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3 years ago

15

There is a picnic table located along Path A. The table is located 1.5 miles along the path from the campsite. Which map shows t

he picnic table in the correct location?

2 answers:

photoshop1234 [79]3 years ago

7 0

Answer: the answer is D

Step-by-step explanation:

rodikova [14]3 years ago

4 0

Answer:the answer is D

Step-by-step explanation:

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An item on sale costs

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The sale price would be 18 dollars. Hope this helps you!

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3 years ago

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If y varies inversely as x, find the constant of variation if y=36 when x=9

Jobisdone [24]

Answer:

k = 324

Step-by-step explanation:

Y varies inversely as x

Let k be the constant of variation

Y = k/ x

Y= 36 and x= 9

Substitute the value of Y and x

36 = k/9

Make k the subject of the formula

k= 36*9

k =324

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3 years ago

an open rectangular cardboard box with a square base is to have a volume of 256cm^3. Find the dimensions of the box if the area

Anit [1.1K]

Let
x------> the length side of the square base of the box
y-------> the height of the box

we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1

<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>

surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x

step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm

the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm

5 0

3 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

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3 years ago

Chapter one course 2

Marysya12 [62]

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3 years ago