Which is closest to the quotient 2,967 ÷ 0.003?

Consider the polynomial: StartFraction x Over 4 EndFraction – 2x5 + StartFraction x cubed Over 2 EndFraction + 1 Which polynomia

Phoenix [80]

Answer:

$- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$

Step-by-step explanation:

Given

$\frac{x}{4} - 2x^5 + \frac{x^3}{2} + 1$

Required

The standard form of the polynomial

The general form of a polynomial is

$ax^n + bx^{n-1} + cx^{n-2} +........+ k$

Where k is a constant and the terms are arranged from biggest to smallest exponents

We start by rearranging the given polynomial

$- 2x^5+ \frac{x^3}{2} +\frac{x}{4} + 1$

Given that the highest exponent of x is 5;

Let n = 5

Then we fix in the missing terms in terms of n

$- 2x^5+ 0x^{n-1} + \frac{x^3}{2} +0x^{n-3}+\frac{x}{4} + 1$

Substitute 5 for n

$- 2x^5+ 0x^{5-1} + \frac{x^3}{2} +0x^{5-3}+\frac{x}{4} + 1$

$- 2x^5+ 0x^{4} + \frac{x^3}{2} +0x^{2}+\frac{x}{4} + 1$

Hence, the standard form of the given polynomial is $- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$

3 0

2 years ago

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

5 0

2 years ago

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A rectangular block measures 3 cm x 4 cm x 3 cm how much water would it displace?

nika2105 [10]

Answer:

36c^3m^3x^2

Step-by-step explanation:

you first multiply 3 cm by 4 cm by 3 cm to get 36 cm.
its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter).
1.0 g/cm3
then you get the answer 36c^3m^3x^2

4 0

2 years ago

a photo collage consists of seven equal sized square photo arranged in a row to form a rectangle if the total area of the colleg

Keith_Richards [23]

Answer:

Step-by-step explanation:

I have attached a written explanation to help :).

Let's say each side of the square = $x$

If we put 7 squares in a row to make the rectangle,

length of the rectangle = $7x$

Area of a rectangle = length multiplied by width

Area of rectangle = $7x$ multiplied by $x$ = $7x^2$

We are also told that the total area = 567

So $7x^2 = 567$

Now solve for $x$ .

Divide both sides by 7.

$\frac{7x^2}{7} = \frac{567}{7}$

$x^2 = 81$

Then square root both sides to find $x$

$x = \sqrt{81}$ = 9

Finally, the question asks to find the length of the collage which we said was $7x$ and we know $x = 9$

Length of collage = $7x = 7$ multiplied by $9$ = ?

7 0

2 years ago

Suppose f(x)= x^2 and g(x)=(1/3x)^2 which statement best compares the graph of g(x) with the graph of f(x)

Leni [432]

The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".

Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.

The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3

8 0

2 years ago

Read 2 more answers