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Mila [183]
1 year ago
11

A good practice in mathematics is to always check your work. Explain why it is very important to do so when you are solving equa

tions that involve radical expressions?
Mathematics
1 answer:
luda_lava [24]1 year ago
5 0
If you don't double check your answers by substituting them back into the original equation, you may be introducing extraneous solutions into the problem which is why you should always check to confirm your answer is accurate. I hope this helps! :)

 

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Given two vectors a⃗ =4.00i^+7.00j^ and b⃗ =5.00i^−2.00j^ , find the vector product a⃗ ×b⃗ (expressed in unit vectors). what is
FinnZ [79.3K]

The vector product of \boxed{a \times b =  - 43\hat k} and the magnitude of a \times b is \boxed{43}.

Further explanation:

Given:

Vector a is \vec a = 4.00\hat i + 7.00\hat j.

Vector b is \vec b = 5.00\hat i - 2.00\hat j.

Explanation:

The cross product of a \times b can be obtained as follows,

\begin{aligned}a \times b &= \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k} \\4&7&0\\5&{ - 2}&0 \end{array}}\right|\\&= \hat i\left( {0 - 0} \right) - \hat j\left( {0 - 0} \right) + \hat k\left( { - 9 - 35} \right)\\&= 0\hat i - 0\hat j - 43\hat k\\&= - 43\hat k\\\end{aligned}

The vector can be expressed as follows,

a \times b =  - 43\hat k

The magnitude of a \times bcan be obtained as follows,

\begin{aligned}\left| {a \times b} \right| &= \sqrt {{0^2} + {0^2} + {{\left( { - 43} \right)}^2}}\\&= \sqrt {{{43}^2}}\\&= 43\\\end{aligned}43404

The vector product of \boxed{a \times b =  - 43\hat k} and the magnitude of a \times b is \boxed{43}.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: two vectors, vector product, expressed in unit vectors, magnitude, vector a, vector b, a=4.00i^+7.00j^, b=5.00i^-2.00j^, unit vectors, vector space.

8 0
2 years ago
Read 2 more answers
Susan, a recent college graduate, makes a base salary of $70,000 per year. Susan has federal income tax withholding of $12,000,
Damm [24]

Answer:

Susan's take-home pay <u>$48,645</u>.

Step-by-step explanation:

Given:

Susan, a recent college graduate, makes a base salary of $70,000 per year. Susan has federal income tax withholding of $12,000, and state tax withholding of $4,000. Employers are required to withhold a 6.2% Social Security tax and a 1.45% Medicare tax.

Now, to find Susan's take-home pay.

Basic salary = $70,000.

Now, her tax withholdings:

Federal income tax = $12,000.

State tax = $4,000.

<u><em>Social security tax = 6.2% of $70,000.</em></u>

=\frac{6.2}{100} \times 70,000\\\\=0.062\times 70,000\\\\=\$4340.

<u><em>Medicare tax = 1.45% of $70,000.</em></u>

=\frac{1.45}{100} \times 70000\\\\=0.0145\times 70000\\\\=\$1015.

Now, to get the take-home pay of Susan's we subtract all the tax holdings of federal, state, social and medicare from the basic salary:

70,000-(12,000+4,000+4340+1015)

=70,000-(21,355)

=70,000-21,355

=\$48,645.

Therefore, Susan's take-home pay $48,645.

7 0
1 year ago
Pavi has a credit line of $8,000 on his credit card. Review the summary of his credit card statement. How much credit does Pavi
jekas [21]

Answer:

A. $3992.50

Step-by-step explanation:

Credit line - $8,000.00

Summary

  • Previous Balance Payments - $2,500.00
  • Credits  -  $1,500.00
  • New Purchases -  $3,000.00
  • Finance Charge -  $7.50
  • New Balance  - $4,007.50

Available credit= credit line - new balance = $8000 - $4007.50= $3992.50

8 0
2 years ago
Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in bonds. Call t
makvit [3.9K]

Answer:

The solve of that problem is that Hernry invested $18.000 in stocks and $6.000 in bonds.

Step-by-step explanation:

First, to explain you have to do a multiplication about 6 on three. Like three times more than bonds, the result is 18. Then you have to do a  subtraction on $24.000 less $18.000, and the result is $6.000, so six is the amount on bonds. And is three times less than stocks, like the questions ask.

4 0
2 years ago
Read 3 more answers
Sydney earns a yearly salary of $32,000. Sydney's salary is equal to 40% of her boss' yearly salary. What is the yearly salary o
Oliga [24]

Answer: $80,000

Step-by-step explanation:

40%___$32,000

100%___X=$80,000

(100*32,000)/40 = 80,000

6 0
2 years ago
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