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2 years ago

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Mathematics

1 answer:

Vikentia [17]2 years ago

7 0

Answer:

3x^2 + 3 --> 6, 15, 30, 51

2x^2 - 1 --> 1, 7, 17, 31

x^2 + 2 --> 3, 6, 11, 18

Step-by-step explanation:

Let's start with the first equation; 3x^2 + 3

Substitute 1 (the first digit in a sequence) for x.

3(1^2) + 3

3(1) + 3

3 + 3 = 6

3(2^2) + 3 Then the second digit.

3(4) + 3

12 + 3 = 15

Since the two numbers we have so far are 6 and 15, there is only one sequence this could match. 6, 15, 30, 51.

2(1^2) - 1

2(1) - 1

2 - 1 = 1

This equation represents 1, 7, 17, 31.

These same steps apply to the other equation as well.

1^2 + 2, then 2^2 + 2, then 2^2 + 2, and so on. (But we don't need to do extra work to figure that out.)

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Write 9,540,000 in expanded form using exponents to show powers of 10

krek1111 [17]

Answer:

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Step-by-step explanation:

Given : 9,540,000

To find : Write 9,540,000 in expanded form using exponents to show powers of 10.

Solution : We have given 9,540,000

Here 9 is at million place 9000000

5 is at hundred thousand place = 500,000.

4 is at tens thousand place = 40,000

We expanded it as

9, 000,000 + 500,000+40,000.

In term of power of 10.

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Therefore,

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

6 0

3 years ago

Find the measure of the missing angle.

natulia [17]

Answer:

x = 76

Step-by-step explanation:

The inscribed angle x is half the measure of its intercepted arc.

x = $\frac{1}{2}$ × (102 + 50) = 0.5 × 152 = 76

6 0

2 years ago

Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360

Natasha2012 [34]

$\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]$

$\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]$

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

$\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]$

5 0

3 years ago

A rectangular block of copper metal has a mass of 1800 grams. The dimensions of the block

Hoochie [10]

Use formula p=m/v
P is density
M is mass
V volume
So you have the volume already now 8x5x4= 160 which is the volume
P= 1800/160 after you divide you get 11.25
The density is 11.25

3 0

3 years ago

Determine the quadrant(s) in which (x, y) could be located. (Select all that apply.)

Eva8 [605]

None of these because they all are 0

8 0

3 years ago