the angle of elevation of the top of the mast from a point 53m to its base on level ground is 61°. find the height of the mast to the nearest meter
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Answer:

€36 = 30.62 pounds sterling

9514 1404 393

Answer:

  sin(tan^-1(x)) = x/√(x² +1)

Step-by-step explanation:

We know that for an angle in a right triangle...

  Tan = Opposite/Adjacent

and

  Sin = Opposite/Hypotenuse

so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...

  Hypotenuse² = Opposite² + Adjacent² = x² +1

Then the sine of the angle is ...

  sin(tan^-1(x)) = x/√(x² +1)

Step-by-step explanation:

G=2m

m+G=30

m +2m =30

3m=30

m=10

Answers:

[tex]\text{Perimeter} = 14\sqrt{5}\\\\\text{Area} = 50\\\\[/tex]

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

Work Shown:

[tex]L = 2\sqrt{5} = \text{length}[/tex]

[tex]W = 5\sqrt{5} = \text{width}[/tex]

P = perimeter

[tex]P = 2*(L+W)\\\\P = 2*(2\sqrt{5}+5\sqrt{5})\\\\P = 2*(7\sqrt{5})\\\\P = 14\sqrt{5}\\\\[/tex]

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

A = area

[tex]A = L*W\\\\A = (2\sqrt{5})*(5\sqrt{5})\\\\A = (2*5)(\sqrt{5}*\sqrt{5})\\\\A = 10\sqrt{5*5}\\\\A = 10\sqrt{25}\\\\A = 10*5\\\\A = 50\\\\[/tex]

Answer:

Total Distance = 20km = 20 × 1000 = 20,000 m

Distance walked = 800m

Distance travelled by cycle = 20,000 - 800 = 19,200m

Percentage of journey by cycle = (distance travelled by cycle ÷ total distance) × 100

Percentage of journey by cycle = (19200 / 20000) * 100

Percentage of journey by cycle = 96%

Answer:

z(max) = 16

z(min) = -24

Step-by-step explanation:

2x - y = 12  multiply by 2

4x - 2y = 24  (1)

4x + 2y = 0  add equations

8x = 24

x = 3

4(3) + 2y = 0

y = -6

so (3, -6) is a common point on these two lines

z = 2(3) + 5(-6) = -24

4x - 2y = 24   (1)

x + 2y = 6   add equations

      5x = 30

        x = 6

6 + 2y = 6

         y = 0

so (6, 0) is a common point on these two lines

z = 2(6) + 5(0) = 12

4x + 2y = 0    multiply by -1

-4x - 2y = 0

  x + 2y = 6  add equations

       -3x = 6

         x = -2

-2 + 2y = 6

         y = 4

so (-2, 4) is a common point on these two lines

z = 2(-2) + 5(4) = 16

Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be

5th: 15 + c

6th: (15 + c) + c = 15 + 2c

7th: (15 + 2c) + c = 15 + 3c

and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,

n-th: 15 + (n - 4) c

Then the 9th term in the sequence is

15 + (9 - 4) c = 35

and solving for c gives

15 + 5c = 35   ==>   5c = 20   ==>   c = 4

Then the 15th term would be

15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59

Answer:

8 cm^2

Step-by-step explanation:

If the triangle is isosceles the sides are the same

Let the sides be x

We know that we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse

x^2+x^2 = (4 sqrt(2))^2

2x^2 =16(2)

2x^2 = 32

Divide by 2

2x^2/ 32/2

x^2 = 16

Taking the square root of each side

sqrt(x^2) = sqrt(16)

x = 4

The area of the triangle is

A =1/2 bh

A = 1/2 (4) (4)

A = 1/2(16)

A = 8

Answer:

8

Step-by-step explanation:

a^2 + b^2 = c^2

c = [tex]4\sqrt{2}[/tex]

[tex]c^{2} = 32[/tex]

a^2 + b^2 = 32

a=b (isosceles triangle)

a=b=4

base = 4

height = 4

area = 1/2 bh = 1/2(4)(4) = 8

Answer:

D

Step-by-step explanation:

Surface area is area of base plus all 4 sides.  Base is a square with s = 8 so area is 64sq yd.  Sides are triangles, with A = 1/2 bh, so 1/2(8)(5) = 20.  Four sides would be 80sq yds.  Add base and sum is 144 sq yds.

Answer:

vertical asymptotes

x=6, x=-6

horizontal asymptotes

y=0

zeros (0,0)

Step-by-step explanation:

f(x) = 6x / ( x^2 - 36)

First factor

f(x) = 6x / ( x-6)(x+6)

Since nothing cancels

The vertical asymptotes are when the denominator goes to zero

x-6 = 0   x+6=0

x=6          x= -6

Since the numerator has a smaller power than the denominator (1 < 2), there is an asymptote at y = 0

To find the zeros, we find where the numerator = 0

6x=0

x=0

[tex]\\ \rm\Rrightarrow y=\dfrac{6x}{x^2-36}[/tex]

The h orizontal asymptote

As x has less degree than x²

Vertical asymptote

Answer:

you will add the numerator and the denominator and or you look for lowest common factor

The final amount is $7,615.27

A = P(1 + r/n)^t

Where,

A = Final amount

P = principal = $7, 200

r = interest rate = 2.5% = 0.025

n = number of periods = 4

t = time = 9 years

A = P(1 + r/n)^t

= 7,200(1 + 0.025/4)^9

= 7,200(1 + 0.00625)^9

= 7,200(1.00625)^9

= 7,200(1.0576769512798)

= 7,615.2740492152

Approximately,

A = $7,615.27

https://brainly.com/question/14003110

Answer:

in five (5) ways a committee can be formed from 7 men and 5 women

Answer:

210 miles in 1 hour

Step-by-step explanation:

steps are in picture

Answer:

Step-by-step explanation:

3

Answer:

A

Step-by-step explanation:

The graph is a square root function

9514 1404 393

Answer:

  asymptotes: x = ±6

  zero: x = 0

Step-by-step explanation:

The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy ...

  x^2 -36 = 0

  x^2 = 36

  x = ±√36 = ±6

The vertical asymptotes of the function are x = -6 and x = +6.

__

The zero of the function is at the value of x that makes the numerator zero. This will be the value of x that satisfies ...

  6x = 0

  x = 0 . . . . . divide by 6

The zero of the function is x=0.

__

As a check on this work, we have had a graphing calculator graph the function and identify the zero.

Step-by-step explanation:

6k + 12 + 9=9

6k + 12 = 9 - 9

6k + 12 = 0

12 = -6k

12/-6 = -6k/-6

2/-1 = k

k = -2

Answer:

k=-2

Step-by-step explanation:

6k+12+9=9

subtract 9 from both sides

6k+12=0

subtract 12 from not sides

6k= -12

divide both sides by 6 (isolating the variable)

k= -12/6

simplify

k= -2

Answer:

Step-by-step explanation:

The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.

Simply put it says

Try 5

Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.

Answer:

No

Step-by-step explanation:

4:1

Multiply each side by 3

4*3 : 1*3

12: 3

This is not equal to 12:9

Answer:

no

Step-by-step explanation:

12 : 9

4 : 3 ≠ 4 : 1

Answer:

Substitute the functions and the value of the functions.

Step-by-step explanation:

Doing all will be long, so i'll present a and d

Here,(no a)

f(x)=3x-1, g(x)=x^2+2

Now,

f(g(x))=f(x^2+2)=3(x^2+2)-1=3x^2+6-1=3x^2+5

g(f(x))=g(3x-1)=(3x-1)^2+2=9x^2-6x+1+2=9x^2-6x+3

Here, (no d)

f(x)=x^2-9, g(x)=√(x+4)

Now,

f(g(x))=f(√(x+4))=(√(x+4))^2-9=x+4-9=x-5

g(f(x))=g(x^2-9)=√(x^2-9+4)=√(x^2-5)

Answer:

5765865876+5737555586=11503421462

Answer: 18π

okokok gg

Step-by-step explanation:

Here angle is given in degree.We have convert it into radian.

[tex] {1}^{\circ} =( { \frac{\pi}{180} } )^{c} \\ \therefore \: {80}^{\circ} = ( \frac{80\pi}{180} ) ^{c} = {( \frac{4\pi}{9} })^{c} \: = \theta ^{c} [/tex]

Area of green shaded regions = A

[tex] \sf \: A = \frac{1}{2} { {r}^{2} }{ { \theta}^{ c} } \\ = \frac{1}{2} \times {9}^{2} \times \frac{4\pi}{9} \\ = 18\pi \: {cm}^{2} [/tex]

Answer:

what is this sy man i dnt get it

Step-by-step explanation:

Answer:

60 cm^3

Step-by-step explanation:

The equation to find the volume for a rectangular prism is length times width time height.

So just multiply 5 times 3 times 4

V=(5)(3)(4)

V=60

Answer:

60cm^3

Step-by-step explanation:

w=3cm

h=4cm

l=5cm

[V=whl]

V=3×4×5=60

Answer:

true

Step-by-step explanation:

what else would it be. that is exactly the reason why we have constants.