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2 years ago

A square pyramid is shown:

1 answer:

Colt1911 [192]2 years ago

7 0

Area of triangles:
0.5x9=4.5
4.5x2=9 (i divided 4 (the amount of triangles) by 2 instead of dividing 4.5 by 2)

area of square:
0.5x0.5=0.25

surface area of whole thing:
9+0.25=9.25

so the answer is 9.25

hope this helps :)

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Line DA is tangent to circle B. What is the measure of angle ACB?

alexdok [17]

A tangent line creates a 90 degree angle with a radius line that touches the tangent Line.

Line BC is a radius that touches the tangent line at point C

The angle created is 90 degrees.

The answer is C. 90 degrees.

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3 years ago

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800 is 100 times as much as

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800/100 = 8
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3 years ago

A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with

marysya [2.9K]

Answer:

Choose either strategy both are equally successful

Step-by-step explanation:

Given:-

- The probability of success for both husband (H) and wife (W) are:

P ( W ) = 0.8 , P ( H ) = 0.8

Find:-

- Which of the following is a better strategy for the couple?

Solution:-

Strategy 1

- First note that P ( W ) & P ( H ) are independent from one another, i.e the probability of giving correct answer of husband does not influences that of wife's.

- This strategy poses an event such that either wife knows the answer and answer it correctly or the husband knows and answers in correctly.

- We will assume that probability of either the husband or wife knowing the answer is 0.5 and the two events of knowing and answering correctly are independent. So,

P ( Wk ) = P (Hk) = 0.5

- The event P(S1) is:

P(S1) = P ( Hk & H ) + P ( Wk & W )

P(S1) = 0.5*0.8 + 0.5*0.8

P(S1) = 0.8

- Hence, the probability of success for strategy 1 is = 0.8

Strategy 2

- Both agree , then the common answer is selected otherwise, one of their answers is chosen at random.

- The success of strategy 2, will occur when both agree and are correct, wife is correct and answers while husband is not or husband is correct and he answers.

- The event P(S2) is:

P(S2) = P ( H & W ) + P ( H / W' & Hk ) + P ( H' / W & Wk )

P(S2) = P ( H & W ) + P ( H / W') P ( Hk ) + P ( H' / W) P (Wk)

P(S2) = P ( H & W ) + P ( H / W')*0.5 + P ( H' / W)*0.5

P(S2) = 0.5* [ P ( H & W ) + P ( H / W') ] + 0.5* [ P ( H' / W) + P ( H & W )]

P(S2) = 0.5*P(H) + 0.5*P(W)

P(S2) = 0.5*0.8 + 0.5*0.8

P(S2) = 0.8

- Hence, the probability of success for strategy 2 is = 0.8

Both strategy give us the same probability of success.

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3 years ago

One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for

Marat540 [252]

Answer:

Step-by-step explanation:

f(x) has two complex roots and one real root.

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2 years ago

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Solve/answer the question and help me understand this question please

faltersainse [42]

Answer:

5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

<h3>understanding the direction</h3>

In navigation problems, direction angles are specified a couple of different ways. A <em>bearing</em> is usually an angle in the range [0°, 360°), <em>measured clockwise from north</em>. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

<h3>the two vectors</h3>

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

magnitude∠direction
magnitude <em>cis</em> direction

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

<h3>vector sum</h3>

The final position is the sum of these two changes in position:

3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

= 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

<em>Additional comment</em>

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

(0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

OB = √(1.434² +5.048²) ≈ 5.248

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1 year ago