Resources

Resources

Solve quadratic equations: word problems

-0

31

-260

2

9

500

A shoe manufacturer determines that its monthly revenue,

\newline

R(q)

, in dollars, is given by the function, where

\newline

q

is the number of pairs of shoes sold each month. What is the maximum value of the company's monthly revenue in dollars?

\newline

A) \(9\),\(500\)\(\newline\)B)

10

000

\newline

C) \(11\),\(000\)\(\newline\)D)

12

000

A sheet of glass has a density of

2.5 ext{ g/cm}^3

. What is the density of the glass in

ext{kg/m}^3

A sheet of glass has a density of

2.5 ext{ g/cm}^3

. What is the density of the glass in

ext{kg/m}^3

Yoku is putting on sunscreen. He uses

2 \mathrm{ml}

50 \mathrm{~cm}^{2}

of his skin. He wants to know how many milliliters of sunscreen

(c)

he needs to covel

325 \mathrm{~cm}^{2}

\newline

How many milliliters of sunscreen does Yoku need to cover

325 \mathrm{~cm}^{2}

\newline

\square

\mathrm{ml}

question: \dfrac{\left(\dfrac{a}{b}+

1

\right)}{\left(\dfrac{b}{a}

-1

question: \dfrac{\left(\dfrac{a}{b}+

1

\right)}{\left(\dfrac{b}{a}

-1

130

mile trip, a car traveled an average speed of

\newline

55

mph and then reduced its speed to

40

mph for the remainder of the trip. The trip took

2.5

hours. For how long did the car travel at

\newline

40

1.8

megawatt wind turbine can produce about

8,000,000

kilowatt hours of electricity each year. Write

8,000,000

in scientific notation.

8,000,000 =?\times10^{?}

NASA launches a rocket at

t=0

seconds. Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9 t^{2}+223 t+241

\newline

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

\newline

The rocket splashes down after

\square

\newline

How high above sea-level does the rocket get at its peak?

\newline

The rocket peaks at

\square

meters above sea-level.

A person's systolic blood pressure, which is measured in millimeters of mercury

(\mathrm{mm} \mathrm{Hg})

, depends on a person's age, in years. The equation:

\newline

P=0.006 y^{2}-0.03 y+122

\newline

gives a person's blood pressure,

P

y

\newline

A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age

44

years._________

\newline

B.) If a person's systolic pressure is

130.86 \mathrm{~mm} \mathrm{Hg}

, what is their age (rounded to the nearest whole year)?_______

Given the factored form of the function

\newline

y=(x-4)(x-3)

, find the following:

\newline

x

\newline

b.) Find the vertex

Rachel is a stunt driver, and she's escaping from a building that is about to explode!

D

represents Rachel's remaining distance (in meters) as a function of time

t

(in seconds). In

D = -38t + 220

, what's Rachel's speed?

A private jet left Sydney at

09:00

and arrived in Perth at

13:00

local time. Sydney time is

2

hours ahead of Perth time.

\newline

If the distance flown was

3024

kilometres, what was the jet's average flying speed?

\newline

504\text{km/h}

\newline

540\text{km/h}

\newline

706\text{km/h}

\newline

756\text{km/h}

A human hair is approximately

40

microns wide. If

1

micron is equal to

10^{-6}

1

nanometer is equal to

10^{-9}

m, then how many nanometers wide is a human hair?

Danny is measuring two pyramids whose bases are squares.

\newline

Given the height

h

V

of the first pyramid, Danny uses the formula

\newline

a=\sqrt{\left(\frac{3V}{h}\right)}

\newline

to compute its base's side length

a

5

\newline

The second pyramid has the same volume, but has

4

times the height. What is the side length of its base?

Mindy is a sculptor. She has a cylinder of stone with a radius of

3 \text{ m}

and a height of

2\text{ m}

. She needs to carve out a sphere of radius

1\text{ m}

from the cylinder. Mindy must cut away

\frac{v}{3}\pi \text{ cubic meters } (\text{m}^{3})

of stone from the cylinder in order to be left with the sphere. What is the value of

v

A conical glass holds

131

cubic centimeters of water. It has a height of

5

centimeters. The radius of the top of the glass is

\sqrt{\left(\frac{m}{5\pi}\right)}

centimeters, where

m

is a constant. What is the value of

m

\newline

\square

\newline

20l+25g-10

gives the number of dollars that Josie makes from mowing

l

lawns and raking

g

gardens. How many dollars does Josie make from raking

4

gardens and mowing

3

\newline

\square

The length of an

8000

square foot rectangular gymnasium is

20

feet greater than its width. What is its width, in feet?

\newline

A small pizza has an area of

730

square centimeters.

\newline

Write an inequality that describes

p

, the area of a pizza that is larger than a small pizza.

\newline

\square

A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of

80\,\text{in}

60\,\text{in}

, and a height of

44\,\text{in}

. She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of

8\,\text{in}

4\,\text{in}

, and heights of

2\,\text{in}

. How many bricks can the contractor fit in the storage area of her truck?

\newline

A multi-layer cake is in the shape of a right cylinder. The height of the cake is

20\,\text{cm}

, and its radius is

10\,\text{cm}

. If each of the cake layers has a volume of approximately

1,250\,\text{cubic centimeters}

, then how many layers does the cake have?

\newline

Aditya's dog routinely eats Aditya's leftovers, which vary seasonally. As a result, his weight fluctuates throughout the year. The dog's weight

W(t)

\text{kg}

) as a function of time

t

(in days) over the course of a year can be modeled by a sinusoidal expression of the form

a

\cdot

\cos(b

\cdot

t

)

+d

\newline

t=0

, the start of the year, he is at his maximum weight of

9.1\,\text{kg}

. One-quarter of the year later, when

t=91.25

, he is at his average weight of

8.2\,\text{kg}

\newline

W(t)

\newline

t

should be in radians.

\newline

W(t)

=

The following function gives the cost, in dollars, of producing

x

kilograms of fertilizer:

\newline

C(x)=0.001 x^{3}-0.14 x^{2}+7 x

\newline

What is the instantaneous rate of change of the cost when

50

kilograms are produced?

\newline

1

\newline

-6

5

kilograms per dollar

\newline

-6

5

dollars per kilogram

\newline

0

5

kilograms per dollar

\newline

0

5

dollars per kilogram

The following function gives the cost, in dollars, of producing

x

gallons of wood stain:

\newline

C(x)=0.0004 x^{3}-0.001 x^{2}+1

\newline

What is the instantaneous rate of change of the cost when

100

gallons are produced?

\newline

1

\newline

11

9

\newline

11

9

dollars per gallon

\newline

3600

\newline

3600

dollars per gallon

The following function gives the cost, in dollars, of producing

x

kilograms of fertilizer:

\newline

C(x)=0.001 x^{3}-0.14 x^{2}+7 x+160

\newline

What is the instantaneous rate of change of the cost when

50

kilograms are produced?

\newline

1

\newline

-6

5

kilograms per dollar

\newline

-6

5

dollars per kilogram

\newline

0

5

kilograms per dollar

\newline

0

5

dollars per kilogram

A water tank is drained. The following function gives the volume, in liters, of the water remaining in the tank

t

minutes after the drain is opened:

\newline

V(t)=3000(1-0.05 t)^{2}

\newline

What is the instantaneous rate of change of the volume after

10

\newline

1

\newline

-150

liters per minute

\newline

-150

minutes per liter

\newline

750

liters per minute

\newline

750

minutes per liter

The radius of a sphere is decreasing at a rate of

4

centimeters per second.

\newline

At a certain instant, the radius is

10

\newline

What is the rate of change of the surface area of the sphere at that instant (in square centimeters per second)?

\newline

1

\newline

-64 \pi

\newline

-320 \pi

\newline

-400 \pi

\newline

-160 \pi

\newline

The surface area of a sphere with radius

r

4 \pi r^{2}

The radius of a cone is increasing at a rate of

3

centimeters per second and the height of the cone is decreasing at a rate of

4

centimeters per second.

\newline

At a certain instant, the radius is

8

centimeters and the height is

10

\newline

What is the rate of change of the volume of the cone at that instant (in cubic centimeters per second)?

\newline

1

\newline

-\frac{736 \pi}{3}

\newline

-\frac{224 \pi}{3}

\newline

\frac{736 \pi}{3}

\newline

\frac{224 \pi}{3}

\newline

a

cone with radius

r

h

\pi r^{2} \frac{h}{3}

The surface area of a sphere is increasing at a rate of

14 \pi

square meters per hour.

\newline

At a certain instant, the surface area is

36 \pi

\newline

What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?

\newline

1

\newline

36 \pi

\newline

(\sqrt{14 \pi})^{3}

\newline

\frac{7}{12}

\newline

21 \pi

\newline

The surface area of a sphere with radius

r

4 \pi r^{2}

\newline

The volume of a sphere with radius

r

\frac{4}{3} \pi r^{3}

The radius of a sphere is increasing at a rate of

0

5

centimeters per minute.

\newline

At a certain instant, the radius is

17

\newline

What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)?

\newline

1

\newline

3275 \pi

\newline

289 \pi

\newline

578 \pi

\newline

\frac{1}{6} \pi

\newline

The volume of a sphere with radius

r

\frac{4}{3} \pi r^{3}

The radius of the base of a cylinder is decreasing at a rate of

12

kilometers per second.

\newline

The height of the cylinder is fixed at

2

5

\newline

At a certain instant, the radius is

40

\newline

What is the rate of change of the volume of the cylinder at that instant (in cubic kilometers per second)?

\newline

1

\newline

-2400 \pi

\newline

-4000 \pi

\newline

-1600 \pi

\newline

-360 \pi

\newline

The volume of a cylinder with radius

r

h

\pi r^{2} h

The radius of a sphere is decreasing at a rate of

1

meter per hour.

\newline

At a certain instant, the radius is

4

\newline

What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?

\newline

1

\newline

-\frac{256 \pi}{3}

\newline

-64 \pi

\newline

-\frac{4 \pi}{3} \pi

\newline

-16 \pi

\newline

The volume of a sphere with radius

r

\frac{4}{3} \pi r^{3}

The radius of a sphere is increasing at a rate of

0

5

centimeters per minute.

\newline

At a certain instant, the radius is

17

\newline

What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)?

\newline

1

\newline

\frac{1}{6} \pi

\newline

289 \pi

\newline

578 \pi

\newline

3275 \pi

\newline

The volume of a sphere with radius

r

\frac{4}{3} \pi r^{3}

The volume of a sphere is increasing at a rate of

25 \pi

cubic meters per hour.

\newline

At a certain instant, the volume is

\frac{32 \pi}{3}

\newline

What is the rate of change of the surface area of the sphere at that instant (in square meters per hour)?

\newline

1

\newline

\frac{32 \pi}{9}

\newline

25 \pi

\newline

\frac{25}{16}

\newline

(\sqrt[3]{25 \pi})^{2}

\newline

The surface area of a sphere with radius

r

4 \pi r^{2}

\newline

a

sphere with radius

r

\frac{4}{3} \pi r^{3}

A hovercraft takes off from a platform.

\newline

Its height (in meters),

x

seconds after takeoff, is modeled by:

h(x)=-3(x-3)^{2}+108

\newline

How many seconds after takeoff will the hovercraft land on the ground?

\newline

\square

Rachel is a stunt driver, and she's escaping from a building that is about to explode!

\newline

D

represents Rachel's remaining distance (in meters) after

t

\newline

D=-38t+220

\newline

How long is the distance Rachel has to drive?

\newline

\square

The altitude of the International Space Station

t

minutes after its perigee (closest point), in kilometers, is given by

\newline

A(t)=415-\sin \left(\frac{2 \pi(t+23.2)}{92.8}\right) .

\newline

The International Space Station reaches its perigee once in every orbit.

\newline

How long does the International Space Station take to orbit the earth? Give an exact answer.

\newline

\square

Hungry Harry is a giant ogre with an even bigger appetite.

\newline

After Harry wakes up from hibernation, his daily hunger

H(t)

\mathrm{kg}

of pigs) as a function of time

t

(in hours) can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

When Harry wakes up at

t=0

, his hunger is at a maximum, and he desires

30 \mathrm{~kg}

of pigs. Within

2

hours, his hunger subsides to its minimum, when he only desires

15 \mathrm{~kg}

\newline

H(t)

\newline

t

should be in radians.

\newline

H(t)=

Hugo's bike tire has a piece of gum stuck to it.

\newline

G(t)

\mathrm{cm}

) between the gum and the sidewalk as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

\newline

t=0

, the gum is halfway between the ground and its maximum height, at

35 \mathrm{~cm}

. The gum reaches its maximum height of

70 \mathrm{~cm}

from the ground

\frac{\pi}{20}

\newline

G(t)

\newline

t

should be in radians.

\newline

G(t) = \square

A spring is hanging from a ceiling.

\newline

L(t)

\mathrm{cm}

) of the spring as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

\newline

t=0

, when the spring is exactly in the middle of its oscillation, its length is

7 \mathrm{~cm}

0

5

seconds the spring reaches its maximum length, which is

12 \mathrm{~cm}

\newline

L(t)

\newline

t

should be in radians.

\newline

L(t)=

Rania is riding the ferris wheel.

\newline

Her vertical height

H(t)

\mathrm{m}

) off the ground as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, when she starts moving, she is at a height of

10 \mathrm{~m}

off the ground, which is as low as she goes. After

20 \pi

seconds, she reaches her maximum height of

30 \mathrm{~m}

\newline

H(t)

\newline

t

should be in radians.

\newline

H(t)=

R(t)

\mathrm{mm}

) over the course of a year in Bali, Indonesia as a function of time

t

(in days) can be modeled by a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

\newline

t=0

, in mid-April, the expected daily rainfall is

2.3 \mathrm{~mm}

, which is the average value throughout the year. One-quarter of the year later, at

t=91.25

, the rainfall is at its minimum, at an expected daily value of

1.4 \mathrm{~mm}

\newline

R(t)

\newline

t

should be in radians.

\newline

R(t)=\square

A cylindrical glass of water is

2.5

centimeters tall and holds a volume of

20

cubic centimeters of water. The radius of the glass is

\sqrt{\frac{p}{\pi}}

centimeters, where

p

\newline

What is the value of

p

\newline

\square

Members of the swim team want to wash their hair. The bathroom has less than

5600

liters of water and at most

2.5

liters of shampoo.

\newline

70L + 60S < 5600

represents the number of long-haired members

L

and short-haired members

S

who can wash their hair with less than

5600

liters of water.

\newline

0.02L + 0.01S \leq 2.5

represents the number of long-haired members and short-haired members who can wash their hair with at most

2.5

liters of shampoo.

\newline

Does the bathroom have enough water and shampoo for

8

long-haired members and

7

short-haired members?

A bowler throws a cricket ball at a speed of

36\,\text{km/hr}

. How long does this ball take to travel a distance of

20\,\text{metres}

to reach the batsman?

The water level of Oshawa Creek is rising as the snow melts. On the first day of Spring, the creek rise a certain number of centimetres. One the second day, it rises

4

more centimetres than the amount it rose the first day. On the third day, it rose

4

more centimetres than it did on the second day, and so on. On the

5^{\text {th }}

day, the combined increase from the first

5

days of Spring was

5

centimetres higher than

1

(100 \mathrm{~cm})

\newline

How many centimetres did the Oshawa Creek rise each day?

100 + 20m

gives the volume of water, in liters, in Marcel's pool after Marcel spends

m

minutes filling his pool. What is the volume of water, in liters, in Marcel's pool after he fills it for

5 \frac{1}{4}

A hovercraft takes off from a platform.

\newline

Its height (in meters),

x

seconds after takeoff, is modeled by:

\newline

h(x)=-2 x^{2}+20 x+48

\newline

What is the maximum height that the hovercraft will reach?

\newline

\square

Your business client has booked accommodation for a staff conference in December and has asked for a G.S.T receipt for the accounts.

\newline

10

poolside double rooms at the Oasis Beach Resort in Taupo for

2

\newline

The total cost comes to

\$ 4880.00

including G.S.T.

\newline

How much of this is G.S.T?

\newline

\$ \_\_\_\_\_