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allsm [11]
3 years ago
14

What is the difference in length between 1 1/4 inch button and a 3/8 inch button

Mathematics
1 answer:
jeka943 years ago
3 0

You have two buttons of different lengths.

First with length 1\dfrac{1}{4} in and second with length \dfrac{3}{8} in. The first one is larger, then the difference in length between them is:

1\dfrac{1}{2}-\dfrac{3}{8}=\dfrac{3}{2}-\dfrac{3}{8}=\dfrac{3\cdot 4-3}{8}=\dfrac{12-3}{8}=\dfrac{9}{8}=1\dfrac{1}{8}\ in.

Answer: 1\dfrac{1}{8} in.

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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
Find the volume of the following compound shape.<br>​
Bess [88]
<h3>Given:</h3>
  • Cone
  • Cylinder
<h3>Volume of the cone:</h3>

v =  \frac{1}{3} \pi {r}^{2} h

v =  \frac{1}{3}  \times \pi \times  {10}^{2}  \times 10

v = 1047.20 \:  {cm}^{3}

<h3>Volume of the cylinder:</h3>

v = \pi {r}^{2} h

v = \pi \times  {10}^{2}  \times 10

v = 3141.59 \:  {cm}^{3}

<h3>Total volume:</h3>

v = 1047.20 + 3141.59

v = 4188.79 \:  {cm}^{3}

<u>Hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>cone</u><u> </u><u>shape</u><u> </u><u>is</u><u> </u><u>4188.7</u><u>9</u><u> </u><u>cubic</u><u> </u><u>centimeters</u><u>.</u>

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1 year ago
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One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for
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Answer:

B.

Step-by-step explanation:

f(x) has two complex roots and one real root.

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The student council raised $150 during the school dance if they charge $3per ticket and received $24 in other donations what is
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3t + 24 = 150 this is the answer
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