1.

a surveyor measures the distance to the two landmarks as shown in the diagram what is the distance d. between the landmarks

Inessa [10]

<h3>The distance between two landmarks is 123 meters</h3>

<em><u>Solution:</u></em>

We have to find the distance between two landmarks

<em><u>Use the law of cosines</u></em>

The third side of a triangle can be found when we know two sides and the angle between them

$c^2 = a^2 + b^2 - 2ab\ cos c$

Here, angle between 90 meters and 130 meters is 65 degrees

From figure,

a = 90

b = 130

c = d

Therefore,

$d^2 = 90^2 + 130^2 - 2(90)(130)\ cos 65\\\\d^2 = 8100 + 16900 - 23400\ cos\ 65\\\\d^2 = 25000 - 23400 \times 0.4226\\\\d^2 = 25000 - 9889.267\\\\d^2 = 15110.73\\\\d = 122.92\\\\d \approx 123$

Thus, the distance between two landmarks is 123 meters

8 0

3 years ago

Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in

UNO [17]

Answer:

$rate\ of\ increase = 28.8\ billion\ dollars\ per\ year$

model: $y = 28.8(t-2003) + 2$

profit in year 2017: $y = 405.2\ billion\ dollars$

Step-by-step explanation:

The sales increased from 2 billion dollars to 146 billion dollars in five years, so to find the increase in billion dollars per year, we just need to divide the increase by the amount of time:

$rate\ of\ increase = (146 - 2)/5 = 144 / 5 = 28.8\ billion\ dollars\ per\ year$

To construct a model for these sales, we can use the year 2003 as the initial point of a linear equation:

$y = ax + b$

the variable y will represent the profit in billion dollars, the variable x will represent our time, so we can use (t - 2003) in its place to represent the number of years since 2003 (t is the year we want to calculate), the constant 'a' will be our rate of 28.8, and the constant 'b' is the inicial value for the year 2003, that is, 2 (billions). So we have:

$y = 28.8(t-2003) + 2$

In the year 2017, we would have:

$y = 28.8(2017-2003) + 2$

$y = 28.8*14 + 2$

$y = 405.2\ billion\ dollars$

6 0

3 years ago

Which linear function represents the line given by the point slope equation y + 7= 2/3(x+6)

Andrews [41]

Hello from MrBillDoesMath!

Answer: f(x) = (2/3)*x -3 -- which is not a provided answer..

Discussion:

We are given that y + 7 = (2/3) * (x + 6). Multiply out the right hand side:

y + 7 = (2/3) * x + (2/3) * 6 = (2/3) *x + 12/3

= (2/3)*x + 4

Subtract 7 from both sides:

y + 7 - 7 = (2/3)*x + 4 - 7

or

y = (2/3)*x -3

Thank you,

MrB

y + 7= 2/3(x+6)

7 0

3 years ago

James invested $4,000 at 5% interest per year; how long will it take him to earn $200 in simple interest?

tester [92]

Answer:

It takes 1 year.

Step-by-step explanation:

You have to apply simple interest formula, I = (P×R×T)/100 where I represent interest amount, P is principle, R is interest rate and T is number of years :

$I = \frac{PRT}{100}$