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3 years ago

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Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y

-coordinate is given by y(t) = 10 cos(200t + 3) + 40. what is the center and radius?

1 answer:

Aleks [24]3 years ago

3 0

Answer:

we have centre of circle as (30,40) and radius = 1

Step-by-step explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

$x(t) = 10 sin(200t + 3) + 30$

and

$y(t) = 10 cos(200t + 3) + 40$

$x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40$

when we square and add both the equations we get

$(x-30)^2 + (y-40)^2 = 1$

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1

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54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens = ________(1 Point)

Afina-wow [57]

Answer:

38,660

Step-by-step explanation:

54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens

54 thousands = 54000

6 hundreds = 600

12 ten = 12*10 = 120

54 thousands 6 hundreds 12 tens = 54000+600+120 = 54720

15 thousands = 15000

8 hundreds = 800

26 tens = 26*10 = 260

15 thousands 8 hundreds 26 tens = 15000+800+260 = 16060

Thus,

54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens

= 54720- 16060 = 38,660 (Answer)

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3 years ago

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SIZIF [17.4K]

Answer:

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Step-by-step explanation:

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3 years ago

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MissTica

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.

alina1380 [7]

Answer:

$v_1=(\frac{1}{10},-\frac{3}{10})$

$v_2=(-\frac{1}{10},\frac{3}{10})$

Step-by-step explanation:

First we define two generic vectors in our $\mathbb{R}^2$ space:

$v_1 = (x_1,y_1)$
$v_2 = (x_2,y_2)$

By definition we know that Euclidean norm on an 2-dimensional Euclidean space $\mathbb{R}^2$ is:

$\left \| v \right \|= \sqrt{x^2+y^2}$

Also we know that the inner product in $\mathbb{R}^2$ space is defined as:

$v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2$

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

$\left \| v_1 \right \|= \sqrt{x^2+y^2}=1$

and

$\left \| v_2 \right \|= \sqrt{x^2+y^2}=1$

As second condition we have that:

$v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0$

$v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0$

Which is the same:

$y_1=-3x_1\\y_2=-3x_2$

Replacing the second condition on the first condition we have:

$\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}$

Since $x_1^2= \frac{1}{10}$ we have two posible solutions, $x_1=\frac{1}{10}$ or $x_1=-\frac{1}{10}$ . If we choose $x_1=\frac{1}{10}$ , we can choose next the other solution for $x_2$ .

Remembering,

$y_1=-3x_1\\y_2=-3x_2$

The two vectors we are looking for are:

$v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})$

5 0

3 years ago

Last week Andi had exams in Chemistry and in Spanish. On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a scor

ValentinkaMS [17]

Answer:

Chemistry

Step-by-step explanation:

To solve the above question, we use the z score formula

Andy took two Exams, Chemistry and Spanish. So we find the z score for both exams.

a) Chemistry Exam

On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (45 - 30)/5

z = 15/5

z = 3

b) On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65.

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (65 - 60)/6

z = 5/6

z = 0.8333333333

Comparing the z score of both Exams,

Andy had a z score of 3 in the Chemistry exam and 0.8333333333 in the Spanish exam.

Therefore, Andy should be expecting a better grade in the Chemistry exam because his z score in the Chemistry exam was higher than that of the Spanish exam.

7 0

3 years ago