Ask question

Ask question

All categories

3 years ago

12

Two scuba divers, Jim and Tara, are 20m apart below the surface of the water. They both spot a shark that is below them. The ang

le of depression from Jim to the shark is 47 degrees, and the angle of depression from Tara to the shark is 40 degrees. How far is Jim from the shark?

1 answer:

LenaWriter [7]3 years ago

4 0

Answer:

Jim is 12.87 meters away from the shark.

Step-by-step explanation:

We are given that,

Distance between Jim and Tara = 20 meters.

The angle of depression of the shark from Jim and Tara is 47° and 40° respectively as shown in the figure below.

So, the third angle of the triangle formed is given by,

47° + 40° + ∠S = 180°

i.e. ∠S = 180° - 87°

i.e. ∠S =93°

So, now using the sine ratio formula, we have,

$\frac{20}{\sin 93}=\frac{x}{\sin 40}$

i.e. $x=\frac{20\times 0.6428}{0.9986}$

i.e. $x=\frac{12.856}{0.9986}$

i.e. x = 12.87 meters

Thus, Jim is 12.87 meters away from the shark.

You might be interested in

A female executive selecting her wardrobe purchased five blazers, three blouses, and five skirts in coordinating colors. How man

Viktor [21]

She can create a total of 75 ensembles

8 0

3 years ago

PLS help ill give 50 points to the person who answers correctly The instructions of an art project tell students to cut a piece

MrMuchimi

Answer:

no guaranteed classification

Step-by-step explanation:

We know that the quadrilateral has two pairs of congruent sides. Both a rectangle and a parallelogram have two pairs of congruent sides. The difference between them is their angles. But we don't know anything about the angles in the figure, so we cannot know which kind it is.

4 0

3 years ago

The baltimore ravens kansas city chiefs

FinnZ [79.3K]

What’s your question

6 0

3 years ago

Read 2 more answers

Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

<u>case A)</u> $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

<u>case B)</u> $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

<u>case C)</u> $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

<u>case D)</u> $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

3 years ago

Read 2 more answers

Tamira invests $5,000 in an account that pays 4% annual interest. How much will there be in the account after 3 years if the int

Talja [164]

Answer:

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

There will be $5636.359 in the account after 3 years if the interest is compounded monthly

Step-by-step explanation:

Tamira invests $5,000 in an account

Rate of interest = 4%

Time = 3 years

Case 1:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 1

Formula : $A=P(1+r)^t$

$A=5000(1+0.04)^3$

A=5624.32

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

Case 2:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 2

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{2})^{2 \times 3}$

A=5630.812

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

Case 3:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{4})^{4 \times 3}$

A=5634.125

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

Case 4:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=5000(1+\frac{0.04}{12})^{12 \times 3}$

A=5636.359

There will be $5636.359 in the account after 3 years if the interest is compounded monthly

8 0

3 years ago