Given that AB = 370 m and AC = 510 m, find
(i) the distance between B and C,
(ii) ACB,
(iii) the bearing of C from B,
(iv) the shortest distance from A to BC.​

Given That AB = 370 M And AC = 510 M, Find(i) The Distance Between B And C,(ii) ACB,(iii) The Bearing

Answers

Answer 1

Answer:

(i) The distance between B and C is approximately 552.9 m

(ii) ∠ACB is approximately 40.49°

(iii) The bearing of C from B is approximately 184.49°

(iv) The shortest distance from A to BC is approximately 331.155 m

Step-by-step explanation:

The given parameters are;

The length of segment AB = 370 m

The length of segment AC = 510 m

The bearing of B from A = 68°

The bearing of C from A = 144°

(i) From the bearing of B from A = 68° and the bearing of C from A = 144°, we have;

∠BAC = 144° - 68° = 76°

∠BAC = 76°

Let A represent ∠BAC, c represent segment AB, b represent segment AC, and a represent segment BC, by cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

By substituting the known values, we get;

a² = 510² + 370² - 2 × 510 × 370 × cos(76°)

a² ≈ 397000 - 91301.3234 ≈ 305698.677

BC = a ≈ √(305,698.677) ≈ 552.9

The distance between B and C, BC ≈ 552.9 m

(ii) By sine rule, we have;

a/(sin(A) = b/(sin(B)) - c/(sin(C))

Therefore;

552.9/(sin (76°)) = 370/(sin(C))

sin(C) = 370/(552.9/(sin (76°))) ≈ 0.649321

C = arcsine(0.649321) ≈ 40.49°

∠C = ∠ACB ≈ 40.49°

(iii) Angle ∠B = ∠ABC = 180° - 76° - 40.49° ≈ 63.51°

The bearing of A from B = 360° - (180° - 68°) = 248°

Therefore, the bearing of C from B ≈ 248° - 63.51° ≈ 184.49°

(iv) The shortest distance from A to BC = 370 m × sin(63.51°) ≈ 331.155 m


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Please answer!! I added a screenshot

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Answer:

S + 2.5S + (2.5S - 3.3)

Step-by-step explanation:

To get the perimeter of ANY shape, simply add up all the sides.

plss
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Answers

Answer:

$6,600

Step-by-step explanation:

231/0.035= 6,600

Ill give brainliest

Describe a situation where you might need to know the percent that something changed.

Answers

Answer:

Change: subtract old value from new value. Example: You had 5 books, but now have 7. The change is: 7−5 = 2. Percentage Change is all about comparing old to new values.

Step-by-step explanation:

hope this helps :)

Answer:

When finding the climate of an area

Step-by-step explanation:

Ex. Rainfall increased 30% since 2019 in florida (not true just an example)


Convert 60 inches to feet. There are 12 inches in a foot

Answers

Answer:

60/12= 5

5 feet

Answer:

5 feet

Step-by-step explanation:

Divide the length value (inches) by 12.

simplify 3 to the 2nd power + 1 x 2

Answers

18 i’m pretty sure (:

How many solutions will this system of equations have??
Please explain your thinking

Answers

7 because I’m smart and I have the expect same problem

Simplify the following by combining like terms: 10 + 7r+b-4r*
10+ 3r
O 10 + 3r + b
O 13r + b

Answers

10+3r+b
Explanation trust in de way

Three hundred cars drove over a bridge in 23 minutes. At that rate, how
many cars would drive over the bridge in 138 minutes?

Answers

Answer:

1800

Step-by-step explanation:

300 cars in 23 minutes so 300/25 = how many cars each minute

that equals 13.04347....

so on your calculator multiply that by 138 which gives you 1800 cars

Answer:

138/23×300=1800cars drove over the bridge

Step-by-step explanation:

I NEED HELP PLEASE I DON’T WANT TO FAIL PLEASE PLEASE HELP ME

Answers

The slope is 4/3 because when the y axis increases by four, the x axis increases by three. The y intercept is -2 because the line intercepts the y axis at -2. This means that it’s equation would be y=4/3-2. I hope this helps :)

Find the measure of the missing angle.

Answers

Answer:

Hi

U should do like this

90-51=39...

Answer: 39 degrees

Step-by-step explanation:

Right angle is 90 degrees so 51 plus a will equal 90

A is 39 degrees

Solve for x and find AB
Solve for y and find BX

Answers

9514 1404 393

Answer:

x = 7; AB = 30y = 5; BX = 25

Step-by-step explanation:

Opposite sides of a parallelogram are the same length.

  AB = CD

  5x -5 = 3x +9

  2x = 14

  x = 7

  AB = 5(7) -5)

  AB = 30

__

The diagonals of a parallelogram are bisected by each other.

  XB = XD

  7y -10 = 5y

  2y = 10

  y = 5

  BX = 7(5) -10

  BX = 25

Help I will mark brainliestttt

Answers

Answer:

11 or more

Step-by-step explanation:

55-40=15

160/15=10.666

11 or more

use the quotient rule to find the derrivatives of 3/x^2

With full process ​

Answers

Answer:

[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Power Rule: [tex]\displaystyle \frac{d}{dx}[ x^n] = nx^n^-^1[/tex]  

Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

3(-2)x⁻³ = -6x⁻³

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].

Quotient Rule: [tex]\displaystyle \frac{d}{dx} \Big [ \frac{f(x)}{g(x)} \Big ]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]

Substituting 3 for f(x) and x² for g(x), we get:

[tex]\displaystyle \frac{(x^2)(0)-(3)(2x)}{(x^2)^2}[/tex]

Simplify.

[tex]\displaystyle \frac{-6x}{x^4}[/tex]

Using exponent rules, we can rewrite this as:

[tex]-6x^1^-^4 = -6x^-^3[/tex]

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.

Answer:

[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:

[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].

In this question:

The numerator of the fraction is [tex]f(x) = 3[/tex] (a constant function.)The denominator of the fraction is [tex]g(x) = x^{2}[/tex].

Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].

Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].

For [tex]{g}^{\prime}(x)[/tex], consider the power rule:

if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].

Apply this rule to find [tex]{g}^{\prime}(x)[/tex].

[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].

Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:

[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].

Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].

Simplify the expression:
4+4+7d

Answers

Answer:

8+7d

Step-by-step explanation:

So forest you combine like terms

4+4=8

There are no longer any like terms so your finished product is 8+7d


2 sides of a triangle have measures of 5 inches and 11 inches which measure could be the length of the third side

Answers

Answer:

the third side must be greater than 6 but less than 16

Step-by-step explanation:

use triangle inequality theorem - 3 scenarios (one of which is discounted because it produces a negative and a side of a triangle cannot be negative)

5 + 11 > 3rd side (n)    n < 16

5 + n > 11       n > 6

11 + n > 5;   n > -6   discounted

The number 1-50 are placed in a bag. What is the probability of selecting:

A) a number greater than 50______
B) multiple of 5________
C) a prime number _________
D) a composite number_______

Answers

A: 0

B: 10/50

C: 15/50

D: 34/50

Answers:

A)  0B)  1/5 = 0.2C) 3/10 = 0.3D) 17/25 = 0.68

Nearly all of those answers involve a fraction form and an equivalent decimal form.

===========================================

Work Shown:

Part A

The largest number in the bag is 50, so we cannot select anything larger than that. The probability of getting something larger than 50 is 0% which converts to the decimal form 0

----------------------------

Part B

List out the multiples of 5 to get {5,10,15,20,25,30,35,40,45,50}

Note how 50/5 = 10, which shows there are 10 multiples listed above.

We have 10 items in that set out of 50 items in the set {1,2,3,...,49,50}. The probability of getting a multiple of 5 is 10/50 = 1/5. This converts to the decimal form 0.2

----------------------------

Part C

The prime numbers between 1 and 50 are:

{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}

There are 15 items in that list out of 50 items in the bag, so 15/50 = (5*3)/(5*10) = 3/10 is the answer. Converting to decimal form gets us 3/10 = 0.3

----------------------------

Part D

There are 50 items in the bag and 15 primes. This means there are 50-15 = 35 composite items. Well this is close to the actual count. It turns out that the number "1" is not composite, and it's not prime either. So we really have 35-1 = 34 composite values.

We get 34/50 = (17*2)/(25*2) = 17/25 as the answer. That converts to 17/25 = 0.68

PLEASE PLEASE HELP I STG IVE BEEN ASKING THE SAME QUESTIONS FOR SO LONG AND NOONES ANSWERING ITS DUE SOON im just gonna fail tbh

Answers

Answer:

3) 5/2

Step-by-step explanation:

5x - 2y = 20

(First, put it in slope intercept form: y = mx + b).

5x - 2y - 5x = 20 - 5x --> Subtracted 5x on both sides of the equation

- 2y  = -5x + 20 --> Simplified

-2y/-2 = (-5x + 20)/-2 --> Divided by -2 on both sides

y = 2.5x - 10 --> Simplified

Since formula is, y = mx + b, then:

m (slope): 2.5

b (y-intercept): -10

Therefore, the answer is 3) 5/2

Hope this helped! <3

Let's solve for y.

5x − 2y = 20

Step 1: Add -5x to both sides.

5x−2y+−5x=20+−5x

−2y=−5x+20

Step 2: Divide both sides by -2.

−2y/−2  =  −5x + 20/−2

y =  5/2x − 10

Answer:

y =  5/2x − 10

Slope = x, therefore, the slope = 5/2.

What number should go in the box? 34816=▢+4000+800+10+6

Answers

Answer:

30,000 number should go in the box

Answer:

30000.

Step-by-step explanation:

34816=▢+4000+800+10+6

34816 = ▢ + 4816

▢ =  34816 - 4816

= 30000

1) Write an equation of a line that
is parallel to y = -5x + 2 and
passes through (-1, 4).

Answers

Answer:

y=-5x + 4

Step-by-step explanation:

Answer:

y=-5x-1

Step-by-step explanation:

It goes through the point (-1,4)

Two rectangles are similar. The
ratio of the length of rectangle A
to the length of rectangle B
is 1:4. If the length of rectangle
B is 14 meters, what is the
length of rectangle A?

Answers

3.5 meters
length of rectangle A

Giving 5 stars and brainlist to whoever answers this correct!!!!
The table shows the number of animals in the most popular exhibit at the zoo.

Flamingo - 12
Crocodile - 4
Elephants - 3
Monkeys - 11

If an animal is selected at random to be fed in front of an audience, which expression can be used to determine the probability the animal will NOT be an elephant?

A. 1/10
B. 9/10
C. 3/10
D. 3/3

Answers

Answer:

its A because it can't be B or D obviously, and since there are the least amount of elephants, its gonna be the one will less of a percentage. So its A.

Step-by-step explanation:

jabsbabsbavvsbabs

(-5,2) and (1,-2) what’s the rise/run?

Answers

Answer:

m= -2/3

Step-by-step explanation:

Use the slope formula to find the slope m .

-3/2 is correctttttttttttttttt

Can you guys help meh pls

Answers

16500, 1650, ?, 0.165
This pattern is to move the the number to the right by 2 decimal places.
So pattern number 3 is 16.50

Isabel finished her history assignment in 1/5 hours. Then she completed her math assignment in 1/2 hours. What was the total amount of time Isabel spent doing these two assignments?

Write your answer as a fraction in simplest form.

Answers

Answer:70/100 or 7/10

Step-by-step explanation:

one hour is 60 mins

1/5 of an hour is 12 mins

1/2 of an hour is 30

30 + 12 = 42

42/60 simplified is 7/10

Jasmine sold half of her Barbie doll Collection
and then bought 9 dolls. She now has 13 dolls.
Barbie dolls did she begin with?
How many

Answers

Answer: 8 dolls.

Explanation: 13 - 9 = 4, 4 x 2 = 8.

Work the equation backwards... she has bought 9 extra dolls to add on the the half of her original amount. Without the extra 9 dolls (13 - 9), Jasmine has half of her original amount left (4) and so to find the original amount of dolls, think that if 4 is half the amount, what is 4 half of? 4 is half of 8 and so 8 is the original amounting dolls she had.

Find the value of x.

Answers

Answer:

81 degrees

Step-by-step explanation:

Step-by-step explanation:

Here,

X+128+100+51=360

X+279=360

X=360-279

:.x=81

Can someone plz help me with the red #6 the graph is on the screen plz anyone fast ☹️

Answers

The answers is Y=-1x+5
The 1 is negative because it’s going down

HELP!!! NEED ANSWER ASAP!

Answers

Answer:

Yeah he's right...

Step-by-step explanation:

Which statement about the dilation of these triangles is true?

The scale factor is
The scale factor is 2
The scale factor is 3.
The scale factor is 4.

Answers

Answer

when 2 triangle scales are similar the ration reduces and become a scale factor

Answer:

The scale factor is 2

Step-by-step explanation:

Which Pixar characters do you think were the hardest to bring to the screen, and why?

Answers

Pepita from coco (big flying cat). Do you seeee how colorful and detailed that thing was
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