All categories

3 years ago

(08.05 LC) Which two-dimensional shape can be rotated about the y-axis to create a cone?

Mathematics

2 answers:

gogolik [260]3 years ago

6 0

Answer:

Right triangle

Step-by-step explanation:

Just imagine a rotating door in the shape of a right triangle.

Illusion [34]3 years ago

4 0

Any right triangle can.

You might be interested in

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

Can someone help me with this, im not really good at math and i dont understand this :(

cluponka [151]

Answer:

y = 2x + 4

Step-by-step explanation:

First find 2 points on the line to determine slope.

(0, 4) and (2, 8)

Slope = $\frac{8-4}{2-0}=2$

y = 2x + b

b = y - intercept

b = 4

y = 2x + 4

4 0

3 years ago

Read 2 more answers

(2.5 • 10^4) - (1.5 • 10^3)<br><br> Evaluate please, can you show the steps

Usimov [2.4K]

According to PEMDAS, you would look in the parenthesis first. In the first set of parenthesis we have an exponent. 10x10x10x10 is 10,000. Then we multiply this by 2.5. We now have 25,000. We put this to the side..

Next, we do the same thing on the other side -- 10x10x10 is 1,000 and then you multiply that answer by 1.5 and we have 1,500. Now we can subtract. 25,000 - 1500 = 23,500 :)

8 0

3 years ago

Suppose a triangle has sides a, b, and c let theta be the angle opposite the side of length a. If cos theta < 0 what must be

Levart [38]

Suppose a triangle has sides a, b, and c let theta be the angle opposite the side of length a. If cos theta < 0 The statement that is true is <span>b^2+c^2>a^2. The answer is letter A.</span>

6 0

3 years ago

Read 2 more answers

Help help math math math

Anarel [89]

Answer:

i think this is right i hope it helped :)

Step-by-step explanation:

5m - 8 = 2m + 1

5m + 2m - 8 = 1

7m - 8 = 1

7m = 7

m = 1

6 0

2 years ago

Read 2 more answers