You have agreed to loan some money to a friend at a simple interest rate of 140% To make it easy on your friend who never took M
1 answer:
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The quotient is:
The remainder is: 0
Step-by-step explanation:
Solve using synthetic division:
The division is shown in figure attached.
The quotient is:
The remainder is: 0
Keywords: Synthetic division
Learn more about Synthetic division at:
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Answer:
Verified
Area = 13.12 square units.
Step-by-step explanation:
Let the given points / vertices of the parallelogram be represented as follows:
A(2,-1,1),
B(5, 1,4),
C(0,1,1),
D(3,3,4)
In vector notation, we can have;
A = 2i - j + k
B = 5i + j + 4k
C = 0i + j + k
D = 3i + 3j +4k
One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.
(i) Now, let's find the various sides of the assumed parallelogram. These sides are:
AB = B - A = [5i + j + 4k] - [2i - j + k] <em>open the brackets</em>
AB = 5i + j + 4k - 2i + j - k <em>collect like terms and solve</em>
AB = 5i - 2i + j + j - k + 4k
AB = 3i + 2j+ 3k
BC = C - B = [0i + j + k] - [5i + j + 4k] <em>open the brackets</em>
BC = 0i + j + k - 5i - j - 4k <em>collect like terms and solve</em>
BC = 0i - 5i + j - j + k - 4k
BC = -5i + 0j - 3k
CD = D - C = [3i + 3j +4k] - [0i + j + k] <em>open the brackets</em>
CD = 3i + 3j + 4k - 0i - j - k <em>collect like terms and solve</em>
CD = 3i - 0i + 3j - j + 4k - k
CD = 3i + 2j + 3k
DA = A - D = [2i - j + k] - [3i + 3j +4k] <em>open the brackets</em>
DA = 2i - j + k - 3i - 3j - 4k <em>collect like terms and solve</em>
DA = 2i - 3i - j - 3j + k - 4k
DA = - i - 4j - 3k
AC = C - A = [0i + j + k] - [2i - j + k] <em>open the brackets</em>
AC = 0i + j + k - 2i + j - k <em>collect like terms and solve</em>
AC = 0i - 2i + j + j + k - k
AC = - 2i + 2j +0k
BD = D - B = [3i + 3j + 4k] - [5i + j + 4k] <em>open the brackets</em>
BD = 3i + 3j + 4k - 5i - j - 4k <em>collect like terms and solve</em>
BD = 3i - 5i + 3j - j + 4k - 4k
BD = - 2i + 2j + 0k
(ii) From the results in (i) above, it has been shown that;
AB is equal to CD, and that implies that AB is parallel to CD. i.e
AB = CD => AB || CD
<em>Also,</em>
AC is equal to BD, and that implies that AC is parallel to BD. i.e
AC = BD => AC || BD
(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.
(B) Now let's calculate the area of the parallelogram.
To calculate the area, we find the magnitude of the cross product between any two adjacent sides.
In this case, we choose sides AC and AB.
Area = | AC x AB |
Where;
AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)
AC X AB = 6i + 6j - 10k
|AC X AB| =
|AC X AB| =
|AC X AB| =
|AC X AB| = 13.12
Therefore the area is 13.12 square units.
PS: The diagram showing this parallelogram has been attached to this response.
Answer:
- 6
- 9
- 1/8
- -10/11
Step-by-step explanation:
You can rewrite the given log expressions to express them in terms of ln(a), ln(b), and ln(c). Then substituting the given values will produce the value of the expression.
Or, you can define the variables 'a', 'b', and 'c' and let your calculator compute these directly.
__
<h3>1.</h3>
_____
The applicable rules of logarithms are ...
- ln(ab) = ln(a) +ln(b)
- ln(a/b) = ln(a) -ln(b)
- ln(a^b) = b·ln(a)
- ln(a) = b ⇔ a = e^b
Of course, a square root is the same as a 1/2 power.
