. A circular window has a diameter of 40 centimeters. What is the circumference of the window? Use 3.14 for π π 251.2 cm

Solve the system of two linear equations below graphically y= -x + 1 y= -1/3+ 3

Nesterboy [21]

Answer:

Step-by-step explanation:

4 0

2 years ago

Statistics

Westkost [7]

Answer:

no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44

7 0

2 years ago

. Find the value of sec θ for the angle shown. (2 points) A line is drawn from the origin through the point seven comma six. The

choli [55]

Answer: $\frac{\sqrt{85}}{7}$

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

(7, 6)

Use Pythagorean Theorem to find the hypotenuse:

7² + 6² = c²

49 + 36 = c²

85 = c²

√85 = c

adjacent = 7, opposite = 6, hypotenuse = √85

sec θ = $\frac{hypotenuse}{adjacent}$ = $\frac{\sqrt{85}}{7}$

8 0

3 years ago

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Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$

Doing the operations inside of the brackets the derivatives are:

1 ) $(\frac{d((1/2)t^2)}{dt} )^2= t^2$

2) $\frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1$

Entering these values of the integral is

$r(t)= \int\limits^{16}_{0} \sqrt{t^2 +2t+1} dt$

It is possible to factorize the quadratic function and the integral can reduced as,

$r(t)= \int\limits^{16}_{0} (t+1) dt= \frac{t^2}{2} + t$

Thus, evaluate from 0 to 16

$\frac{16^2}{2} + 16$

The value is $r= 144 units$

5 0

3 years ago

The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m

Keith_Richards [23]

Answer:

a) $\left(x,y\right)=\left(4.95,-4.95\right)$

b) $r\angle\theta = 7\angle0.5236\,\text{radians}$

Step-by-step explanation:

Polar coordinates are represented as: $r\angle\theta$ , where 'r' is the length (or magnitude) of the line, and ' $\theta$ ' is the angle measured from the positive x-axis.