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andrey2020 [161]
3 years ago
7

How solve this calculus 2 problems

Mathematics
1 answer:
babunello [35]3 years ago
3 0
Im really really really confused


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12. Is 3 a solution to the equation 3x - 5<br> = 4 + 2x ? Explain<br> I
Savatey [412]

Answer:

No

Step-by-step explanation:

3x-5= 4+2x

Or, x=4+5

x=9

4 0
3 years ago
Read 2 more answers
3 years ago a father was 3 times as old as his son, in five years time he will be twice as old as his son, what will be the sum
ivolga24 [154]

Answer: 46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son     = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x     = 3y - 9 + 3

x     = 3y - 6 .......................................... equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x       = 2y + 10 - 5

x       = 2y + 5 ........................ equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4      = 15

sum of their ages in four years time will be

31 + 15 = 46 years

5 0
3 years ago
Read 2 more answers
Find four distinct complex numbers (which are neither purely imaginary nor purely real) such that each has an absolute value of
Luda [366]

Answer:

  • 0.5 + 2.985i
  • 1 + 2.828i
  • 1.5 + 2.598i
  • 2 + 2.236i

Explanation:

Complex numbers have the general form a + bi, where a is the real part and b is the imaginary part.

Since, the numbers are neither purely imaginary nor purely real a ≠ 0 and b ≠ 0.

The absolute value of a complex number is its distance to the origin (0,0), so you use Pythagorean theorem to calculate the absolute value. Calling it |C|, that is:

  • |C| = \sqrt{a^2+b^2}

Then, the work consists in finding pairs (a,b) for which:

  • \sqrt{a^2+b^2}=3

You can do it by setting any arbitrary value less than 3 to a or b and solving for the other:

\sqrt{a^2+b^2}=3\\ \\ a^2+b^2=3^2\\ \\ a^2=9-b^2\\ \\ a=\sqrt{9-b^2}

I will use b =0.5, b = 1, b = 1.5, b = 2

b=0.5;a=\sqrt{9-0.5^2}=2.958\\ \\b=1;a=\sqrt{9-1^2}=2.828\\ \\b=1.5;a=\sqrt{9-1.5^2}=2.598\\ \\b=2;a=\sqrt{9-2^2}=2.236

Then, four distinct complex numbers that have an absolute value of 3 are:

  • 0.5 + 2.985i
  • 1 + 2.828i
  • 1.5 + 2.598i
  • 2 + 2.236i
4 0
3 years ago
In the geometric progression 1, 2, 4… what term is 512?
Levart [38]

The next term is double the previous term, so that the n-th term is given recursively by

\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}

This rule tells us that

a_2=2a_1

a_3=2a_2=2^2a_1

a_4=2a_3=2^3a_1

and so on, with the explicit rule

a_n=2^{n-1}a_1=2^{n-1}

for n\ge1.

If 512 is the k-th term in the sequence, then

512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10

8 0
3 years ago
Alaska has 1,700,000 square kilometers. Flordia has a landarea one tenth the size of Alaska. What is the landarea of Florid
Scrat [10]
The land area of Florida is 170 000 square kilometres, this is because 1 700 000 divided by 10 is 170 000. 
8 0
3 years ago
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