I am not sure if you wrote a repeating decimal with the line next to the 0.025 so comment if you need it. If it wasn't repeating it would be simply 1/40 if there is no repeating and you only want 0.025 is a fraction in simplest form.

8 0

4 years ago

Two patrol boats leave Cape May at the same time, the same speed, but on different bearings. One has bearing 41°45

VMariaS [17]

Based on the information given, the computation shows that the distance between them is 2.47 miles.

<h3>Solving the distance.</h3>

Since one has bearing 41°45', this will be: = 41° + (45/60) = 41° + 0.75 = 41.75°.

The other has bearing 59°13'. This will be:

= 59° + (13/60) = 59° + 0.22 = 59.22°.

The difference of the angles will be:

= 59.22° - 41.75°

= 17.47°

Let the distance between them be represented by c. Therefore, we'll use cosine law to solve the question. This will be:

c² = a² + b² - 2ab cos 17.47°

c² = 20² + 20² - (2 × 20 × 20 × 0.19)

c² = 6.07459

c = 2.47

Learn more about distance on:

brainly.com/question/2854969

8 0

2 years ago

Solve the exponential function

nikklg [1K]

Answer:

See below.

Step-by-step explanation:

Just like 18, continue with 19-21. Solve for x by rewriting each equation in log form.

$e^x = 4.9\\\\x = ln 4.9\\\\x = 1.59$

When rewriting the form, the base of the exponent becomes the base of the log.

8 0

4 years ago

Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts.

jasenka [17]

Answer:

We have the function, $f(x)=(x+3)^{2}-4$

On simplifying, we get,

$f(x)=x^2+6x+9-4$

i.e. $f(x)=x^2+6x+5$

Thus, the standard form of the function is $f(x)=x^2+6x+5$ .

Now, the factors of the given functions are (x+1) and (x+5).

<em>Since, the intercept form of the function is the factored form of the function.</em>

So, we have, intercept form of the function is $f(x)=(x+1)(x+5)$ .

Now, we know that,

Value of x-coordinate of the vertex is $\frac{-b}{2a}$ i.e. $\frac{-6}{2\times 1}$ i.e. $\frac{-6}{2}$ i.e. x= -3

Then, $f(-3)=(-3)^2+6\times (-3)+5$ i.e. $f(-3)=9-18+5$ i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>

So, when x=0, we have, $f(0)=0^2+6\times 0+5$ i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>

Then, for f(x)=0, we have $0=x^2+6x+5$ i.e. $0=(x+1)(x+5)$ i.e. x= -1 and x= -5

Thus, the x-intercept are (-1,0) and (-5,0).

8 0

3 years ago