A customer/member owes $11.02 and pays $100.00 in cash. Change due is $88.98.

Find the volume of the sphere.

Volgvan

Step-by-step explanation:

v=4/3*π*r^3

v=4/3*22/7*(1/2)^3

v=4/3*22/7*1/8

v=11/21

v=0.52 units^3

4 0

2 years ago

You install 638 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 152 feet. What is the length

vovikov84 [41]

The length is 486

Step-by-step explanation:

638 subtract 152

6 0

3 years ago

Approximate the change in the volume of a sphere when its radius changes from r= 5ft to r= 5.1ft (v(r)= 3/4 pi r^3)?

leva [86]

Answer:

18.03 cubic feet

Step-by-step explanation:

Hello,

Step 1

find the volume of the sphere when radius= 5 ft

$v(r)= \frac{3}{4} \pi r^3\\v(5)= \frac{3}{4}\pi (5\ ft)^3\\v(5)= \frac{3}{4}\pi *125\ ft^{3} \\v(5)=294.52\ cubic\ feet\\$

Step 2

find the volume of the sphere when radius= 5.1 ft

$v(r)= \frac{3}{4}\pi r^3\\v(5.1)= \frac{3}{4} \pi (5.1\ ft)^3\\v(5.1)= \frac{3}{4}\pi *132.651\ ft^{3} \\v(5.1)=312.551\ cubic\ feet\\\\$

Step 3

Compare the Volumes to find the change

$\frac{v(r_{2})}{v(r_{1})} =\frac{312.551}{294.52} =1.06$

the volumen of the sphere with radius = 5.1 is 1.06 times bigger than the first one(r=5)

Now, find the change

$change= {v(r_{2})-{v(r_{1})}} \\change=312.551\ cubic\ feet\ -294.52 cubic feet \\ change=18.031\ cubic\ feet$

change=18.03 cubic feet

Have a great day.

4 0

3 years ago

Y=1/3x+11/15 find x if y=6

Svetlanka [38]

Step-by-step explanation:

plug in y

6=1/3x+11/15

multiply both sides by 15 to get rid of the fraction

90 = 5x +11

move terms to make them like terms

-5x =11- 90

-5x = -79

divide both sides by -5

evaluate for x

3 0

3 years ago

explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do t

mamaluj [8]

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

$ax^2+bx+c$

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

$a(x-h)^2+k$

There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

$a(x-p)(x-q)$

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.

4 0

3 years ago