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3 years ago

Trig problem i need help with

Mathematics

1 answer:

zaharov [31]3 years ago

8 0

Answer:

Distance between boat and light house = 134 m

Step-by-step explanation:

Given data:

Height of light house = 46 m

Angle of elevation from boat to the top of light house = 19°

From the data given to us we can construct a right triangle ABC.

For the Δ ABC

AB= 46 m

∠C= 19°

We can apply trigonometric ratio to find side BC which is the distance of light house from the boat.

$\tan19\°=\frac{AB}{BC}$

Multiplying both sides by BC.

$BC\tan19\°=\frac{AB}{BC}\times BC$

$BC\tan19\°=AB$

Dividing both sides by tan 19°

$\frac{BC\tan19\°}{tan 19\°}=\frac{AB}{tan 19\°}$

$BC=\frac{AB}{tan 19\°}$

Substituting value of AB and tan 19°

$BC=\frac{46}{0.344}$

$BC=133.59\ m\approx134\ m$

Distance between boat and light house = 134 m

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. Find the inverse of the function below on the given interval and write it in the form yequalsf Superscript negative 1 Baseline

Elena L [17]

Answer:

The inverse of the function is $f^{-1}(x)=\frac{x-5}{3}$ .

Step-by-step explanation:

The function provided is:

$f (x)=3x+5$

Let $f(x)=y$ .

Then the value of x is:

$y=3x+5\\\\3x=y-5\\\\x=\frac{y-5}{3}$

For the inverse of the function, $x\rightarrow y$ .

⇒ $f^{-1}(x)=\frac{x-5}{3}$

Compute the value of $f[f^{-1}(x)]$ as follows:

$f[f^{-1}(x)]=f[\frac{x-5}{3}]$

$=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x$

Hence proved that $f[f^{-1}(x)]=x$ .

Compute the value of $f^{-1}[f(x)]$ as follows:

$f^{-1}[f(x)]=f^{-1}[3x+5]$

$=\frac{(3x+5)-5}{3}\\\\=\frac{3x+5-5}{3}\\\\=x$

Hence proved that $f^{-1}[f(x)]=x$ .

8 0

3 years ago

2.14x - 42.9 for x = 22.4 ? A. -18.36 B. 5.026 C. 47.939 D. 90.839

Fynjy0 [20]

Answer:

Step-by-step explanation:

Your answer would be B., because you would multiply

2.14 x 22.4 =

47.939

then you will subtract that by 42.9

47.939 - 42.9 =

5.026

7 0

3 years ago

Plz help asap thank youuu

wariber [46]

Answer:

1. y = 0, b/a

2. y = 0, a/b

3. y =0, c/b

4. y =0, c/a

Step-by-step explanation:

The slope formula for y = mx + b which is known as standard form is Ax + By ≥ C

slope = A/B

x-intercept = C/A

y-intercept = C/B

and now we are dueling with y, so we will use y-intercept

1. cx + ay = b

where c is x, a = y and b=c

Y-int = C/B

y = 0, b/a

2. cx + by = a

y = 0, a/b

3. ax + by = c

y =0, c/b

4. bx+ ay = c

y =0, c/a

Hope this helps

7 0

3 years ago

2 b) the urcumference circle=2tr. What is the diametly = 20km? T = 3.14 (3)

zhuklara [117]

comfort room

Step-by-step explanation:

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3 0

3 years ago

Car A's fuel efficiency is 34 miles per gallon of gasoline, and car B's fuel efficiency is 23 miles per gallon of gasoline. At t

Verdich [7]

Answer:

22 more gallons.

Step-by-step explanation:

Given:

Car A's fuel efficiency is 34 miles per gallon of gasoline.

Car B's fuel efficiency is 23 miles per gallon of gasoline.

Question asked:

At those rates, how many more gallons of gasoline would car B consume than car A on a 1,564 miles trip?

Solution:

Car A's fuel efficiency is 34 miles per gallon of gasoline.

By unitary method:

Car A can travel 34 miles in = 1 gallon

Car A can travel 1 mile in = $\frac{1}{34} \ gallon$

Car A can travel 1564 miles in = $\frac{1}{34} \times1564=46\ gallons$

Car B's fuel efficiency is 23 miles per gallon of gasoline.

Car B can travel 23 miles in = 1 gallon

Car B can travel 1 mile in = $\frac{1}{23} \ gallon$

Car B can travel 1564 mile in = $\frac{1}{23} \times1564=68\ gallons$

We found that for 1564 miles trip Car A consumes 46 gallons of gasoline while Car B consumes 68 gallons of gasoline that means Car B consumes 68 - 46 = 22 gallons more gasoline than Car A.

Thus, Car B consumes 22 more gallons of gasoline than Car A consumes.

6 0

3 years ago