140 for 21 minutes how much for 18.minutes

A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed

Anastasy [175]

Answer:

498 m

Step-by-step explanation:

The AAA theorem states that triangles are similar if all three corresponding angles are equal.

1. Compare triangles FHS and ILS

(a) Reason for similarity

∠F = ∠I = 90°

∠S is common.

∴ ∠H = ∠L

(b) Calculate SL

$\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}$

2. Compare triangles ILS and GLE

(a) Reason for similarity

∠I = ∠G = 90°

∠L is common.

∴ ∠S = ∠E

(b) Calculate LE

$\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}$

3. Calculate EH

LE + EH + HS = LS

304.0 m + EH + 380 m = 1182 m

EH + 684 m = 1182 m

EH = 498 m

The distance from E to H is 498 m.

5 0

3 years ago

Hey there please help me with this question

olga_2 [115]

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio, 2 + 1 = 3 parts , thus

81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio

2 parts = 2 × 27 = 54 cm²

Area of A = 54 cm² and area of B = 27 cm²

The side of the original square = $\sqrt{81}$ = 9 cm

The width of both rectangles is 9 cm ( width remains unchanged after cut )

Thus

Rectangle A

9 × length = 54 ( divide both sides by 9 )

length = 6 cm

Rectangle B

9 × length = 27 ( divide both sides by 9 )

length = 3 cm

Rectangle A → length = 6 cm, width = 9 cm

Rectangle B → length = 3 cm , width = 9 cm

5 0

3 years ago

Read 2 more answers

The geometric sequence a i a i a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 =8a, start subscr

frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0

2 years ago

Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope. We don't have to bother to take the square root. We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6). slope=-6/-1=6 AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1). slope=1/-6=-1/6. BC²=(-6)²+1²

CD=D-C=(1, 6). slope=6/1=6 CD²=1²+6²=37

DA=A-D=(6,-1) slope=-1/6 DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides. We see they all have squared distance 37. Equal perpendicular sides proves its a square.

If we do these problems enough we learn: There's no point taking the square root. In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides: (-1, -6) (-6, 1) (1, 6) (6,-1)

5 0

3 years ago

The coach of a college basketball team categorizes the number of points

stealth61 [152]

A graph is a way to represent a lot of data in a visual format. thus the number of games in the category 51-57 are 3.

<h3>What is a graph?</h3>

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. the line of the graph is a function that follows the graph.

The categories and the data points can be arranged as;

51 - 57 = 51, 56, 55

58 - 64 = 63, 59, 60, 64

65 – 71 = 70, 67

72 or more = 75

Therefore, the number of games in the category 51-57 are 3.

Learn more about Graph:

brainly.com/question/14375099

#SPJ1

8 0

1 year ago