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2 years ago

Leo is constructing a tangent line from point Q to circle P. What is his next step?

Mathematics

1 answer:

artcher [175]2 years ago

7 0

Answer:

Mark the point of intersection S of circles R and P, and construct line QS.

Step-by-step explanation:

In the figure attached, the problem is shown. The construction of the tangent lines from point Q to circle P is almost done. The last step is to draw the lines that pass through point Q and the intersection of the circles.

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The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%. Between station A and station B, which

saveliy_v [14]

Answer:

x = 3.1 %

Step-by-step explanation:

Let x be the slope the track.

Given:

Distance between station A and B = 270 ft

Track rise = $8\frac{1}{2} = \frac{17}{2} = 8.5\ ft$

We need to find the slope of the railway track between station A an B.

Solution:

The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.

We know that slope of the railway track is equal to gradient of the tracks.

So. the slope of the railway track is defined as the ratio of the distance between the stations and track rises.

$Slope\ of\ the\ the\ tracks =\frac{Distance\ between\ two\ stations}{track\ rises}$

$x=\frac{8.5}{270}\times 100$

x = 3.1 %

So x = 3.1 % less than the maximum grade allowed between two stations in a rapid-transit rail system is 3.5%.

Therefore, x = 3.1 % meets the rapid-transit rail standards.

5 0

1 year ago

Find the value of a/b when a = $13.93 and b= 0.07

lara [203]

Answer:

If you divide the numbers you should get 199.

5 0

1 year ago

Flying fish use their pectoral fins like airplane wings to glide through the air. Suppose a flying fish reaches a maximum height

GrogVix [38]

The flight is in the shape of a parabola with a vertex 5 feet above the water and 1/2 * 33 = 16.5 feet horizontally from the point of leaving the water

y = a(x - h)^2 + k

where (h,k) is the vertex of the parabola and here it is (5 , 16.5), so we have the function:-

y = a(x - 16.5)^2 + 5

when x = 0 y = 0 so

0 = a(-16.5)^2 + 5

which gives a = -0.018365

So our function for the flight path is

y = -0.018365(x - 16.5)^2 + 5 Answer

7 0

1 year ago

Read 2 more answers

One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN

VLD [36.1K]

Answer:

See the proof below

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

Hence the coordinate of Q is (4, 1)

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

Hence the coordinate of R is (6,5)

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

8 0

1 year ago

Enter the values for a, b, and c in the factored form. P(x) = (x – 5)(ax2 + bx + c)

pochemuha

Ax^3 - 5ax^2 + 5bx + cx -5c

8 0

2 years ago

Read 2 more answers