Which of the following would produce a cross section that is the shape of a triangle?

A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the ins

Viefleur [7K]

Answer: $\frac{253}{44}$

Step-by-step explanation:

ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.

Similar triangles so we can do $\frac{50}{x+y} = \frac{6}{y}$ .

Solve for it we get 44y = 6x

Differentiate relative to time t, we get 44y' = 6x'.

change in x (x') is equal to 5. And we get the answer y' = $\frac{33}{44}$ .

the $\frac{33}{44}$ ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.

7 0

2 years ago

3) Mr. Brust is addicted to Red Bull and has decided that he wants to plaster his room at school with Red Bull cans.

Bogdan [553]

Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.

<h3>What is area of rectangle?</h3>

Area of rectangle is the product of its sides

i.e., Area of rectangle = length x breadth

<h3>What is area of circle?</h3>

The area of a circle is pi times the radius squared (A = π r²).

<h3>What is circumference of circle?</h3>

The circumference of a circle is defined as the linear distance around it.

( C= 2πr)

The can of red bull is in shape of cylinder.

If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.

Like the given figure given.

The can is 6.5 inches tall and has a diameter of about 2.5 inches.

It shows that the two circle will have the diameter 2.5 inches.

d= 2.5 inch

= 0.208 ft

radius, r= $\frac{d}{2}$

r= $\frac{0.208}{2}$

r= 0.104 ft

To get the length of the rectangle , we have to calculate the circumference of the circle.

Circumference of the circle be,

= 2πr

= 2 x 3.14 x 0.104

= 0.653 ft

The rectangular sheet will have,

length= 0.653 ft, breadth= 6.5 inches = 0.541 ft

Now, area of rectangular sheet be,

= length x breadth

= 0.653 x 0.541

= $0.3532 ft^{2}$

Area of 2 circle( top and bottom of can) be,

= 2 x π $r^{2}$

= 2 x 3.14 x 0.104 x 0.104

= 6.28 x 0.010816

= 0.0679 $ft^{2}$

Total area of can be,

= Area of rectangular sheet + Area of 2 circle( top and bottom of can)

= 0.3532 + 0.0679

= 0.4211 $ft^{2}$

Now, we have the wall of dimensions

length= 9 ft, breadth= 20 ft

Area of wall be,

= length x breadth

=9 x 20

= 180 $ft^{2}$

Number of cans required to cover the whole wall be,

= $\frac{area \;of\; wall}{area \;of\; can}$

= $\frac{180}{0.4211}$

= 427.45 cans

≈ 428 cans

Learn more about the concept of area here:

brainly.com/question/16193772

#SPJ1

7 0

2 years ago

Define a polynomial that is a difference of squares. How do you know that it is the difference of squares? How is it factored?

yulyashka [42]

Answer:

When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

Step-by-step explanation:

lol it’s on wassa name ;) mark me brainliest? Btw

Here you go, your equation should look a lot like this:

x²-16 -----> (x+4)(x-4).

8 0

3 years ago

Let A be the point (0,a), and B be the point (0,a+b) on the xy-plane. Let P denote a variable point (x,0), where x > 0. Find

olga_2 [115]

Answer:

x = √(a(a+b))

Step-by-step explanation:

We can also assume a > 0 and b > 0 without loss of generality. (If a and a+b have opposite signs, the maximum angle is 180° at x=0.)

We choose to define tan(α) = -(b+a)/x and tan(β) = -a/x. Then the tangent of ∠APB is ...

tan(∠APB) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

= ((-(a+b)/x) -(-a/x))/(1 +(-(a+b)/x)(-a/x))

= (-bx)/(x^2 +ab +a^2)

This will be maximized when its derivative is zero.

d(tan(∠APB))/dx = ((x^2 +ab +a^2)(-b) -(-bx)(2x))/(x^2 +ab +a^2)^2

The derivative will be zero when the numerator is zero, so we want ...

bx^2 -ab^2 -a^2b = 0

b(x^2 -(a(a+b))) = 0

This has solutions ...

b = 0

x = √(a(a+b))

The former case is the degenerate case where ∠APB is 0, and the value of x can be anything.

The latter case is the one of interest:

x = √(a(a+b)) . . . . . . the geometric mean of A and B rotated to the x-axis.

_____

<em>Comment on the result</em>

This result is validated by experiments using a geometry program. The location of P can be constructed in a few simple steps: Construct a semicircle through the origin and B. Find the intersection point of that semicircle with a line through A parallel to the x-axis. The distance from the origin to that intersection point is x.

3 0

4 years ago

Find the area of the regular polygon below. leave your answer in simplest radical form.

Licemer1 [7]

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

<h3> 1/2 x perimeter x apothem</h3>

<em>Perimeter = the sum of the lengths of all the sides </em>

<em>Suppose length of one side = x</em>

<em>Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3</em>

<em />

Since the polygon have 6 sides so

perimeter = 6x

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

384√3 in²

6 0

4 years ago

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