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3 years ago

Why did the math teacher open a window company?

Mathematics

2 answers:

makkiz [27]3 years ago

5 0

He Want To Help The Kids

umka2103 [35]3 years ago

4 0

A math teacher opened a window company because he loves seeing shapes or geometrical polygons such as rectagles, squares or quadrilaterals in general as well as triangles in his works. Of course, the math teacher is already familiar with these shapes and how to calculate the angles in between.

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Explain whether the following given sets are closed under addition:

Ivan

Answer:

Step-by-step explanation:

a) Yes.

$\forall\ a,b\ \in\ B,\ a+b\in B\ (since\ 0+0=0)$

b) Yes

$W=\{0,1,2,3,..,\}\ (whole\ numbers)\\\forall\ a,b\ \in\ 3W,\ a+b\in 3W\\since:\\a\ \in\ 3W \Longrightarrow\ \exists\ k_1\in W | a=3*k_1\\\\b\ \in\ 3W \Longrightarrow\ \exists\ k_2\in W | b=3*k_2\\\\a+b=3*k_1+3*k_2=3*(k_1+k_2) \in 3W\\$

c) Yes

$\forall n\ \in\ \mathbb{N}: \Longrightarrow\ n+1 \in\ \mathbb{N}\\$

d) No

$3\in V , 3+3=6\notin V\\$

7 0

3 years ago

Consider two vectors A and B A=14i and B= -4i+8j

DaniilM [7]

Assuming $\mathbf a,\mathbf b\in\mathbb R^3$ , you have

$\mathbf a\cdot\mathbf b=(14)(-4)+(0)(8)=-56$

so

$((\mathbf a\cdot\mathbf b)\,\mathbf i)\cdot\mathbf a=(-56\,\mathbf i)\cdot(14\,\mathbf i)=(-56)(14)=-784$

Next,

$\mathbf a+\mathbf b=(14\,\mathbf i)+(-4\,\mathbf i+8\,\mathbf j)=10\,\mathbf i+8\,\mathbf j$

Then

$(\mathbf a+\mathbf b)\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\10&8&0\\-4&8&0\end{vmatrix}=112\,\mathbf k$

$((\mathbf a+\mathbf b)\times\mathbf b)\times\mathbf k=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&112\\0&0&1\end{vmatrix}=\mathbf 0$

4 0

3 years ago

write the standard form of the equation of the circle with endpoints of a diameter at the points (9,2) and (-7,5)

AnnyKZ [126]

Answer:

Step-by-step explanation:

Answer:

(x-1)²+(y-3.5)² = 265/4

Step-by-step explanation:

first find the midpoint (center of the circle)

(9+-7)/2, (2+5)/2

(1, 3.5) = center

then distance formula to find diameter

√(9- -7)²+(2-5)²=√256+9 = √265

The radius is half the diameter = (√265)/2

Formula for circle is (x-h)²+(y-k)²=r², where (h, k) is the center

Now you can plug everything in.

(x-1)²+(y-3.5)² = 265/4

4 0

3 years ago

According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while

KonstantinChe [14]

Answer:

0.0656

Step-by-step explanation:

For each message, we have these following probabilities:

90% probability it is spam.

10% probability it is legitimate.

Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:

The first four all spam, each with a 90% probability.

The fifth legitimate, with a 10% probability.

$P = (0.9)^{4} \times 0.1 = 0.0656$

3 0

3 years ago

What is (-4,-7) and (-6,9) in slope intercept form

quester [9]

Answer:

y = - 8x - 39

8 0

3 years ago