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2 years ago

A Circle has a circumference of 62.8 miles. What is the radius of the circle

Mathematics

1 answer:

Archy [21]2 years ago

3 0

62.8/pi = 20
20 is the diameter, which is twice the radius
The radius is 10 miles

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Find the equation of the tangent line and normal line to the curve y=(6+4x)2 at the point (6,900). Write the equations of the li

Ksenya-84 [330]

Answer:

Equation of the tangent to the curve

y = 240x - 215994

Equation of the normal

y = (-1/240)x + 9.75 = - 0.00417x + 9.75

Step-by-step explanation:

y = (6 + 4x)² = 36 + 48x + 16x² = 16x² + 48x + 36

dy/dx = 32x + 48

At the point (6,900),

dy/dx = 32(6) + 48 = 240

Equation of the tangent at point (a,b) is

(y - b) = m(x - a)

a = 6, b = 900, m = 240

y - 6 = 240(x - 900)

In the y = mx + b form,

y - 6 = 240x - 216000

y = 240x - 215994

The slope of the normal line = -(1/slope of the tangent line) (since they're both perpenducular to each other)

Slope of the normal line = -1/240

Equation of normal

y - 6 = (-1/240)(x - 900)

y - 6 = (-x/240) + 3.75

y = (-1/240)x + 9.75

y = - 0.00417x + 9.75

8 0

3 years ago

this value of y is a of t(y). because is for all values of y, it follows that the value of y found in the previous step corres

Radda [10]

For f(t) = 3 sin(t), the minimum is -3, the maximum is 3.

For additional information:

The period T of the function y=3sin(4t) is;

The period of y = 3 sin (4t) is (2pi) / 4 = pi / 2

The sine function with amplitude A = 0.75 and period T = 10, is

y = 0.75 sin( (2pi / 10) x )

= 0.75 sin( (pi/5) t)

y(4) = 0.75 sin( (pi/5) (4) )

= 0.75 sin ( (4/5) pi ) = .4408

Drawing the sine and cosine function on the same plot shows

that they are identical except for a horizontal shift.

The cosine

function leads the sine function by a shift of (2pi/4) = pi/2.

For the last part, y(4) = 0.75 cos( (2pi/10) (4) ) = - 0.6067

To learn more

visit : brainly.com/question/4842623

#SPJ4

5 0

2 years ago

Turn -2x+4y=0 into slope-intercept form

yanalaym [24]

Y=1/2x +0. You add the 2x to the other side, and then divide everything by 4 to have only 1y.

3 0

2 years ago

21.) A rectangle has an area of 36 square units. As the length and width change, what do you know about their

natima [27]

Answer:

the length and the width are inversely proportional to each other ( $l=\frac{36}{w}$ or $w=\frac{36}{l}$ )

Step-by-step explanation:

Let

l units = length of the rectangle,

w units = width of the rectangle.

The area of the rectangle is

$\text{Area}=\text{Length}\cdot \text{Width}$

A rectangle has an area of 36 square units, so

$l\cdot w=36$

Complete the table with some values of l and w that fit the previous formula:

$\begin{array}{ccc}\text{Length}&\text{Width}&\text{Area}\\ \\36&1&36\cdot 1=36\ un^2.\\18&2&18\cdot 2=36 \ un^2.\\12&3&12\cdot 3=36\ un^2.\\ 9&4&9\cdot 4=36\ un^2.\\l&w&l\cdot w=36 \ un^2.\end{array}$

As you can see, the length and the width are inversely proportional to each other ( $l=\frac{36}{w}$ or $w=\frac{36}{l}$ )

4 0

3 years ago

Work out, giving your answer in its simplest form

Svetach [21]

Answer:

Step-by-step explanation:

⅔ ×3³/5

⅔×18/5

10×54 = 540

15 15

=36

5 0

1 year ago