What is the correct solution to the inequality?

Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,

irakobra [83]

Question:

Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,

A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41° How tall is the lighthouse?

Answer:

The height of lighthouse is 52.2 yards

Solution:

Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41 degree

The diagram is attached below

Consider a right angled triangle ABC

AB is the height of the lighthouse

BC is the distance between the base of a lighthouse and Photographer

As per given, BC = 60 yards

Angle between the ground and the top of the lighthouse is 41 degree

Angle ACB = 41 degree

To find: height of lighthouse i.e AB = ?

We know that,

$tan(\angle ACB) = \frac{Perpendicular}{Base}$

Here Base is BC and perpendicular is AB

$\tan 41^{\circ}=\frac{A B}{B C}$

Substituting the values,

$\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}$

Thus the height of lighthouse is 52.2 yards

8 0

3 years ago

One watering system needs about three times as long to complete a job as another warning system when both systems operate at the

algol13

Answer:

One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

Step-by-step explanation:

Given:

Both the system can complete the job = 9 minutes

We need find the time required by each system to do the job.

Solution:

Let the time required by another watering system to complete the job be 'x' mins.

Now given:

One watering system needs about three times as long to complete a job as another watering system.

Time required by one watering system = $3x$

Rate to complete the job by another watering system = $\frac{1}{x}\ job/min$

Rate to complete the job by One watering system = $\frac{1}{3x}\ job/min$

Rate at which both can complete the job = $\frac{1}{9}\ job/min$

So we can say that;

Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.

framing in equation form we get;

$\frac{1}{x}+\frac{1}{3x}=\frac19$

Now taking LCM to make the denominator common we get;

$\frac{1\times3}{x\times 3}+\frac{1\times1}{3x\times1}=\frac19\\\\\frac{3}{3x}+\frac{1}{3x}=\frac19\\\\\frac{3+1}{3x}=\frac{1}{9}\\\\\frac{4}{3x}=\frac{1}{9}$

By Cross multiplication we get;

$4\times9 =3x\\\\3x =36$

Dividing both side by 3 we get;

$\frac{3x}{3}=\frac{36}{3}\\\\x=12\ min$

Time required by One watering system = $3x =3\times 12 =36\ min$

Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

6 0

3 years ago

13 + 3y= 37 solve for y

Nikitich [7]

Answer:

y = 8

Step-by-step explanation:

Step 1: Write out equation

13 + 3y = 37

Step 2: Subtract 13 on both sides

3y = 24

Step 3: Divide both sides by 3

y = 8

3 0

3 years ago

Read 2 more answers

Hey! Can someone check my answers?

Andrew [12]

The greatest common factor is the biggest number taken from the values.

Q1. The answer is A. 5y^6

$20 y^{9} +5 y^{6}= 4*5 y^{9}+5 y^{6}$
Since $x^{a}* x^{b} =x^{a+b}$ , then $x^{9}= x^{3}* x^{6}$

Back to our expression:
$4*5 y^{9}+5 y^{6}=4*5 y^{3}*y^{6}+5 y^{6}=4 y^{3}*5y ^{6}+ 5y ^{6}*1=5 y^{6} (4y ^{3} +1)$
The greatest common factor is thus $5 y^{6}$

Q2. The answer is D. 12xy^2

$12x y^{5}+60 x^{4} y^{2} -24 x^{3} y^{3}=12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}$
We will use the rule $x^{a}* x^{b} =x^{a+b}$ to factorise the exponents:
$12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}= \\ =12x*y^{2}*y^{3}+5*12*x* x^{3} *y^{2}-2*12x* x^{2} *y*y^{2}= \\ =12xy^{2}*y^{3}+12xy^{2}*5 x^{3} -12xy^{2}*2 x^{2} y= \\ =12xy^{2}(y^{3}+5 x^{3}-2 x^{2} y)$
The greatest common factor is thus $12xy^{2}$

3 0

3 years ago

What is 3 1/3 divided by 1/3

saveliy_v [14]

Convert 3 1/3 into a improper fraction:
= 10/3

Then flip the other fraction around and multiply them together:
1/3 -> 3/1
(10*3)/(3*1) = 30/3 = (30/3)/(3/3) = 10/1 = 10

The answer is 10

4 0

4 years ago

Read 2 more answers