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Alex
3 years ago
7

A plane flies x mph. How far can it go in y hours?

Mathematics
1 answer:
wel3 years ago
8 0
The answer is xy hours.
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If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 wi
Dmitry [639]

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴  ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

3 0
3 years ago
If the dimensions of a square based pyramid are tripled what happens to the volume?
11Alexandr11 [23.1K]
Plug in numbers. if originally, it was V=1/2 * 1 * 1 * 2=1 

<span>tripling the dimensions would be V=1/2 * 3 * 3 * 6=27 </span>

<span>it would be 27 times larger. this could also be found by 3^3, just as doubling would render 2^3

</span>
7 0
3 years ago
Read 2 more answers
What is the additive inverse of -5
liraira [26]

Answer:

You should be thinking about a negative number. In fact, you should be thinking about a number that is the opposite of 5! -5! So, the additive inverse of 5 is -5

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
3)Solve F(x) for the given domain.<br> F(x) = x 2 + 3x - 2<br> F(-1) =<br><br> a)-4<br> b)-6<br> c)2
Alja [10]
The answer to the question is a) -4.

6 0
2 years ago
A recipe whuch makes 8 servings calls for 2 cups if sugar. How many cups if sugae will it takr to make 18 servings
yan [13]
Answer:
4.5 cups of sugar
Explanation:
set up the problem like servings/cups. it would look like 8/2. then add the 18 servings and make it 8/2=18/x so you can cross multiply. cross multiply and you get 8x=36. divide it by 8 and you get x=4.5 cups. hope this helps!
3 0
2 years ago
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