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2 years ago

5

Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between

the both boats after two hours.

1 answer:

ivolga24 [154]2 years ago

7 0

Answer:

197.93 km

Step-by-step explanation:

Let the base camp is point A and boats' locations after two hours are points B and C.

By connecting the three points together we get a triangle ABC with sides:

AB = 50*2 = 100 km
AC = 70*2 = 140 km

The angle between AB and AC is:

60 + 50 = 110 degrees (opposite directions from south)

We are looking for the distance BC, which can be found by using the law of cosines:

BC² = AB² + AC² - 2AB*AC*cos ∠BAC

BC² = 100² + 140² - 2*100*140*cos 110°
BC² = 39176.56 (rounded)
BC = √39176.56 = 197.93 km (rounded)

The distance between the boats is 197.93 km.

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. Given ????(5, −4) and T(−8,12):

damaskus [11]

Answer:

a) $y=\dfrac{13x}{16}-\dfrac{129}{16}$

b) $y = \dfrac{13x}{16}+ \dfrac{37}{2}$

Step-by-step explanation:

Given two points: $S(5,-4)$ and $T(-8,12)$

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: $y = mx + c$ where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

$m = \dfrac{12 - (-4)}{(-8) - 5}$

$m = \dfrac{-16}{13}$

to find the perpendicular of this gradient: we'll use:

$m_1m_2=-1$

both $m_1$ and $m_2$ denote slopes that are perpendicular to each other. So if $m_1 = \dfrac{12 - (-4)}{(-8) - 5}$ , then we can solve for $m_2$ for the slop of ther perpendicular!

$\left(\dfrac{-16}{13}\right)m_2=-1$

$m_2=\dfrac{13}{16}$ :: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope $m$ and the points $(x,y)$ . And plug into the equation: $(y - y_1) = m(x-x_1)$

side note: you can also use the $y = mx + c$ to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

$(y - y_1) = m(x-x_1)$

we have the slope of the perpendicular to ST i.e $m=\dfrac{13}{16}$

and the line should pass throught S as well, i.e $(5,-4)$ . Plugging all these values in the equation we'll get.

$(y - (-4)) = \dfrac{13}{16}(x-5)$

$y +4 = \dfrac{13x}{16}-\dfrac{65}{16}$

$y = \dfrac{13x}{16}-\dfrac{65}{16}-4$

$y=\dfrac{13x}{16}-\dfrac{129}{16}$

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for $T(-8,12)$

$(y - y_1) = m(x-x_1)$

$(y -12) = \dfrac{13}{16}(x+8)$

$y = \dfrac{13x}{16}+ \dfrac{104}{16}+12$

$y = \dfrac{13x}{16}+ \dfrac{37}{2}$

this is the equation of the line that is perpendicular to ST and passes through T

7 0

3 years ago

Can you help me with number 5?

Verizon [17]

We can divide that up into two rectangles, say the bottom one 8 feet wide and 2 feet high. That leaves 5.5 by 6-2=4 feet for the other.

Cost = price × area = 2.25(8×2 + 5.5×4) = $85.50

Answer: $85.50

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3 years ago

Not a question. just wanted to say I'm making a wand and it looks pretty sick

zhannawk [14.2K]

Answer:

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Step-by-step explanation:

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3 years ago

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. Which pair of angles are congruent? *

Pachacha [2.7K]

Answer:

a

Step-by-step explanation:

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3 years ago

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If you are self-employed, you don't have to pay FICA on all your salary, just on 92.35% of it. If your salary is $128,255 what i

Artist 52 [7]

Answer:

The amount that I am required to pay monthly as FICA if my salary remains constant is $18,121.85¢

Step-by-step explanation:

Federal insurance contributions act is a law that mandates all employers of labour to withhold medicare and certain taxes from the wages that are paid to employees or workers. These taxes are remitted to the government later which is then used for the provision of basic amenities and quality health care.

Since, I am only required by law to pay FICA on only 92.35% of my monthly salary, we need to calculate the the actual amount that makes up 92.35 percent of my monthly salary.

If $128,255 is my current monthly salary, then 92.35% of it will be:

92.35/100 × 128,255

= 0.9235 × 128,255

= $118,443.49¢

This is the part of his monthly salary that he is required by law to pay FICA on.

Then, if FICA is 15.3% of a worker's taxable income, then I am required to pay 15.3% of the taxable $118,443.49¢ since I am self employed and mustn't pay it on the entire $128,255 that I earn monthly.

My monthly FICA contribution is then:

15.3/100 × 118,443.49

= 0.153 × 118,443.49

= $18,121.85¢.

Therefore, if my salary remains constant, the amount that I am required by law to pay monthly as FICA is $18,121.85

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4 years ago

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