Name a pair of vertical angles with vertex V

Find the area of a circle with (a) a radius of 9.2 centimeters and (b) a diameter of 50.5 inches.

astra-53 [7]

NAH I HATE PI IM OUT

6 0

2 years ago

A farmer fills his field proportionately with soybeans and corn. Last year he planted 200 acres of corn and 50 acres of soybeans

malfutka [58]

Answer:

Part A) Is a directly proportional

Part B) The constant of proportionality is $k=0.25$

Part C) The equation is $y=0.25x$

Part D) $62.5$ acres of soybeans

Step-by-step explanation:

Part A) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional?

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$

Let

x-----> the number of acres of corn

y----> the number of acres of soybeans

so

$y/x=k$

if the number of acres of corn increases then the number of acres of soybeans increases

if the number of acres of corn decreases then the number of acres of soybeans decreases

therefore

The relationship is a directly proportional

Part B) What is the constant of proportionality?

we have that

For x=200, y=50

substitute

$y/x=k$

$k=50/200$

$k=0.25$

Part C) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

The linear equation that represent the direct variation is equal to

$y/x=k$

we have

$k=0.25$

substitute

$y/x=0.25$

$y=0.25x$

Part D) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn?

For x=250

Find the value of y

substitute in the linear equation the value of x and solve for y

$y=0.25(250)=62.5$ -----> acres of soybeans

7 0

3 years ago

The value of a car decreases $500 for every 1,000 miles it is driven. The current value of the car is $23,000, and the car is dr

Hoochie [10]

Answer: C

Step-by-step explanation:

If we know the value of the car decreases $500 for every 1,000 miles, and that the car is driven about 10,000 miles every year, that means that you need to take the total value of the car (23,000) and subtract it from the amount of money it is losing per year. Again, the car is driven about 10,000 miles per year, so that means that the car will most likely continue to be driven 10,000 miles per year. If you do the math, for one year, the value of the car will drop $5,000 ($500 x 10, because it is $500 per every 1,000 miles) So, for each year, you can just multiply the number of years by $5,000 to find out how much the vehicle has depreciated over time.

Hope this helped you and made sense! Feel free to ask me any questions you have!

4 0

2 years ago

A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs

LenKa [72]

Answer:

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

Step-by-step explanation:

Volume of the Cylinder=400 cm³

Volume of a Cylinder=πr²h

Therefore: πr²h=400

$h=\frac{400}{\pi r^2}$

Total Surface Area of a Cylinder=2πr²+2πrh

Cost of the materials for the Top and Bottom=0.06 cents per square centimeter

Cost of the materials for the sides=0.03 cents per square centimeter

Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)

C=0.12πr²+0.06πrh

Recall: $h=\frac{400}{\pi r^2}$

Therefore:

$C(r)=0.12\pi r^2+0.06 \pi r(\frac{400}{\pi r^2})$

$C(r)=0.12\pi r^2+\frac{24}{r}$

$C(r)=\frac{0.12\pi r^3+24}{r}$

The minimum cost occurs when the derivative of the Cost =0.

$C^{'}(r)=\frac{6\pi r^3-600}{25r^2}$

$6\pi r^3-600=0$

$6\pi r^3=600$

$\pi r^3=100$

$r^3=\frac{100}{\pi}$

$r^3=31.83$

r=3.17 cm

Recall that:

$h=\frac{400}{\pi r^2}$

$h=\frac{400}{\pi *3.17^2}$

h=12.67cm

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

3 0

3 years ago

The definition of parallel lines requires the undefined terms line and plane, while the definition of perpendicular lines requir

Tomtit [17]

Point, line, and plane are the undefined expression that relinquish the starting location for geometry. When we define words, we ordinarily use simpler words, and these simpler words are in turn defined using yet simpler words. This procedure must eventually abort; at some stage, the definition must use a word whose meaning is accepted as intuitively clear. Because that meaning is accepted without definition, we refer to these words as undefined terms. These terms will be used in defining other terms. Although these expressions are not formally defined, a brief intuitive dialogue is needed. A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point constitute position only. A line (straight line) can be thought of as a connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has boundless length, zero width, and zero height. Any two points on the line name it. The symbol ↔ written on top of two letters is used to denote that line. <span>A plane may be contemplating as an infinite set of points creating a connected flat surface extending infinitely far in all directions. It is usually represented in drawings by a four‐sided figure. A single capital letter is used to designate a plane.</span>

4 0

3 years ago

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