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3 years ago

Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

Mathematics

1 answer:

Len [333]3 years ago

3 0

A parabola is a curve where any point is at an equal distance from:

a fixed point (the focus ), and a fixed straight line (the directrix )

The curve is defined by: y2 = 4ax.

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The floor of the entryway to an office building will be triangular. Two angles of the triangle will measure 40º, and the side be

ruslelena [56]

Answer:

The drawing in the attached figure

Step-by-step explanation:

we know that

An isosceles triangle, has two equal sides and two equal interior angles

In this problem, the floor of the entryway to an office building is in the shape of an isosceles triangle

step 1

Find the measure of the vertex angle

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

Let

x ---> the measure of the vertex angle of triangle

$x=180^o-2(40^o)=100^o$

step 2

Find the length of the congruent sides of triangle

Applying the law of sines

Let

c ----> the length of one congruent side

$\frac{a}{Sin(A)}=\frac{b}{Sin(B)}$

we have

$a=8\ m\\A=100^o\\B=40^o$

substitute

$\frac{8}{Sin(100^o)}=\frac{b}{Sin(40^o)}$

solve for b

$b=\frac{8}{Sin(100^o)}(Sin(40^o))$

$b=5.22\ m$

step 2

Make a scale drawing of the entryway

The scale drawing is 1 cm : 2 cm

That means

1 cm in the drawing represent 2 cm in the actual

1 cm in the drawing represent 0.02 m in the actual

Find the dimensions in the drawing

For a=8 m

$8\ m=8/0.02=400\ cm$

For b=5.22 m

$5.22\ m=5.22/0.02=261\ cm$

step 3

Draw the triangle

see the attached figure

3 0

3 years ago

Help me please for 50 points I'll also give brainliest

ICE Princess25 [194]

Answer: B. 150°

Step-by-step explanation:

The angle is obviously obtuse and is therefore greater than 90°.

This rules out A. and C.

Also, this angle is not 180° because then it would be flat.

This rules out D.

Leaving the correct answer to be B. 150°

4 0

2 years ago

eric is ten years older than sal & mick is twice sals age their combined age equals 110 how old is sal

Olenka [21]

2x + x + 10 + x = 110
4x + 10 = 110 (Subtract ten from both sides)
4x = 100 (divide both sides by four)
x = 25

Plug in values to check...

2(25) + 25 + 25 + 10 = 110
50 + 50 + 10 = 110
110 = 110

Mick is 50 years of age.
Sal is 25 years of age.
Eric is 35 years of age.

7 0

3 years ago

Need help with question 13B i can not figure it out please help.

Vsevolod [243]

Short Answer 10
The tough part is the number of drinks.
Let the number of them be x
4.5 x + 3 + (10/100) * (4.5x + 3) + (7/100) * (4.5 x + 3) ≤ 60

The tip is not included in the tax, and the tax does not include the tip. You can shorten this up quite a bit.
4.5 x + 3 + (10/100) * (4.5x + 3) + (7/100) * (4.5 x + 3) ≤ 60
(1 + 10/100 + 7 /100) (4.5x + 3) ≤ 60 Combine the tax, tip, scone and Lattes

(1.17) * (4.5x + 3) ≤ 60 Divide by 1.17
4.5x + 3 ≤ 60 / 1.17
4.5x + 3 ≤ 51.28 Subtract 3
4.5x ≤ 48.28 Divide by 4.5
x ≤ 48.28 / 4.5
x ≤ 10.72

Discussion.
There's a problem. He can't buy 0.72 of a Latte. He can only buy 10 of them. In this case we must round down so what happens if he buys 10 lattes? Does the price the taxes and the tip allow him to get another Latte? The answer should be no because then you would be 11 lattes and the tip and taxes would push you over 60 dollars. But be careful, sometimes things like this can alter you answer..

Answer: 10 <<<<

7 0

3 years ago

Find the surface area of the figure

Maurinko [17]

Answer:

Step-by-step explanation:

circumference of cylinder = πd = 5π in

lateral area of cylinder = 5π×9 = 45π in²

Each colored face has a matching face on the other side of the figure.

green areas = 2(17×15) = 510 in²

blue areas = 2(12×17) = 408 in²

gray areas = 2(5×6) = 60 in²

yellow areas = 2(5×12) = 120 in²

red areas = 2(12×15) = 360 in²

total surface area = 45π + 510 + 408 + 60 + 120 + 360 ≅ 1,599.37 in²

6 0

3 years ago