:

y = m x + b.23

Step-by-step explanation:

4 0

3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (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

Studies show that a typical giant hummingbird can flap its wings once in 0.08 of a second.

Licemer1 [7]

Answer:

a. 90

b. 360

Step-by-step explanation:

The time taken by humming bird to flap its wings= 0.08 sec

by flying 7.2 seconds a typical giant hummingbird flap its wings $\frac{7.2}{0.08}$ times

= 90 times

Since, A ruby-throated hummingbird can flap its wings 4 times faster than a giant hummingbird, it will flap its wings in every 0.02 sec

so in 7.2 seconds it will flap $\frac{7.2}{0.02}$ times = 360 times

4 0

3 years ago

(Find the HCF of):<br>p^2+4pq+4q^2, p^4 + 8pq^3 and 3p^4 - 10p^2q^2+ p^3q

kow [346]

Answer:

12pq

Step-by-step explanation:

i dont know tbh but i try my best to help out now anyways

5 0

3 years ago

Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can?

spin [16.1K]

First we need to find the heigh of the soda can be rearanging the volume formula, . We can make that We know that V is 36 and radius is half of the diameter, so radius is 2.

h = 2.87

Now, we can use the height to figure out the volume of a cone. The volume of a cone is
R is 2 again and h is 2.87

12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can

6 0

3 years ago

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