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tester [92]
3 years ago
11

Help please, thanks in advance

Mathematics
1 answer:
ycow [4]3 years ago
5 0

Answer: Philip can earn back his initial investment in 12.4 years


Step-by-step explanation:


Amount Invested by Philips in period annuity = 800,000

Annual Percentage Rate (APR) = 5.2%

APR compounded monthly for a period of 20 years.


Amount to be received per annuity period = 800,000 * (((1+(0.052/12))^240)*(0.052/12))/(((1+0.052/12))^240)-1)

= 5368.43


Time taken ( in months ) by Philip to earn back his initial investment = 800,000/5368.43 = 149.02 months



Time taken ( in years ) by Philip to earn back his initial investment = 149.02/12 = 12.4 years


Hope it helps.

Thank you :)



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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

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user100 [1]
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Answer:

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Step-by-step explanation:

13. The figure is a trapezoid

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Where,

a = 3 cm

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14. Area of the triangle = ½*b*h

The area is given to be 45 cm²

base (b) = 16 cm

height (h) = y

Plug in the values and solve for y

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45/8 = 8y/8

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nexus9112 [7]

The measure of angle RML is of 130º.

<h3>What is the value of x?</h3>

Angle NML is the sum of angles NMR and RML, hence:

NML = NMR + RML.

The given measures of the angles are:

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Hence we can solve the equation for RML to find the measure of angle RML, as follows:

NML = NMR + RML

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RML = 130º.

The measure of angle RML is of 130º.

A similar problem, in which the measures of the angles are calculated, is given at brainly.com/question/25716982

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