High School Calculus Questions

point Library Michigan Chap16Sec3 Q47 pg Let W be the solid half cone bounded by z x y z 1 and the yz plane with x 0 and let Let W be the solid half cone bounded by z x y z 4 and the xz plane with y 0 V For each of the following decide without calculating its value whether the integral is positive negative or zero a Jw x y2 dV is positive negative zero b Jw yzdV is positive negative zero c Jw Vx y2dV is positive negative zero

Which of the following values are in the domain of th function graphed below Check all that apply A 2 B 2 C 1 D 5 5 5

Use the angle conversion capabilities of a graphing utility to convert the angle measure to decimal degree form Round your answer to three decimal places if necessary 116 45

Use the angle conversion capabilities of a graphing utility to convert the angle measure to D M S form 113 5

Find if possible the complement and supplement of the angle Enter NONE in any unused answer blanks 5 6 complement

Find the difference of the angles Write your answer in D M S form 120 45 29 and 18 36 6

Convert each radian measure to degree measure Do not use a calculator a 11 12 b 7 4

Convert the angle measure from degrees to radians Round your answer to three decimal pl 47 24 rad

7 Kofi Haris and Sharon are in a disagreement about how to solve for QU shown in the figure Kofi suggests setting up the proportion cos 27 and solving for QU 18 QU Haris suggests using the Law of Sines but Sharon says there is not enough information to do so since no angle and its opposite side are given Who is correct Explain your reasoning 111 S 27 U 18

Kara wants to solve for m N using the Law of Sines What one additional measurement does Kara need in order t do this Explain H 65 11 M

4 Which of the following statements is FALSE A sin S sin O x Y z X B sin H sin O C z sin O y sin H D X sin S 2 sin H 2 S X Y H

8 Solve the triangle by finding all missing side lengths and angle measures Round to the nearest tenth 5 39 R 94

An aqueous solution contains 0 150 M HCI at 25 0 C The pH of the solution is O A 0 82 O B 7 00 O C 0 150 O D 13 00 O E 1 00

A C TC 3 13 cos 1 1 A 73 C 9 15 sin cot A 2 3 B B D TC 3 2 D 3 TU B C 0 D TC In 2 TO 6

3 y 2sec 3x 1 Per Asymptote

5 Solve over the interval 0 0 2 2cos tane tane 6 Find ALL solutions to this equation in radians 2cos2x1 0

Find all solutions to each equation in radians 17 2 3 2tan 0 Solve each equation for 0 0 2 19 2cos 1 cos 1 0 21 sin 0 2sin 0 0

23 3x 2 9 3 7 4x 2 22 St a Period b Equation of all asymptotes c Possible equation for this graph acul d If the graph is defined as f x find where f x 1 over the interval 0 x 2

Precalculus 2024 Kuta Software LLC All rights Assignment 1 What parent function matches the given graph 27 3M T

A guy wire is a cable used to restrain objects from moving They are used to support towers or poles A guy wire is attached to a cell tower The 50 foot long guy wire is attached to a tower such that the angle formed by the ground and the wire measures 35 The guy wire is replaced by a guy wire 120 feet long The point at which the new guy wire attaches to the tower is the same as it was with the original wire What is the approximate measure of the angle formed by this new guy wire and the ground

Solve the following Write all irrational and complex answers in simplest form 1 9d2 8 41 2 2y 12 14y 3 2 14v 97 0 4 5r2 2r 1 0

The graph of y Tanx is shown Write the coordinates of point A as an ordered pair y arctan x m 2

Simplify the expression 1 sin cot

graph of the O is Shown in the figure below Which of the following coul be the graph or f 2 E y y f 2 B

In ANOP p 870 cm m N 127 and m 0 30 Find the length of n to the nearest centimeter

Given is the graph of f x Answer the following questions Make sure you justify your answers q Determine intervals where f x is decreasing 10 Determine the x value s of any relative maximum s on the graph of f x 8 7 6 5 3 2 1 2 3

For the table to the right selected values of x and f x are given Assume that f x and f x do not change signs II Is f x increasing or decreasing 12 Is f x concave up or concave down X f x O 3 5 23 8 12

p Given f x x 3e x 0 8 on what intervals is f increasing CALCULATOR

What are the domain and range of the function f x 2 6 Domain 0 O Range 6 Domain 6 O Range 0 Domain 6 O Range 00 0 Domain 0 O Range 6

graph of the derivative of in the figure below Which of the to the graph or f 0 y y f X is Shown following could B E

Answer the following questions Be sure to show all work and justify when necessary 1 Given the function f x 4x3 3x2 17 over what intervals is f x decreasing

7 The graph of the derivative off is shown in the figure bellow W of f A C D E

Geometry 5 Find the measure of each indicated angle Favorite Type of Music B a AE b ACE R B 17 A Pop Country H 66 55 C Hip Hop Rap 26 G 89 28 Folk Other F 32 47 Christian E Rock D d BHC e FD c GDC f FBD

f x x2 3x 4 X 2

a To graph the relation P 1 5 x 2 4x 60 we ll plot points for different values of x and calculate the corresponding P values using equation Then we ll plot these points on a graph b This relation is quadratic because it has a squared term x 2 in the equation Another way to see this is by noting that the graph of a quadratic equation is a parabola and the given equation has the form of a quadratic function the c The direction of opening of the parabola is downward because the coefficient of the x 2 term 1 5 is negative Since the coefficient of the x 2 term negative the parabola opens downward indicating that the profit function has a maximum We know this because the coefficient of x 2 is negative is d To find the P intercept we set x 0 in the equation and solve for P P 1 5 0 2 4 0 60 60 The P intercept is 0 60 This represents the initial profit of the company in 2020 when x 0 Yes it makes sense that this is a new company because at the beginning in 2020 the profit is 60 million As the company grows and operates the profit can increase or decrease based on various factors

x x 3x 4 X 2

x ux 2 CX 232

3 Find the dimensions of a rectangle of area 324 ft that has the smallest possible perimeter

2 2 Ex 5y 1 We consider equation E xyEN We Suppose that xy is d caple solutias of the equation E parity 1 Can x and y have the some 2 KEN copy and complete the tablet 6 E 5 1 2 3 4 4 5 3 Deduce x 1 5 or x 4 5 4 Find a non triviale solution different from 1 0

1 10 points What is the maximum vertical distance between the parabola y x 2 1 and the line y 2x 5 6 d 4 yz x 2 1 2x 5 y 2 x 2 2 2x 4 2 2x 6 3 y 2 max vertical distance 0

2 2

C cos OS 1 cos 777 COS 6

6 sin

The graph below is the function f x 5 4 3 2 1 5 43 2 1 1 2 3 5 x 2 1 2 3 4 5 Select all statements below that you agree with Note You may be checking more than one box No partial credit f 2 is defined lim f x exists f x f 2 lim x 2 The function is continuous at x 2 The function is not continuous at x 2

log 8 x

11 log 3x log 10 log 6 63

14 log 4 log 2x 1

13 log 4 2x log 4 3 3

2 85x 1 3x 11 8

3 Inx In7 In63