2 1/10 as a percentage

Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6

alina1380 [7]

The tangent vector to r(t) at any t in the domain is

$\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j$

At t = π/6, the tanget vector is

$\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j$

To get the unit tangent, normalize this vector by dividing it by its magnitude:

$\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2$

So the unit tangent at the given point is

$\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j$

4 0

3 years ago

A.40

Ber [7]

Answer:

The answer is E

Step-by-step explanation:

if you find the common numbers you get 45

8 0

3 years ago

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For each of these lists of integers, provide a simple formula orrule that generates the terms of an integer sequence that begins

Anuta_ua [19.1K]

Answer:

b) next three terms of the sequence are 47, 51, 55

c) The next three terms are 1100, 1101, 1110

d) The next three items in the sequence are therefore, 8,8,8

f) The next three terms are 654729075, 13749310575, 316234143225

g) Therefore the next three items in the sequence are 0,0,0

Step-by-step explanation:

b)7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...

the common difference, d = $T_{2} - T_{1} = 11 - 7 = 4$

$a_{n} = a_{n-1} + 4$

43 + 4 = 47

47 + 4 = 51

51 + 4 = 55

next three terms of the sequence are 47, 51, 55

c) 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...

Each of these terms are binary numbers of 1,2,3,4........

The 1st next term is the 12th term = 1100₂

The second next term is the 13th term = 1101₂

The third next term is the 14th term = 1110₂

The next three terms are 1100, 1101, 1110

d) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...

1 is repeated 1 time , 2 is repeated 3 times, 3 is repeated 5 times, 5 is repeated 7 times, the next number will sure be repeated 9 times( the repetition follows an odd number pattern)

To know the next number that will be repeated 9 times:

1+2 = 3

2+3 = 5

3 + 5 = 8

The pattern is that the previous summation adds to the preceding number

The next three items in the sequence are therefore, 8,8,8

f) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...

The above sequence follows the pattern $a_{n} = a_{n-1} (2n -1)\\$

The next three terms are the 10th, 11th and 12th terms

a₁₀ = 34459425((2*10)-1)

a₁₀ = 654729075

a₁₁ = 654729075((2*11)-1)

a₁₁ = 13749310575

a₁₂ = 13749310575((2*12)-1)

a₁₂ = 316234143225

The next three terms are 654729075, 13749310575, 316234143225

g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,...

The sequence changes between 1 and 0. 6 zeros are expected next

Therefore the next three items in the sequence are 0,0,0

8 0

2 years ago

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there are 150 students in the marching band, and 30 of them play the trumpet. Which number line represents the percent of the sr

shepuryov [24]

Answer:

30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet.

Step-by-step explanation:

Draw two number lines:

One number line to represent number of students from 0 to 150. For convenience, divide the number line into intervals of 15 so that 30 is also present on the line.
Second number line to represent percentage and divide it in intervals from 1 to 100.

Now, place the other number line just below the other number line and draw a vertical line as shown the attached figure.

We find out that 30 is at 20% of 150.

It means that 20% (30 of total 150) of total 150 students in the marching band, play trumpet.

3 0

3 years ago

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide, if the reduced diagram

sertanlavr [38]

Answer:

12 cm

Step-by-step explanation:

This is a proportionality/similarity problem.

10 cm turned to 4 cm. So by how much has it decreased? In other words, 10 multiplied by WHAT is 4?

$10*x=4\\x=\frac{4}{10}\\x=0.4$

0.4 is also known as the scale factor from the large diagram to the small diagram.

So how much would 30 cm become? It would be 30 multiplied by the scale factor, which is 0.4.

$30*0.4=12$

Hence, the length of the reduced diagram would be 12 cm.

7 0

3 years ago

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