Kai has begun to list, in ascending order, the positive integers which are not factors of

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

b) The house is 5 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x, hence:

(x - 3)² + (y - 4)² = 9

(x - 3)² + (5 - 4)² = 9

(x - 3)² + 1 = 9

(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

8 0

2 years ago

The grades on a history midterm at Gardner Bullis are roughly symmetric with μ = 69 μ=69mu, equals, 69 and σ = 3.5 σ=3.5sigma, e

katrin2010 [14]

Answer:

-1.14

Step-by-step explanation:

The given information in statement is

mean=μ=69

standard deviation=σ=3.5

Let X be the Ishaan's exam score

X=65

The Z score can be computed as

$z=\frac{x-mean}{standard deviation}$

$z=\frac{65-69}{3.5}$

z=-1.1429

z=-1.14 (rounded to two decimal places).

Thus, the computed z-score for Ishaan's exam grade is -1.14.

4 0

2 years ago

1. The graph shows the number of miles Peter's car traveled and the gallons of gas used.

steposvetlana [31]

Answer:

C. d = 24g

Step-by-step explanation:

The problem boils down to determining the ratio between d and g. That is, for some equation ...

d = k·g

we want to determine the value of k. Solving the equation for that value, we find ...

k = d/g

So, we need only to read a point from the graph with sufficient accuracy to determine a good estimate for k.

(gallons, miles) = (g, d) = (5, 120) is a suitable point

Then ...

k = d/g = 120/5 = 24

The equation is d = 24g.

4 0

2 years ago

Complete the missing parts of the paragraph proof. Draw a perpendicular from P to AB. Label the intersection C. We are given tha

zvonat [6]

1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.

When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent.

2) We know that angles PCA and PCB are right angles by the definition of perpendicular.

Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.

3) PC ≅ PC by the reflexive property congruence.

The reflexive property congruence states that any shape is congruent to itself.

4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent).

CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.

5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector.

The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB.

6 0

2 years ago

Read 2 more answers

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. T

Nina [5.8K]

Given:
12-foot wire is secured from the ground to the tree at a point 10 feet off the ground.
The tree meets the ground at a right angle.

When you visualize the scenario, the 12 foot wire would be the measure of the hypotenuse and the 10 feet off the ground will be the short leg or opposite. The long leg or adjacent is unknown.

We need to solve for sine theta because the value of hypotenuse and opposite is given.

sin θ = opposite / hypotenuse
sin θ = 10 feet / 12 feet
sin θ = 0.833
θ = 0.83 / sin
θ = 56°

The wire would meet the ground at approximately 56° angle.

3 0

2 years ago