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3 years ago

Find the angle of depression from the top of a lighthouse, 260 feet above water to a ship that's 270 feet offshore?

Mathematics

1 answer:

expeople1 [14]3 years ago

4 0

Answer: OPTION C.

Step-by-step explanation:

Observe the triangle ABC attached.

Notice that the angle of depression is represented with $\alpha$ .

Knowing that the top of a lighthouse is 260 feet above water and the ship is 270 feet offshore, you can find the value of $\alpha$ by using arctangent:

$\alpha= arctan(\frac{opposite}{adjacent})$

In this case you can identify that:

$opposite=260\\adjacent=270$

Therefore, substuting values into $\alpha= arctan(\frac{opposite}{adjacent})$ , you get that the angle of depression is:

$\alpha= arctan(\frac{260}{270})\\\\\alpha=43.92\°$

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If 2 is added to both the numerator and denominator of a fraction its value becomes half. If two is subtracted from both the num

Hitman42 [59]

Answer:

The original fraction is $\frac{6}{14}$ .

Step-by-step explanation:

Solution,

Let the fraction be' $\frac{x}{y}$ '.

Where 'x' is the numerator and 'y' is the denominator.

Now according to question, if 2 is added to both the numerator and denominator the value of the fraction becomes 1/2.

So, framing the above sentence in equation form, we get;

$\frac{x+2}{y+2}=\frac{1}{2}$

On using cross multiplication method, we get;

$2(x+2)=y+2\\\\2x+4=y+2\\\\2x+4-2=y\\\\\therefore\ y=2x+2\ \ \ \ equation\ 1$

Now according to question, if 2 is Subtracted to both the numerator and denominator the value of the fraction becomes 1/3.

So, framing the above sentence in equation form, we get;

$\frac{x-2}{y-2}=\frac{1}{3}$

On using cross multiplication method, we get;

$3(x-2)=y-2\\\\3x-6=y-2\\\\3x-y=-2+6\\\\3x-y=4 \ \ \ \ equation\ 2$

Now Substituting the equation 1 in equation 1 we get;

$3x-y=4\\\\3x-(2x+2)=4\\\\3x-2x-2=4\\\\3x-2x=4+2\\\\x=6$

Now Substituting the value of x in equation 1 we get;

$y=2x+2\\\\y=2\times6+2 = 14$

Hence The original fraction is $\frac{6}{14}$ .

4 0

3 years ago

A baker wanted to enter the apple pie

dimaraw [331]

Answer:

11 pies

Step-by-step explanation:

100-12=88

88/8=11

6 0

3 years ago

Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=2x2i+5y2j+3z2k across the boundary of the recta

aksik [14]

Answer:

The answer is "120".

Step-by-step explanation:

Given values:

$F(x,y,z)=2x^2i+5y^2j+3z^2k \\$

differentiate the above value:

$div F =2 \frac{x^2i}{\partial x}+5 \frac{y^2j}{\partial y}+3 \frac{z^2k }{\partial z} \\$

$= 4x+10y+6z$

$\ flu \ of \ x = \int \int div F dx$

$= \int\limits^1_0 \int\limits^3_0 \int\limits^1_0 {(4x+10y+6z)} \, dx \, dy \, dz \\\\ = \int\limits^1_0 \int\limits^3_0 {(4xz+10yz+6z^2)}^{1}_{0} \, dx \, dy \\\\ = \int\limits^1_0 \int\limits^3_0 {(4x+10y+6)} \, dx \, dy \\\\ = \int\limits^1_0 {(4xy+10y^2+6y)}^3_{0} \, dx \\\\ = \int\limits^1_0 {(12x+90+18)}\, dx \\\\= {(12x^2+90x+18x)}^{1}_{0} \\\\= {(12+90+18)} \\\\=30+90\\\\= 120$

6 0

3 years ago

James divided 144 ounces of water evenly among 4 containers. One of the containers leaked 8 ounces.

Verdich [7]

Answer:

I dont understand your question rither

Step-by-step explanation:

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3 0

3 years ago

A 12 1/2 mile stretch of road needs repaving . A company bids on the repaving project saying they could replace 2 1/4 miles of r

Nataly [62]

2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

8 0

3 years ago