The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle

Answers

Answer 1
Answer:

Answer:

  18√2

Step-by-step explanation:

The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.

  36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle


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88.98 in the smallest bills

Answers

1 50$
1 20$
1 10$
1 5$
3 1$
1 0.50$ 1half dollar
1 0.25$ 1quater
2 0.10$ 2dimes
3 0.01$ 3pennies

Please help me understand I am confused

Answers

9514 1404 393

Explanation:

a) The velocity curve is linearly increasing from 0 to 6 m/s over a period of 2 seconds, then linearly decreasing from 6 m/s to 0 over the same period. The acceleration is the rate of change of velocity, so for the first half of the motion the acceleration is a constant (6 m/s)/(2 s) = 3 m/s². Similarly, over the second half of the motion, the acceleration is a constant (-6 m/s)/(2 s) = -3 m/s².

The distance traveled is the integral of the velocity, so the linearly increasing velocity will cause the distance vs. time curve to have a parabolic shape. The shape will likewise be parabolic, but with decreasing slope, as the velocity ramps down to zero. Overall, the distance versus time curve will have an "S" shape.

The motion (position and velocity) will be continuous, but the acceleration will not be. There will be a significant "j.erk" at the 2-second mark where acceleration abruptly changes from increasing the velocity to braking (decreasing the velocity).

__

b) The attachment shows the (given) velocity curve in meters per second and its integral, the position curve, in meters.

The integral in the attached works nicely for machine evaluation. For hand evaluation, it is perhaps best written piecewise:

  s(t)=\begin{cases}\displaystyle\int_0^t{3x}\,dx\qquad\text{for $x\le2$}\n\n\displaystyle6+\int_2^t{(12-3x)}\,dx\qquad\text{for $2<x\le4$}\end{cases}

I am a 3-digit number. If you switch my first and last digits, I decrease by 297. Also, mymiddle digit is 6 less than my first digit, which is 2 less than 2 times my last digit. What
number am I?

Answers

Answer:

  • 865

Step-by-step explanation:

Let the 3-digit number is abc = 100a + 10b + c.

We have:

  • 100a + 10b + c - 100c - 10b - a = 297
  • b = a - 6
  • a = 2c - 2

Simplify the first equation:

  • 99a - 99c = 297
  • a - c = 3
  • a = c + 3

Solve for c by substitution:

  • 2c - 2 = c + 3
  • 2c - c = 3 + 2
  • c = 5

Find a:

  • a = 3 + 5 = 8

Find b:

  • b = 8 - 2 = 6

The number is:

  • 865

. Given the following diagram. (a) Name the minor arc __________ Name the major arc ___________ (b) If the minor arc is 112°, what is the measure of the rest of the circle arc length? _____________ (c) Which line is the tangent? ___________ Which line is the secant? __________ (d) If XY is 11 and UX is 9, what is the length of UV? Show all work or no credit.

Answers

Answer:

  • (a) minor arc: XY; major arc: XVY
  • (b) XVY = 248°
  • (c) tangent: UV; secant: UX
  • (d) UV = 6√5

Step-by-step explanation:

(a) Any pair of points on the circle that are separated by less than the diameter will define a minor arc. (The minor arc is the shortest arc of the circle between the points.) Possible minor arcs in this diagram are ...

  VX, VY, XY

The corresponding major arc is usually named by adding the name of a point between the two endpoints that is not on the minor arc. For the minor arcs above, the corresponding major arcs are ...

  VYX, VXY, XVY

Given that part (b) tells us the minor arc of interest is 112°, we assume that arc is the one subtended by the chord: XY.

Then, per the discussion above, the corresponding major arc is XVY.

___

(b) The sum of major and minor arcs is the whole circle, 360°. So, the measure of the major arc is ...

  360° -112° = 248°

___

(c) A tangent line intersects a circle at exactly one point. It is perpendicular to a radius to that point of intersection. The tangent line in this diagram is UV.

A secant intersects a circle in two places. The portion of the secant between the points of intersection is called a chord. The secant line UX contains the chord XY.

___

(d) A rule of secants (and chords) is that the product of distances from where the secants (or chords) meet to the two intersection points with the circle is the same. For a tangent line, effectively, the two points of intersection are at the same distance. This means ...

  UV·UV = UX·UY

  UV² = 9·(9+11) = 180

  UV = √180 = √(6²·5)

  UV = 6√5 ≈ 13.42

_____

The attached figure is drawn to scale with arc XY being 112°.

Answer:

(a) minor arc: arc VX

    major arc: arc VYX

(b) 248 degrees

(c) Tangent: UV

    Secant: UY

Step-by-step explanation:

(b) 360 - 112 = 248

(c) UV crosses on the circumference of the circle at exactly one point

    UY crosses through the circle at exactly two points

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y 2 ( y 2 − 4 ) = x 2 ( x 2 − 5 ) , ( 0 , − 2 ) (devil's curve) y2(y2-4)=x2(x2-5), (0,-2) (devil's curve)

Answers

Answer:

y = -2

Step-by-step explanation:

To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx

The equation is

y^2(y^2-4)=x^2(x^2-5)

implicit differentiation give us

(d)/(dx)[y^2(y^2-4)=x^2(x^2-5)]\n\n2y(dy)/(dx)(y^2-4)+y^2(2y(dy)/(dx))=2x(x^2-5)+x^2(2x)\n\n4y^3(dy)/(dx)-8y(dy)/(dx)=2x^3-10x+2x^3\n\n(dy)/(dx)=(4x^3-10x)/(4y^3-8y)

But we know that

m=(dy)/(dx)\ny=mx+b

Hence, for the point (0,-2) and by replacing for dy/dx

m=(dy)/(dx)_((0,-2))=(4(0)+10(0))/(4(-2)^3-8(-2))=0

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:

y=(0)x+b = -2

HOPE  THIS HELPS!!

In order to find the equation of the tangent line to the curve y²(y² - 4) = x²(x² - 5) at the point (0, -2), we will use the method of implicit differentiation. Here are the steps:

Step 1: Differentiate Each Side of the Given Equation with Respect to x

Applying the chain rule to differentiate y²(y² - 4) with respect to x gives:
2y*y'(y² - 4) + y²*2y*y' = d/dx [y²(y² - 4)]
The chain rule is also applied to differentiate x²(x² - 5) with respect to x, yielding:
2x(x² - 5) + x²*2x = d/dx [x²(x² - 5)]

Step 2: Equate the Two Expressions Found from Step 1 and Solve for y'

2y*y'(y² - 4) + y²*2y*y' = 2x(x² - 5) + x²*2x

This equation can be solved by isolating y' (the derivative of y with respect to x), which represents the slope of the tangent line.

Step 3: Use the Given Point (0, -2) to Find the Slope of the Tangent Line

Substitute x = 0 and y = -2 into the equation found in Step 2 to get the specific value for the slope at the given point.

Step 4: Use the Point-Slope Form of the Line to Write the Equation of the Tangent Line

The point-slope form of the line y - y₁ = m(x - x₁) can be used to write the equation of the tangent line. We substitute for x₁ and y₁ with the coordinates of the given point (0, -2), and m with the slope found from Step 3.

The resulting equation represents the tangent line to the curve at the given point (0, -2). Please note that the full calculation may result in a complex slope due to the nature of the given curve equation. Nonetheless, this process illustrates the application of implicit differentiation and the point-slope form of a line in finding the equation of a tangent line to a curve.

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Wendell’ Plumbing Supply sold metal piping at $36.50 per 15 yard length. What would75.4 meter of piping cost? 1.0 meter = 1.09 yards

Answers

The answer would be $198.93