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Pachacha [2.7K]
3 years ago
12

How to find a perfect square

Mathematics
1 answer:
Rzqust [24]3 years ago
8 0

Answer:

Step-by-step explanation:

The square of a number n is denoted by n^2.

Examples:  The square of 2 is 2^2, or 4; the square of 5 is 5^2, or 25.  To find a perfect square of a number n, multiply the number by itself (obtaining the square of n).

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3 years ago
In this question, i is a unit vector due east and j is a unit vector due north. A cyclist rides at a speed of 4 m/s on a bearing
d1i1m1o1n [39]

<u>Answer:</u>

a) 1.04i + 3.86j

b) magnitude = 8; bearing = 302.7°

<u>Step-by-step explanation:</u>

a)

The  first diagram represents the velocity vector of the cyclist.

To express this vector in the form xi + yj, we have to find the components of the vector in the horizontal (i) and vertical (j) directions.

If we consider the horizontal component of the vector to be x, and the vertical component to be y, then:

• horizontal component ⇒ sin (15^{\circ}) = \frac{x}{4}

                                       ⇒ x = 4\space\ sin(15^{\circ})

                                       ⇒ x \approx \bf 1.04

• vertical component ⇒ cos(15^{\circ}) = \frac{y}{4}

                                   ⇒ y = 4 \space\ cos(15^{\circ})

                                   ⇒ y \approx \bf 3.86

Now that we have the values of both the horizontal and vertical component, we can write the vector in the form of xi + yj:

vector ⇒ 1.04i + 3.86j

b)

The second diagram shows the first vector (red), the second vector (blue), and the resultant vector <em>v</em> (black). The dashed lines represent the components of the respective vectors.

To add two vectors given their magnitudes and direction, we have to add their components.

In order to find the horizontal and vertical components of the given vectors, we can use a method similar to that used above, so that:

○ For the first vector (magnitude 6):

• horizontal component ⇒ x = 6 \space\ sin (60^{\circ})

                                       ⇒ \bf 5.2

• vertical component ⇒ y = 6 \space\ cos(60^{\circ})

                                   ⇒ y = \bf 3

○ For the second vector (magnitude 2):

• horizontal component ⇒ x = 2 \space\ cos (40^{\circ})

                                       ⇒ \bf 1.5

• vertical component ⇒ y = 2 \space\ sin(40^{\circ})

                                   ⇒ \bf 1.3

Now we can add the respective components together:

v = 5.2i + 3j  +  1.5i + 1.3j

 ⇒ (5.2 + 1.5)i + (3 + 1.3)j

 ⇒  6.7i + 4.3j

∴ Magnitude of v ⇒ |v| = \sqrt{(6.7)^2 + (4.3)^2}

                             ⇒ |v| \approx \bf 8

To find the bearing of <em>v</em>, we have to first calculate the angle marked \alpha:

tan \alpha = \frac{4.3}{6.7}

⇒ \alpha = tan^{-1}(\frac{4.3}{6.7})

⇒ \alpha = \bf 32.7^{\circ}

∴ Bearing = 270° + 32.7°

                = 302.7°

8 0
2 years ago
Select the correct answer. Identify the axis of symmetry of the function graphed below. A. x = -3 B. x = -1 C. x = 1 D. x = -4
Ainat [17]

Answer:

B

Step-by-step explanation:

The vertex of the parabola is (-1,-4)

So the axis of symetry is x=-1

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4 years ago
Suppose you need to deliver 40 terabytes of data to your co-workers in Atlanta (200 km). You have an available 100 Mbps dedicate
Marat540 [252]

Answer: All data will be sent in 89.39 hours

Step-by-step explanation:

Data transfer rate: 100 Mbps=100 \frac{Mb}{s} ×\frac{1Tb}{1024^{2} Mb}×\frac{3600s}{h}=0.3433 \frac{Tb}{h}

The pigeon can fly 1000 km/day and it needs to fly 400 km (round trip).

Pigeon rate: \frac{1000km}{24h}=41.67 \frac{km}{h}

Time of round trip: 400 km÷\frac{1000km}{24h}=9.6 h

So the pigeon can send 1 Tb every 9.6 hours.

If we sum the rates we can get the time for sending all the data:

40 Tb= (0.3433 Tb/h + 1 Tb/9.6h)×t

T= 89.39 hours

8 0
4 years ago
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