Math - Others Questions

Verify the identity sin 0 sec 0 tan 0 Which of the following four statements verifies the identity O A sin 0 sec 0 sin 0 OB sin 0 sec 0 OC sin 0 sec 0 cos sin 0 sin 0 cos 0 1 cos 0 OD sin 0 sec 0 sec 0 sin 0 1 COS cos sin 0 cos 0 cos sin 0 tan 0 sin 0 cos tan 0 cos 0 sin 0 P tan 0 tan 0

Multiply and simplify csc 0 sin 0 0 COS CSC sc 0 sin 20 cos 0 Simplify your answer

Bob is cleaning his gutters and leans a ladder against the house If the ladder forms a 33 angle with the side of the house what is the measure of the angle between the ladder and the ground

What is the measure of Angle B A C m B 67 53 B

The graph of the hyperbola is given a Use the distance formula to find the distances d d d3 and d b Find the difference of the distances d d c Find the difference of the distances d d How do the results from Parts b and c compare How do the results of Part b and Part c compare to the length of the transverse axis Express numbers as integers or simplified fractions 20 16 12 B ol 4 17 201 20 16 0 10 d Vd 7 da 4 d 0 10 10 12 16 20 Save For Later

2 Part 0 3 3 A boat leaves port and follows a course of N72 E at 9 knots for 3 hr and 20 min Then the boat changes to a new course of S20 E at 12 knots for Part 1 of 3 a How far is the boat from port Round the answer to one decimal place if necessary The boat is approximately 6 nmi from port X

1 point Question Attempt 1 of Unlimited The graph of the parabola is given a Determine the distances d d dz and d b Compare d and d c Compare d3 and d 5 x 4 1 9 da 2 d 4 0 d3 4 8 9 12 12

Question Attempt 1 of Unlimited The graph of the ellipse is given a Use the distance formula to find the distances d d d3 and d4 b Find the sum d d c Find the sum dz d4 d How do the sums from b and c compare e How do the sums of the distance from b and c relate to the length of the major axis Express numbers in exact simplest form Note that the points 0 4 and 0 4 represent the foci 3 0 d Tr 4 6 0 4 d 3 4

Write the standard form of the equation of the hyperbola subject to the given conditions Vertices 3 0 3 8 Foci 3 4 22 3 4 22 The equation of the hyperbola in standard form is 8 0 0 0

The equation of a parabola is given a Write the equation of the parabola in standard form b Identify the vertex the focus and the focal diameter Express numbers as integers or fractions in simplest form 4x 12x 32y 265 0 Part 0 4 Part 1 of 4 The equation of the parabola in standard form is

The equation of a parabola is given y 2y 12x 11 0 a Write the equation of a parabola in standard form b Identify the vertex focus and focal diameter Express numbers in exact simplest form Part 0 4 Part 1 of 4 The equation of a parabola in standard form is

For y x 7 20 Part 0 5 1 a Identify the center c Identify the foci e Graph the hyperbola Give exact answers Express numbers in simplest form using integers fractions or radicals Part 1 of 5 b Identify the vertices d Write equations for the asymptotes a The center is

A college is building a new basketball court that is 100 feet long and 40 feet wide but the wood for the court comes only in 8 meter planks that are 6 centimeters wide How many planks are needed to surface the court The court will require planks X 5

Select the correct answer Melissa and Robbie are flying remote control gliders The altitude of Melissa s glider h s in feet is modeled by this function where s is time in seconds after launch m 8 0 4 8 118 3181 The altitude of Robbie s glider is modeled by function r where s is time in seconds after launch Altitude feet r s 25 20 15 10 5 0 1 2 3 4 5 6 7 8 Time seconds Which glider reaches the greater maximum altitude in the first 6 seconds after launch 5 A B TS Robbie s glider Both gliders reach the same altitude on the given interval Meither glider reor imum altitude on the alven intonal

5 Select the correct answer from each drop down menu Elwood invested 5 000 in a money market account and has been tracking its progress He found that after 3 years the account held 7 100 and after 8 years the account held 10 350 Use this information to complete the statements Over the first 3 years the value of the account increased at value of the account increased at an average rate of approximately Reset annually Next over the last 5 years Over the entire 8 years the

Q2 In Q 5 express the following elements as polynomials in 5 a b 2 5 3 5 5 20

Calculate the value of x 2x 20 X 3x 10

Find the measures of 22 and 11 m 2 m 11 140 1 2 10 9 80 8 11 12 d

A company must pay a 309000 settlement in 3 years a What amount must be deposited now at compounded semiannually to have enough money for the settlement b How much interest will be earned c Suppose the company can deposit now in an account that pays interest continuously What interest rate would they need to accumulate the entire in years

2 The graph of the inverse function f 1 is A y B A S x 3 The equation of the inverse function f is A f x ln x 3 4 C f x In 4 B f x In x 4 3 D f x In 3

Solve the problem If 9 1 what does 81 equal 000 4 16 16 1 0 16

The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source The populations of the smaller animal depends upon the amount a of a certain plant that is its primary food source If P x 3x 4 and s a 2a 2 what is the relationship between the predator mammal and the plant food source OP s a 4a 8a 8 O P s a 12a2 24a 16 P s a 6a 6 P s a 12a 12a 16 OP s a Pa

formula D 50e 0 5h can be used to find the number of milligrams D of a certain drug that is in a patient s bloodstream h hours after the drug was administered When the number of milligrams reaches 4 the drug is to be administered again What is the time between injections The time between injections is

Find a formula for the inverse of the function described below An organization determines that the cost per person of chartering a bus is given by the formula 250 6x C x x where x is the number of people in the group and C x is in dollars OC 1 x 250 x 6 OC x 226 250 E x 6 6 C 1 x x 250 C x 2 50 6

Find the domain of the composite function fog f x 10 2 g x x 1 x 2 11 x1x 21 x x 3 x x is any real number

Change the exponential statement to an equivalent statement involving a logarithm 1 9 a 02 log1 9 01 9 log2 01 9 log2a a log 1 9

For the given functions f x O 5 4 x 7 8 x x Find f o g x 35x 4 4 5x 4 49 35x 4 4 f and g find the requested composite function 4x 28 35x

Solve the equation log2169 2 The solution is I Type integers or simplified fractions

The function f is one to one Find its inverse f x x 8x 1 Of x x Of x 7 8x 1 7x 1 7x 1 Of x x 1 8 7 Of 1 x 1 8x 1

and the inverse of the function and state its domain and range 3 4 1 5 0 2 2 6 5 7 3 4 1 5 0 2 2 6 5 7 D 3 1 0 2 5 R 2 4 5 6 7 3 4 1 5 0 2 2 6 5 7 D 3 1 0 2 5 R 7 6 5 4 2 3 4 1 5 0 2 2 6 5 7 D 3 1 0 2 5 R 7 6 5 4 27 O 4 3 5 1 2 0 6 2 7 5 D 2 4 5 6 7 R 3 1 0 2 5

ve the problem The function f x 800 0 5 100 models the amount in pounds of a particular radioactive material stored in a concrete vault where x is the number of years since the material was put into the vault Find the amount of radioactive materialin vault after 190 years Round to the

Find the domain of the composite function fog f x g x 5x 20 x x2 4 x 1x 20 O xx is any real number xxs 4 or x 201

Evaluate the expression using the values given in the table gof 1 x 5 4 4 1 3 8 5 11 g x 5 11 12 11 1 13 O O O O 4 11 8 5

Solve the equation 2x 3 64 5 35 3 O 6 3 3

4 A round steel bin is filled with wheat at 17 1 m c w b The bin has a diameter of 7 31 m 24 ft and is filled to a depth of 3 0 m 10 ft a Calculate the lateral pressures at the base of the bin wall when the wheat is at 17 1 and 11 0 moisture Estimate density using the appropriate formula chap 2 Assume the depth will remain the same after drying Determine the percent increase in pressure for the 11 0 m c wheat compared to the wheat that is at 17 1 m c b The bin is unloaded through a square orifice 20 3 cm x 20 3 cm 8 in x 8 in located on the side of the bottom of the bin i e it will be a vertical orifice Assume the flow rate will be constant during unloading Estimate the rate at which grain flows from the bin and the total time required to unload the bin c The wheat is conveyed away from the orifice on a flat no slope on the sides horizontal belt conveyor moving at 15 2 m s 50 ft s Using the angle of repose neglect the effects of inertia by assuming the wheat is piled on a non moving belt estimate the minimum width required for the belt I Hint for c The belt should be capable of carrying of grain from the unloading rate calculated by question b The shape of the particles on the belt is triangular prism h e The volumetric flow rate of particles on the belt can be calculated from the cross sectional area given by the above figure and belt moving speed u V u A

A function f x is transformed into the function g x 2 x 4 7 Choose the 3 transformations that occurred O Vertical Shift Down 7 O Vertical Shift Up 7 O Vertical Stretch Horizontal Shift Left 4 units

9 Solve a right triangle 10 pts Solve the following triangle that is find B b and c Don t forget to show your work B a 19

10 pts Solve an exponential equation Don t forget to show your work Solve for x Round your answer to four decimal places if needed 43x 2 34x 3

7 10 pts Solve a logarithmic equation Don t forget to show your work Solve for x Round your answer to four decimal places if needed log4 x log4 x 6 2

5 Consider the angle 120 a 5 pts Sketch the angle Don t forget to show the rotation b 2 pts Find the reference angle for 0

6 Expanding and condensing logarithmic expressions Don t forget to show your work a 5 pts Use the properties of logarithms to expand In a sum difference and or constant multiple of logarithms as b 5 pts Condense 9 ln x 6 ln y 7 4ln z to the logarithm of a single quantity nx 6ln y 7 4khz to

2 7 pts You invested 37 000 in Yug Industries at an annual interest rate of 5 compounded continuously Find the amount received after a six year investment Don t forget to show your work Round your answer to the nearest cent COLLEGE

1 At the beginning of an experiment a scientist has 600 grams of radioactive Guyradium Gy After 100 minutes the sample has decayed to 300 grams a 5 pts Assuming exponential decay find a formula for G t the amount of Guyradium remaining at time t b 5 pts How many grams of Guyradium will remain after 150 minutes Round your answer to four decimal places

4 8 pts Find the length of the arc of a circle of 13 cm subtended by the central angle of 200 Round your answer to two decimal places

3 8 pts A sector of a circle has a central angle of 125 Find the area of the sector if the radius of the circle is 11 cm Round your answer to two decimal places

A certain paper suggested that a normal distribution with mean 3 500 grams and standard deviation 540 grams is a reasonable model for birth weights of babies born in Canada Round your answers to four decimal places a One common medical definition of a large baby is any baby that weighs more than 4 000 grams at birth What is the probability that a randomly selected Canadian baby is a large baby USE SALT b What is the probability that a randomly selected Canadian baby weighs either less than 2 000 grams or more than 4 000 grams at birth c What birth weights describe the 15 of Canadian babies with the greatest birth weights Any baby with a weight of grams or more is in the greatest 15 of birth weights Need Help Read It Submit Answer Rointsl DETAILS Watch It PECKSTAT3 6 5 047 MI S MY NOTES PRACTICE ANOTHER

Suppose that the velocity v t in meters per second of a sky diver falling near the Earth s surface is given by the following exponential function where time is the time after diving measured in seconds v t 61 61e 0 261 How many seconds after diving will the sky diver s velocity be 43 meters per second Round your answer to the nearest tenth and do not round any intermediate computations seconds X

Suppose that 5000 is placed in a savings account at an annual rate of 6 compounded monthly Assuming that no withdrawals are made how long will it take for the account to grow to 8030 Do not round any intermediate computations and round your answer to the nearest hundredth years

Solve a Consumers or Producers Surplus Problem A sports watch has a price demand equation given by p D z 95 2 0 027076 dollars which gives the price per watch when z watches are demanded The price supply equation for the watch is given by p S x 0 9x 2 dollars which gives the price per watch when a watches are supplied If the equilibrium quantity is 44 find the consumers surplus and the producers surplus The consumers surplus is Your answer must begin with S The producers surplus is Your answer must begin with S

Solve a Consumers or Producers Surplus Problem The supplier of a popular board game called Who Dunnit has a price supply equation given by p S x 20 2 6x dollars which gives the price per game when z games are supplied If market equilibrium is reached when 22 games are sold at a price of 77 2 eac find the producers surplus The surplus is Your answer must begin with