X^2+y^2=25 Find the distance of point (x,y) from origin.

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is <em>35.11 ft</em>.

3 0

3 years ago

The perimeter of a rectangular garden is 37.5 feet. The width is x, and the length is 15 ft. Use the equation 2(x + 15) = 37.5 t

charle [14.2K]

Answer:

2.5

Step-by-step explanation:

37.5/15=2.5

3 0

3 years ago

Read 2 more answers

MCR3U1 Culminating 2021.pdf

11111nata11111 [884]

Answer:

(a) $y = 350,000 \times (1 + 0.07132)^t$

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

(c) The rate of increase of the population as a percentage per hour is 7.132%

(d) The doubling time of the population is approximately, 10.06 hours

Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

The time the colony grows, t = 12 hours

The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

$y = a \cdot (1 + r)^t$

Plugging in the values, we get;

$800,000 = 350,000 \times (1 + r)^{12}$

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The model is therefore;

$y = 350,000 \times (1 + 0.07132)^t$

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

(ii) The population after 24 hours is given as follows;

y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571

By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour = r × 100

∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

$2 \cdot y = y \times (1 + 0.07132)^t$

Therefore, we have;

2·y/y =2 = $(1 + 0.07132)^t$

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

8 0

3 years ago

In the diagram, the length of segment AB is 10 units and the radius of the circle centered at A is 4 units. Use this to create t

Leni [432]

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.

The two triangles can be made as shown below, the bigger triangle will be an equilateral triangle with each side measuring 10 units, while the smaller triangle will be an isosceles triangle and the measure of the same length side will be equal to the radius of the circle.

Learn more about Triangle:

brainly.com/question/2773823

#SPJ1

8 0

2 years ago

I need help with this one

Nimfa-mama [501]

One that can’t be solved so D

7 0

4 years ago