Question 1

Round to the nearest tenth unless indicated otherwise.
-The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 20 foot length with diameter 5 inches cost? Round to the
Nearest cent.
A) $485.30
B) $477.60
C) $485.57
D) $480.00

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 2

What are the possible number of real zeros (counting multiplicities) for a polynomial function with real
coefficients of degree four?

Accepted Answer

The answer of What are the possible number of real...

Question 3

Round to the nearest tenth unless indicated otherwise.
-The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an
1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, what force would be required
To keep the same car from skidding on a curve of radius 640 feet at 50 mph? Round your answer to the nearest
Pound of force.
A) 20,962 lb
B) 21,094 lb
C) 21,126 lb
D) 21,664 lb

Accepted Answer

The force $F$ needed to keep a car from skidding on a curve varies jointly as the weight of the car $W$ and the square of the car's speed $v^2$, and inversely as the radius of the curve $r$. This relationship can be expressed as $F = k \cdot \frac{Wv^2}{r}$, where $k$ is a constant of proportionality. Given that a force of 3600 pounds is needed for an 1800 pound car traveling at 20 mph on a curve of radius 600 feet, we can find $k$ by rearranging the formula to $k = \frac{Fr}{Wv^2}$ and substituting the given values. To find the force required for the same car on a curve of radius 640 feet at 50 mph, we use the same formula with the new values for $v$ and $r$, keeping $W$ and $k$ the same. After calculating, the result is rounded to the nearest pound, leading to the correct choice.

Question 4

What is the range of the graph? 
A) $( - 3.43,8.61 )$
B) $( - 8.85 , \infty )$
C) $( - \infty , \infty )$
D) $( - 8.85,44.86 )$

Accepted Answer

The answer of What is the range of the graph?...

Question 5

Round to the nearest tenth unless indicated otherwise.
-Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of $40 \mathrm { mph }$ with a surface area of $34 \mathrm { ft } ^ { 2 }$ experiences a drag of $231.2 \mathrm {~N}$ (Newtons), how fast must a car with $39 \mathrm { ft } ^ { 2 }$ of surface area travel in order to experience a drag force of $483.99 \mathrm {~N}$ ?
A) 75 mph
B) 78 mph
C) 70 mph
D) 73 mph

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 6

How many positive real zeros does this graph have? 
A) 1
B) 3
C) 2
D) 4

Accepted Answer

The answer of How many positive real zeros does this...

Question 7

What is the smallest possible degree of the function for which this graph represents? 
A) 4
B) 3
C) 2
D) 5

Accepted Answer

The answer of What is the smallest possible degree of...

Question 8

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?
A) 1, 3, or 5
B) 0, 2, 4, or 6
C) 2, 4, or 6
D) 6

Accepted Answer

A polynomial of degree n can have up to n real zeros (counting multiplicities), and by the Fundamental Theorem of Algebra, it must have exactly n roots (real or complex) in total. For a sixth-degree polynomial, this means it can have 0, 2, 4, or 6 real zeros, with the rest being complex conjugate pairs if not real.

Question 9

Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, $3,5 , \text { and } 1 + i$

Accepted Answer

The answer of Why is it not possible for a...

Question 10

Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms. What would the
Resistance be for a 25 foot length, with diameter 0.01 inch, of the same kind of wire ?
A) 368 ohms
B) 372.5 ohms
C) 375 ohms
D) 387 ohms

Accepted Answer

The resistance $R$ of a wire varies directly as the length $L$ of the wire and inversely as the square of the diameter $d$ of the wire, which can be represented by the formula $R = k \cdot \frac{L}{d^2}$, where $k$ is a constant. Given a 20-foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms, we can find $k$ by substituting these values into the formula: $3 = k \cdot \frac{20}{(0.1)^2}$. Solving for $k$ gives $k = 0.15$. For a 25-foot length of wire with a diameter of 0.01 inch, the resistance $R$ can be found by substituting these values and the found $k$ into the formula: $R = 0.15 \cdot \frac{25}{(0.01)^2}$, which calculates to 375 ohms.

Question 11

Round to the nearest tenth unless indicated otherwise.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk
Is 3 feet, what is the volume of wood obtained from a tree that is 23 feet tall having a measurement of 4 feet
Around the trunk? 
A) $33.4 \mathrm { ft } ^ { 3 }$
B) $21.4 \mathrm { ft } ^ { 3 }$
C) $29.4 \mathrm { ft } ^ { 3 }$
D) $38.4 \mathrm { ft } ^ { 3 }$

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 12

Provide an appropriate response.
-How many real zeros does this graph have? 
A) 2
B) 1
C) 4
D) 3

Accepted Answer

The answer of Provide an appropriate response.
-How many real zeros...

Question 13

Why does a function defined by a polynomial of degree five with real coefficients have either 1, 3, or 5 real zeros
counting multiplicities?

Accepted Answer

The answer of Why does a function defined by a...

Question 14

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function
of odd degree? One of even degree?

Accepted Answer

The answer of The domain of a polynomial function is...

Question 15

Round to the nearest tenth unless indicated otherwise.
-At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.46 ohm when the diameter is 1 mm and the length is 230 cm, what is the
Resistance when the diameter is 2 mm and the length is 2170 cm?
A) 1.1 ohm
B) 542.5 ohm
C) 249.6 ohm
D) 2.2 ohm

Accepted Answer

The resistance is directly proportional to the length and inversely proportional to the square of the diameter. So, R = k * l / d^2, where k is a constant. We can find k by plugging in the given values: 0.46 = k * 230 / 1^2, so k = 0.002. Now we can use this to find the resistance when the diameter is 2 mm and the length is 2170 cm: R = 0.002 * 2170 / 2^2 = 1.1 ohms.

Question 16

Round to the nearest tenth unless indicated otherwise.
-The volume of a gas varies inversely as the pressure and directly as the temperature (in degrees Kelvin). If a certain gas occupies a volume of 2.2 liters at a temperature of 340 K and a pressure of 16 newtons per square
Centimeter, find the volume when the temperature is 306 K and the pressure is 24 newtons per square
Centimeter.
A) 3.7 L
B) 39.1 L
C) 1.3 L
D) 46.8 L

Accepted Answer

The volume of a gas varies inversely with pressure and directly with temperature, which can be represented by the formula $V = k \frac{T}{P}$, where $V$ is volume, $T$ is temperature, $P$ is pressure, and $k$ is a constant. Given the initial conditions, we can find $k$ and then use it to find the new volume under the changed conditions. The initial conditions give us $2.2 = k \frac{340}{16}$. Solving for $k$, we find that $k = \frac{2.2 \times 16}{340}$. Using this $k$ for the new conditions, $V = k \frac{306}{24}$, we can solve for the new volume, which results in approximately 1.3 liters.

Question 17

What is the domain of the graph? 
A) $( - \infty , \infty )$
B) $( - 8.85,44.86 )$
C) $( - 8.85 , \infty )$
D) $( - 3.43,8.61 )$

Accepted Answer

The answer of What is the domain of the graph?...

Quiz 4: Polynomials and Rational Functions

Round to the nearest tenth unless indicated otherwise. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 20 foot length with diameter 5 inches cost? Round to the Nearest cent.

What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

What is the range of the graph? $What is the range of the graph? A) ( - 3.43,8.61 ) B) ( - 8.85 , \infty ) C) ( - \infty , \infty ) D) ( - 8.85,44.86 )$

How many positive real zeros does this graph have?

What is the smallest possible degree of the function for which this graph represents?

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, $3,5 , \text { and } 1 + i$

Provide an appropriate response. -How many real zeros does this graph have?

Why does a function defined by a polynomial of degree five with real coefficients have either 1, 3, or 5 real zeros counting multiplicities?

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

What is the domain of the graph? $What is the domain of the graph? A) ( - \infty , \infty ) B) ( - 8.85,44.86 ) C) ( - 8.85 , \infty ) D) ( - 3.43,8.61 )$

Quiz 4: Polynomials and Rational Functions

Round to the nearest tenth unless indicated otherwise. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 20 foot length with diameter 5 inches cost? Round to the Nearest cent.

What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

What is the range of the graph?

How many positive real zeros does this graph have?

What is the smallest possible degree of the function for which this graph represents?

What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?

Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, 3,5, and 1+i3,5 , \text { and } 1 + i3,5, and 1+i

Provide an appropriate response. -How many real zeros does this graph have?

Why does a function defined by a polynomial of degree five with real coefficients have either 1, 3, or 5 real zeros counting multiplicities?

The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

What is the domain of the graph?

What is the range of the graph? $What is the range of the graph? A) ( - 3.43,8.61 ) B) ( - 8.85 , \infty ) C) ( - \infty , \infty ) D) ( - 8.85,44.86 )$

Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, $3,5 , \text { and } 1 + i$

What is the domain of the graph? $What is the domain of the graph? A) ( - \infty , \infty ) B) ( - 8.85,44.86 ) C) ( - 8.85 , \infty ) D) ( - 3.43,8.61 )$