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zzz [600]
3 years ago
11

the diagonals PR and QS of a rhombus intersect each other at point O. prove that 2(PQ) + 2(QR) + 2(RS)+ 2(PS) = 4 (2(OP)+2(OQ))

Mathematics
1 answer:
mamaluj [8]3 years ago
4 0

Answer:

It is proved that 2PQ + 2SR + 2QR + 2 PS = 4(2(OP)+2(OQ))

Step-by-step explanation:

In a rhombus, all sides are equal.

Thus, in this question;

PQ = SR = QR = PS

By inspection, QS is the same dimension as the four sides. So, QS = PQ

Thus, OQ = PQ/2

For OP, we can find it using Pythagoreas theorem since the angle that divides the diagonals is 90°

Thus;

|OP|² + |OQ|² = |PQ|²

Earlier, we saw that;OQ = PQ/2

Thus;

|OP|² + |PQ/2|² = |PQ|²

|OP|² = |PQ|² - |PQ/2|²

|OP|² = |PQ/2|²

Taking square root of both sides, we have;

OP = PQ/2

So,going back to the question, on the right hand side, we have;

4(2(OP) + 2(OQ))

Let's put,

PQ/2 for OQ and OP as gotten earlier

So,

4(2(PQ/2) + 2(PQ/2)) = 4(PQ + PQ)

Since PQ = SR = QR = PS, we can rewrite as;

4PQ + 4PQ = (PQ + SR + QR + PS) + (PQ + SR + QR + PS) = 2PQ + 2SR + 2QR + 2 PS

This is equal to the left hand side, so the equation is proved correct.

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murzikaleks [220]

The total cost curve shows the cost of total shipment from the different

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  • a. Please find attached the graph of the total cost to quantity of shipment created with MS Excel.

  • b. The city that provides the lowest overall cost is; <u>Salt Lake City</u>.

Reasons:

The given parameters are;

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The given table is presented as follows;

\begin{tabular}{|l|c|c|c|}Location&Annual Fixed Costs&Variable Cost \\Denver&\$5,000,000&\$4.65 \\Santa Fe&\$4,200,000&\$6.25\\Salt Lake City&\$3,500,000&\$7.25\end{array}\right]

a. Required:

The plot total cost curve for the locations on a single graph.

Solution:

  • Please find attached the graph of the total cost curves created with MS Excel

b. Required:

The city that provides the lowest overall cost.

Solution:

The two cities with the lowest overall costs are Denver and Salt Lake City.

  • From the total cost curve, the area under the curves are;

Area under the curve for Denver;

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Area under the curve for Salt Lake City

(7487500 + 7850000) ÷ 2 × 50,000 = 383437500000

Therefore;

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4 0
2 years ago
3-2|x+4|+3=1 the answer for this​
blagie [28]

Answer:

x={-3/2,-13/2}

Step-by-step explanation:

3-2|x+4|+3=1

-2|x+4|+6=1

-2|x+4|=-5

|x+4|=5/2

x+4=5/2

x+4=-5/2

x=5/2-4

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x=-5/2-4

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2 years ago
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shepuryov [24]

Answer:

<h2>Conditional frequencies offer more specific information to analyse certain data set.</h2>

Step-by-step explanation:

A conditional frequency is a type of relative frequency which involves a condition to be defined.

For example, the conditional frequency of having a house given that the person is female. Notice that this example shows the condition "being female", so the conditional frequency would be all females who own a house.

On the other hand, the relative frequency is just a ratio between the frequency of the data and the total number of  data. It's doesn't includes a condition to be defined, that's the difference.

Therefore, conditional frequencies offer more specific information to analyse certain data set.

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