Benny takes 11 hours to paint a room. it takes melanie 12 hours to complete the same job. how long would it take if they worked
1 answer:
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John's method to determine the width of the stream uses the knowledge
that the tangent of 60° is approximately 1.7.
The proper sequence John would use to find the width of the stream are;
- Step 1; <u>John</u><u> drives a stake opposite the tree to establish a line between two points</u>
- Step 2; <u>John uses a </u><u>compass </u><u>to walk away from the stakes at a right angle</u>
- Step 3; <u>On the path John walks until he finds a </u><u>line </u><u>of sight to the tree that equals 60 degrees</u>
- Step 4; <u>John drives a second </u><u>stake </u><u>in the ground</u>
- Step 5; <u>John measures the the </u><u>distance </u><u>between the two stakes</u>
- Step 6; <u>John </u><u>multiplies </u><u>the distance between the two stakes by</u><u> 1.7</u><u> to find the distance</u>.
Reasons:
The steps that can be used to measure the width of the stream are;
Step 1: Drive a stake opposite the tree on the other side of the stream.
Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.
Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.
Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.
Step 5; Measure the distance between the stakes that are placed in the ground.
Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.
<em>The possible question options are;</em>
<em>John measures the the distance between the two stakes</em>
<em>John uses a compass to walk away from the stakes at a right angle</em>
<em>John multiplies the distance between the two stakes by 1.7 to find the distance</em>
<em>John drives a second stake in the ground</em>
<em>On the path John walks until he finds a line of sight to the tree that equals 60 degrees </em>
<em>John drives a stake opposite the tree to establish a line between two points.</em>
Learn more about trigonometric ratios here:
Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
<u><em>Answer:</em></u>
y^2 = 28x
<em><u>Step-by-step explanation:</u></em>
Since the directrix is horizontal, use the equation of a parabola that opens left or right.
(y−k)^2 = 4p(x−h)
Find the vertex.
(0,0)
Find the distance from the focus to the vertex.
p = 7
Substitute in the known values for the variables into the equation
(y−k)^2 = 4p(x−h).
(y−0)^2 = 4(7)(x−0)
Simplify.
<em>y^2 = 28x</em>
