MATHEMATICS HIGH SCHOOL

The women's department of a store stocks 4 types of black socks for every 5 types of white socks. The men's department stocks 6 types of black socks for every 7 types of white socks. If each department has the same number of black socks, which department stocks more types of white socks?

Answers

Answer 1

Answer:

Answer:

The women's department of a store stocks have more types of white socks.

Step-by-step explanation:

Given:

The women's department of a store stocks 4 types of black socks for every 5 types of white socks.

Ratio of black socks to white socks = 4 : 5

The men's department stocks 6 types of black socks for every 7 types of white socks.

Ratio of black socks to white socks = 6 : 7

Each department has the same number of black socks.

Question asked:

Which department stocks more types of white socks?

Solution:

Let each department has 100 black socks.

For women's department

4 : 5 : : 100 : white socks

$(4)/(5) =(100)/(White\ socks) \n\n By \ cross \ multiplication\n \n 4* White\ socks=100*5\n 4White\ socks=500\nBy\ \ dividing\ both \ sides\ by\ 4\nWhite\ socks=125$

For men's department

6 : 7 : : 100 : white socks

$(6)/(7) =(100)/(White\ socks) \n\n By \ cross\ multiplication\n \n 6White\ socks=100*7\n6White\ socks=700\nWhite\ socks=About\ 117$

We found that out of 100 black socks the women's department of a store stocks have 125 white socks while the men's department stocks have about 117 white socks then by default understood that the women's department of a store stocks have more types of white socks.

Answer 2

Answer:

Answer:

The women have more

Step-by-step explanation:

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Identify the percent of change as an increase or a decrease.50 pounds to 35 pounds

Question 2
Find the percent of change.

Answers

Answer:

50-35 bro easy , 21

Step-by-step explanation:

1. The percent of change is a decrease

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x³, y = √ x about the x-axis V= ?

Answers

Answer:

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves y=x3y=x3 and y=xy=x

about the x-axis, we'll use the method of cylindrical shells.

First, let's sketch the region bounded by these curves to better understand the shape. The intersection points of y=x3y=x3 and y=xy=x

are the points where x3=xx3=x

, which gives x=0x=0 and x=1x=1.

Now, we'll set up the integral to find the volume using cylindrical shells:

The volume VV can be calculated using the formula:

V=2π∫abx⋅(f(x)−g(x)) dxV=2π∫abx⋅(f(x)−g(x))dx

Where aa and bb are the bounds of integration (in this case, 00 and 11), and f(x)f(x) and g(x)g(x) are the heights of the shells. In this case, f(x)=x3f(x)=x3 and g(x)=xg(x)=x

So, the volume can be calculated as:

V=2π∫01x⋅(x3−x) dxV=2π∫01x⋅(x3−x

)dx

Now, simplify the integrand:

V=2π∫01(x4−xx) dxV=2π∫01(x4−xx

)dx

Split the integral into two parts:

V=2π∫01x4 dx−2π∫01xx dxV=2π∫01x4dx−2π∫01xx

Evaluate each integral separately:

V=2π[x55]01−2π[2x5/25/2]01V=2π[5x5]01−2π[5/22x5/2]01

V=2π(15)−2π(25)=2π5V=2π(51)−2π(52)=52π

So, the volume of the solid obtained by rotating the region bounded by y=x3y=x3 and y=xy=x

about the x-axis is 2π552π cubic units.

The volume (V) of the solid obtained by rotating the region bounded by the curves $y = x^3\) and $y = √(x)$ about the x-axis is $\(V = (8)/(15)$ cubic units.$

To find the volume of the solid using the disk method, we integrate the cross-sectional area of each infinitesimally thin disk perpendicular to the x-axis.

The bounds of integration are determined by finding the x-values where the two curves intersect:

$x^3 = √(x) \implies x^6 = x \implies x^5 = 1 \implies x = 1.$

The radius of each disk is $r = x^3 - √(x)$ , and the area of each disk is $$A = \pi r^2 = \pi \left((x^3 - √(x))\right)^2$.$

The integral for the volume becomes:

$V = \int_(0)^(1) \pi \left((x^3 - √(x))\right)^2 \, dx.$

Evaluating this integral gives $$V = (8)/(15)$ cubic units.$

In summary, the volume of the solid obtained by rotating the region bounded by $y = x^3\) and $y = √(x)$ about the x-axis is $\(V = (8)/(15)$ cubic units.$ The volume is calculated by integrating the cross-sectional areas of infinitesimally thin disks formed by rotating the region.

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The equation of line k is y+3= – 1 2 (x–7). Perpendicular to line k is line , which passes through the point (7,6). What is the equation of line ?