Heights & Distances Questions and Answers

A skier is traveling down a mountain at a constant speed of 20 meters per second The angle of incline of the slope is decreasing at a rate of 0 5 degrees per second At what rate is the skier s altitude changing when the angle of incline is 35 degrees

8 A toy store is having a sale All items are half price Rick buys 5 toy cars and 2 dinosaurs Let c represent the regular price of a toy car and let d represent the regular price of a dinosaur Which expression does NOT represent the total cost of his purchases after the discount A B A B 0 5 5c 0 5 2d 5c 2d 2 A B 9 A clothing store has marked down the original price of a hat h by 8 The original price of a pair of pants p was reduced by 17 George bought 2 hats and 2 pairs of pants Which expression below could NOT be used to determine the total cost of his purchase before tax 2h 2p 8 17 2h 2 8 2p 2 17 C D 2 6h 4q 2 6h 2 4q 5c 2d 5c 2d 2 C 2 h 8 2 p 17 2 h 8 p 17 D 10 Mark and Jenny each have h hexagons and q quadrilaterals Which expression below could NOT represent the number of sides they have on their combined shapes C D 6h 4q 6h 4q 2 6h 2 4g

Find the tangent of ZF 68 F 32 H Simplify your answer and write it as a proper fraction improper fraction or whole num tan F

11 Given the figure to the right which of the following statements are NOT true a 21 and 25 are corresponding angles b 22 and 27 are alternate interior angles c 24 and 27 are a linear pair d 25 and 28 are vertical angles 1 3 2 4 5 7 6 8 m

10 26 25 1 Is the triangle above a right triangle 2 If the triangle above IS a right triangle show the math that you used If the triangle above IS NOT a right triangle change one side leng

Determine the scale factor Pre Image Image 1 1 3 4 5 1 3 3 9 12 15 3

21 Write the equation for the absolute value function graphed below 18 2 Type a response 2 2 4 8 6 6 y X

Problem 2 5 points A spherical tank with a radius of 15 feet is full of propane which has a density of 31 pounds per cubic foot Compute the work required to pump all the propane out of a 7 foot spout at the top of the tank Leave your answer in foot pounds rounded to the nearest whole number no dec imals

The curve C is the graph of y f Determine x interval s on which the curve is concave upward C is concave upward on t2 1 2t 2 1 0 dt B Find the antiderivative for the function f t that has constant term rer Graph of y f t The blue line in the graph above defines a linear function y f t A Suppose that 3 is a point that may vary on the t axis Find the accumulated area function A a f t dt that calculates the net area of the shaded region on the interval 0 2 Hint What is the area of a triangle A z x 2 4 2x

30 Given PQRS is a kite with perimeter 32 inches find the length of SR A 4 inches B 12 inches C 16 inches D 24 inches O A OB C S 2x 6x R

The vertices of quadrilateral ABCD have coordinates A 1 2 B 2 5 C 5 7 and D 4 4 Prove that ABCD is a parallelogram Justify mathematically and explain

3 5 POINTS Find the missing bearings for the following traverse 5 75 39 13 1 4 1515142 575 42 34 E 1 486 39 311 444 65 153

1 10 Pts Find a unit vector in the direction of steepest ascent increase and a unit vector that is tangent to the level curve of the function f x y x y at the point P 2 1

As Amaya gazes at the edge of the Grand Canyon she decides to try to determine the height of the wall opposite from her Using an app on her phone she determines that the top of the wall is at a 38 angle above her while the bottom is at a 46 angle below her as shown in the diagram at right If the base of the wall is 253 feet from the point on the ground directly below Amaya determine the height of the wall opposite from her Freda

Find the volume of the box 3 ft 6 ft 5 ft The volume of the box is cubic feet

55 A 60 foot flagpole was placed in front of a post office perpendicular to the ground After many years the flagpole began to lean The distance from the top of the flagpole to the ground is now 50 feet Which expression shows how to determine the angle the flagpole makes with the ground

3 32 cm 41 cm 63 cm True False 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 5 and type your answer type your answer 9 x 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 7 and 14 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 8 and 13 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 10 and 12 type your answer x type your answer 2 points Find the range for the measures of the third side of a triangle given the measure of two sides 5 and 5 type your answer x type your answer paints

Question 9 1 point Given SV X Prove ASTX AVUT What is the reason for 3 Prove SAS Vertical Angles AA Statements 1 2 3 AGHI STX 4UTV AKJL Reasons 1 Given 2 3

If a bone contains 91 of its original carbon 14 how old is the bone Carbon 14 has a half life of 5730 years The bone is years old Round the final answer to the nearest year as needed Round all intermediate values to six decimal places as needed

Given the two lines are parallel below and the Z2 55 which statement is false 27 21 28 55 55 125 5 6 7 8 3 1 4 2

4 point Find than answer for x Type your answer 1 point Given m n find the value for x 8x 4 6x 12 7x 30 6x 10 m

Francisco asks the students in his school what pets they have. He studies the events shown. • Event S: The student has a cat. • Event T: The student has a dog Francisco finds that the two events are independent. Select all the equations that must be true for events S and T. P(SUT) = P(S) · P (T) P(ST) = P(S) P(T|S) = P(T) P(S|T) = P(T) P(T|S) = P(S) P (S∩T) = P (S) · P (T)

A uniform ladder of mass 30kg and length 5 m rests against a smooth vertical wall with its lower end on rough horizontal ground. The ladder is inclined at 60° to the floor. The coefficient of friction between the ladder and the ground is 0.4. Find how far a man of mass 80 kg can climb up the ladder without it slipping.

Find the normal curvature Kn of the curve a(t) = (acost, asint, bt) on a cylindrical surface of radius r=a, where a, b are constants.

Spencer is going snowboarding. He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet. The angle of elevation from the bottom to the top of the mountain is 25°. What is the length of Spencer's run (his trip down the hill)? Round your answer to the nearest tenth of a foot.

A golfer is standing at the tee, looking up to the green on a hill. If the tee is 36 yards lower than the green and the angle of elevation from the tee to the hole is 12°, find the distance from the tee to the hole.

What percent of 120 is 72? 60% 86.4 % 0.6% 1.67%

Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is covered with an irrigation arm of 310 ft?

Nguyen loaded 12 trucks in 1 hour. Find his loading speed in trucks per hour. 12 trucks per hour 12 hours 12 hours per truck 12 trucks

About how many cells are in the human body? 37.2 trillion cells You can assume that a cell is a sphere with radius 103 cm and that the density of a cell is approximately the density of water which is 1g/cm³.

For a minimisation problem, if the objective coefficient of a decision variable x, that is equal tozero at the optimal, decreases within its allowable range, what can or will happen? Fill in the blanks using the following responses, "can", "will not", "can increase", "can decrease", "can increase or decrease", "will stay the same" Optimal basis (corner that the optimal solution sits) ______change Decision variable x value can________ Objective function value can_______

A barrel of fuel oil is a right circular cylinder where the inside measurements of the barrel are a diameter of 24.5 inches and a height of 34.5 inches. There are 231 cubic inches in a liquid gallon. Determine and state, to the nearest tenth, the gallons of fuel that are in a barrel of fuel oil.

Linear Regression Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y = mx + b

Simple interest is given by the formula A = P + Prt. Where A is the balance of the account after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Devante is investing money into a savings account that pays 2% simple interest, and plans to leave it there for 10 years. Determine what Devante needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years. Devante will have to invest $ now in order to have a balance of $20,000 in his savings account after 10 years. Round your answer to the nearest dollar.

This week in the Discussion module, you will be looking into the use of social media for emergency management. While somewhat dated (2013) the FEMA social media document in the reading assignments remains one of the most comprehensive on the topic. After reading the document, and others you may find through research, comment on the pros and cons of social media use in disasters and identify at least one "up to date" or potential future application for social media to address emergency management communications issues.

In the year 1997, the surface elevation of Lake Powell was 3839 feet above sea level. In the year 2005, the surface elevation of Lake Powell was 3221.4 feet above sea level. Interpret the rate of change in this situation. The surface elevation of Lake Powell is Select an answer at a rate of _______Select an answer ✪

10. The first row of a movie theatre has 34 seats. Each successive row has 4 more seats than the row before it. If there are 20 rows in the theatre, what is the seating capacity of the theatre? [P4]

A model is made of a car. The car is10 feet long and the model is 7Inches long. What is the ratio of the length of the car to the length of the model? 07:120 O 120: 7 07:10 O 10:7

Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.

Convert the measurement. 97 inches per second =_ feet per minute

A bicycle is traveling at 20 miles per hour. How many feet will it cover in 55 seconds? Round your answer to the nearest tenth of a foot. 1466.7 X feet

Give the equation of the line with a slope of - 5 2 and a y-intercept of 4.

The store is selling lemons at $0.39 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?

Convert the measurement to the nearest hundredth . 59 feet per second = _ miles per hour

A bicycle is traveling at 12 miles per hour. How many feet will it cover in 25 seconds? Round your answer to the nearest tenth of a foot.

Apollo Spas services 147 hot tubs. If each hot tub needs 165 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs? ___________ L

Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number? A. 1/2 B. 3/20 C. 3/10 D.1/5 E. 1/3

Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be? A 15° B. 30° C. 45° D. 60°

Solve x sin x = 1 using the following: (a) MOSS (root = 0.5) (b) Newton Raphson (root = 0.5) (c) Bisection Method (use roots = 0.5 and 2) (d) Secant Method (use roots = 2 and 1.5)

AC has endpoints A(-1, -3.5) and C(5, -1). Point B is on AC and is located at (0.2, -3). What is the ratio of AB /BC ? Please enter your answer as a decimal, rounded to the hundredths place.