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3 years ago

Find c, the hypotenuse, rounded to four decimal places, in a right triangle with b = 16 and B = 55°

Mathematics

2 answers:

vredina [299]3 years ago

8 0

C is 19.5
I believe not promising

devlian [24]3 years ago

4 0

Answer:

19.5324

Step-by-step explanation:

sin(55)= 16/x

x(0.819) = 16

x= 19.5324

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Gwent pour 256 milliliters of water in to Ravi Henry pours 189 milliters of water in to Ravis .Ravis now contains 800 Milliters

Contact [7]

Answer:

Ravi had 355ml water to begin with.

Step-by-step explanation:

Given that,

amount of water that Gwent pour in Ravi = 256 ml

amount of water that Henry pour in Ravi = 189 ml

amount of water after each have poured = 800 ml

suppose amount of water ravi had before both poured water in it = x

Equation

256 + 189 + x = 800

445 + x = 800

x = 355ml

Initially ravi had 335ml of water.

6 0

3 years ago

Ruth has 7 more brown pencils than blue pencils, and 11 more blue pencils than red pencils. She has 5 red pencils. How many brow

olya-2409 [2.1K]

Answer: There are 5 red pencils, 16 blue pencils and 23 brown pencils.

Step-by-step explanation:

Since we have given that

Number of red pencils = 5

Number of blue pencils are 11 more than red pencils.

So, Number of blue pencils would be

$11+5=16$

Number of brown pencils are 7 more than blue pencils.

So, number of brown pencils would be

$16+7=23$

Hence, there are 5 red pencils, 16 blue pencils and 23 brown pencils.

8 0

3 years ago

Urgent, It is a Calculus question and I’ll appreciate your help. Thanks

BaLLatris [955]

Answer:

4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

(12p)(12r) = -1

r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

$6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}$

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

d^2 = (6r^2 -6p^2)^2 +(r -p)^2

d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

<em>Comment on the solution</em>

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.