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3 years ago

B4.1a) The diagram shows a triangle.

Mathematics

1 answer:

Yuki888 [10]3 years ago

3 0

So angles on a straight line add up to 180°
And angles in a triangle adds up to 180° try if you can work it out now
If you still don’t understand let me know

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Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)

lesantik [10]

2x^2 - 7x - 15 =
(2x + 3)(x - 5) <==

6 0

3 years ago

Read 2 more answers

URGENT!

N76 [4]

Money per Charity = $0

Money Left = $814

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Money Left = 314

Give each charity $60

Money per Charity = $160

Money Left = $14

Give each Charity $2

Money per Charity = $162

Money Left = $4

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3 years ago

Evaluate each value expression for the given value of x: x-5 , x - =22 pls fast

masya89 [10]

Answer:

-18

Step-by-step explanation:

-18

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6 0

3 years ago

A boat heads south at 120 mph while a steamer heads east at 50 mph. If they started from the same dock and at the same time, whe

Snezhnost [94]

Answer:

1 hour after they leave

Step-by-step explanation:

The distance each travels is proportional to its speed. The given speeds are at right angles to each other in a 5:12 ratio. The Pythagorean theorem tells you the hypotenuse of such a right triangle will have length ...

√(5²+12²)=√169 = 13

That is the speeds are in the ratio 5:12:13, where 13 represents the relative separation speed. Actual speeds are then 50 mph : 120 mph : 130 mph.

So the distance between the boat and steamer will be increasing at 130 mph. The distance will be 130 miles after 1 hour.

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3 years ago

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