Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east. Find the distance and bearing of runner B from runner A after 30 minutes

Answer:

BC = 24

Step-by-step explanation:

We know that triangles CAB and CED are similar because all three of their angles are the same. Thus, we know that the side lengths of these triangles have to be proportional to each other. You would match side BC with side DC and sides AC with EC.

AC/EC = BC/DC

30/10 = (32-x)/x

3 = (32-x)/x

Then using algebraic properties, solve for x.

3x = 32 - x

4x = 32

x = 8.

Lastly, plug in 8 for the x in BC, 32 - 8, so the length of BC is 24

Answer:

B

Step-by-step explanation:

Δ CBA and Δ CDE are similar triangles, then the ratios of corresponding sides are equal, that is

[tex]\frac{CB}{CD}[/tex] = [tex]\frac{CA}{CE}[/tex] , substitute values

[tex]\frac{32-x}{x}[/tex] = [tex]\frac{30}{10}[/tex] = 3 ( multiply both sides by x )

32 - x = 3x ( add x to both sides )

32 = 4x ( divide both sides by 4 )

8 = x

Then

BC = 32 - x = 32 - 8 = 24 → B

Answer:

sinA=sin(90-B)

sinA=90_B

now,A+B

=90

Answer:

a = 14.4

Step-by-step explanation:

It's a right angled triangle. so it has to follow Pythagoras Theorem

according to it square of hypotenuse = sum of squares of other two sides

[tex]16 {}^{2} = {x}^{2} + 7 {}^{2} \\ 256 = x {}^{2} + 49 \\ 256 - 49 = x {}^{2} \\ 207 = x {}^{2} \\ x = \sqrt{207 } \\ x = 14.387 \\ x = 14.4[/tex]

after rounding the decimal a= 14.4 in

Answer:

a)    x= 34°

b)    x = 51°

Step-by-step explanation:

Points to keep in mind when solving  triangle problems.

An isosceles triangle has two equal sides and the angles opposite to those sides are also equal angles.

A triangle with all sides equal is called an equilateral triangle, which is also called equiangular triangle.  

Answer:

10  1/5 pi

Step-by-step explanation:

First find the area of the circle

A = pi r^2 = pi *6^2 = 36 pi

Then find the fraction of the circle that is shaded

A circle is 360 degrees

102/360 =17/60

Multiply the fraction by the area

17/60 * 36 pi

51/5 pi

10  1/5 pi

Answer:

32.04

Step-by-step explanation:

firstly area of a sector is angle/360 multiplied by pi *r squared

so in this case it is going to be 102/360 *pi *6^2

6 squared is 36 all multiplied by pi and 106/360

it is advisable that you enter them all at once in your calculator

the final answer will be32.0444507

which is rounded to 32.04

Answer:

[tex] \frac{194}{3} [/tex]

Step-by-step explanation:

[tex]64 \frac{2}{3} [/tex]

[tex]64 + \frac{2}{3} [/tex]

[tex]64 \times \frac{3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3 + 2}{3} [/tex]

[tex] \frac{192 + 2}{3} [/tex]

[tex] \frac{194}{3} [/tex]

Answer:

1. [tex]Area = 28.26[/tex]

2 and 3: See explanation

Step-by-step explanation:

Solving (1)

[tex]r = 3[/tex] --- radius

The area is:

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14* 3^2[/tex]

[tex]Area = 28.26[/tex]

There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.

However, the following formula will be used to calculate the required areas.

[tex]Area = \pi r^2[/tex] --- same process as (1)

Answer:

216π sq ft

Step-by-step explanation:

given that :

d = 12 ft => r = 12/2 = 6ft

h(cyl) = 10 ft

h(cone) = 8 ft

the surface area = ?

the solution :

the slant of cone = √r²+h²

= √6²+8²= √100 = 10 ft

the surface area of silo =

the lateral area of cone + the lateral area of cylinder + the base area

= π×r×slant + 2×π×r×h(cyl) + π×r²

= π×6×10 + 2×π×6×10 + π×6²

= 60π + 120π + 36π

= 216π sq ft

The surface area of the silo will be 216π square feet. Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal.

The surface area is the sum of the surface area of the cone and cylinder. Then we have

The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft.

Surface area = πrl + 2πrh + πr²

The length of the radius will be

r = d /2

r = 12 / 2

r = 6 ft

The length of slant height will be

l² = 6² + 8²

l² = 100

l = 10 ft

Then the surface area of the silo will be

SA = π × 6 × 10 + 2π × 6 × 10 + π6²

SA = 60π + 120π + 36π

SA = 216π square feet

The surface area of the silo will be 216π square feet.

Then the correct option is C.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ2

Answer:

Step-by-step explanation:

here,

base=28 ft

height=24 ft

are of parallelogram=base*height

=28*24

=672 ft^2

Answer:

672 ft²

Step-by-step explanation:

Area of parallelogram is the same as the area of a rectangle.

28 × 24 = 672 ft²

Answer:

I think it's a

I'm not that sure tho

Answer:

D = 48  E= 90 F = 42 FE = 15

Step-by-step explanation:

Sorry, i dont know how to get DF and DE yet

Answer:

5.85

Step-by-step explanation:

100%-> 6.50

100%-10% = 90 %

90%-> 6.50/100 x 90

           =5.85

Answer:

RO = 17.9

Step-by-step explanation:

If they're similar, the fraction between their sides need to be equal, so do this:

NK/NM = RO/RQ

71.6/64 = RO/16

71.6•16/64 = RO

RO = 17.9

Given :

The points P (2, -3) & Q (-5, -3) whose ordinates are same.

To Find :

To which axis the line PQ is parallel.

Solution :

In given points the ordinates are same.

Therefore, the line is parallel to the x- axis.

Hence, this is the required solution.

Answer:

Wikipedia says:

"In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles)."

https://en.wikipedia.org/wiki/Square

Step-by-step explanation:

Answer:

y+2x-5= 0

Step-by-step explanation:

Applying,

(y-y₁) = m(x-x₁)............... Equation 1

Where m = slope

But,

m = (y₂-y₁)/(x₂-x₁)

Given: y₁ = -3, y₂ = 1, x₁ = 4, x₂ = 2

m = (1+3)/(2-4)

m = 4/-2

m = -2

Substituting into equation 1

(y+3) = -2(x-4)

y+3 = -2x+8

y = -2x+8-3

y = -2x+5

y = 5-2x

y+2x-5 = 0

Answer:

C    Zero

Step-by-step explanation:

[tex] -9 \times (\dfrac{0}{-3}) = [/tex]

[tex] = -9 \times 0 [/tex]

[tex] = 0 [/tex]

Answer: C  Zero

Answer:

49ft^2

Step-by-step explanation:

3.5ft X 4= 14ft

Area of parallelogram formula:

(perpendicular height)(base)= area

(14ft)(3.5ft)=49ft^2

Step-by-step explanation:

Given equation :-

Slope intercept form :-

→ 4x + 3y - 8 = 0

→ 3y = -4x + 8

→ y = (-4x + 8)/3

→ y = -4/3x + 8/3

Answer:

y = -4/3x + 8/3.

Step-by-step explanation:

4x + 3y - 8 = 0

3y  - 8 = -4x

3y = -4x + 8

Divide through by 3:

y = -4/3x + 8/3.

Step-by-step explanation:

arc CAD = 2×63= 126°

< ADB = ½×180 = 90°

arc AD = 126-36 = 90°

< ABD = ½×90° = 45°

< BAD = 180-90-45 = 45°

arc BD = 2×45 = 90°

Answer:

1) -5

2) 5

3) -4

4) 7

5) 3

Step-by-step explanation:

1) -20 divided by -4

2) -2 plus 7

3) 20 divided by 5

4) -2 plus 9

5) 20 minus 17

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{Monomial means an algebraic expression that consists of using ONE term}[/tex]

[tex]\mathsf{39n^3: 1, 3, 13, 39, n, n, n}[/tex]

[tex]\mathsf{48n^2: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, n, n}[/tex]

[tex]\large\textsf{Like terms: 1, 2, 3, n, n}[/tex]

[tex]\boxed{\boxed{ \large\textsf{Answer: \bf The GCF (Greatest Common Factor): 3n}^2}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{aAmphitrite1040:)}[/tex]

Answer:

4

Step-by-step explanation:

b² - a² is the formula

5² - 3²

16

√16

= 4

Answer:

The margin of error of his experiment is of 0.1074.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

30 M & M's from a bag, and 3 of them are green.

This means that [tex]n = 30, \pi = \frac{3}{30} = 0.1[/tex]

Standard 95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Margin of error:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.1*0.9}{30}}[/tex]

[tex]M = 0.1074[/tex]

The margin of error of his experiment is of 0.1074.