Find the relation between the Euclidean radius and the spherical radius of spherical circle.
Include a picture.

Find the real zeros of the function f(x) = -(x+1)^3(x-2)^2 and their corresponding multiplicities. Use the information along with a sign chart (diagram) and then the end behavior to provide a rough sketch of the graph of the polynomial.

How many different ways can you solve a quadratic equation? List them.

Create a trinomial that can be factored and write it in standard form.

Factor x^2 – 7x + 10, 4x^2 – 81 and p (x) = 3x^3 – 12x

What key features of a quadratic graph can be identified and how are the graphs affected when constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.

A ball is kicked into the air and follows the path described by h(t)= – 4.9t^2 + 6t + 0.6, where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?

(8) How can geometry be used to promote responsible stewardship?PLEASE TYPE

You can sell 70 pet chias per week if they are marked at $1 each, but only 20 each week if they are marked at $2/chia. Your chia supplier is prepared to sell you 10 chias each week if they are marked at $1/chia, and 60 each week if they are marked at $2 per chia.

(a) Write down the associated linear demand and supply functions.

(b) At what price should the chias be marked so that there is neither a surplus nor a shortage of chias?

We can experiment with two parallelepipeds (boxes) that are similar in shape. The dimensions of the smaller box are 2 in. x 4 in. x 3 in. The larger box has twice the dimensions of the smaller . Draw and label the large box

1. Surface area (SA) of a box is the sum of the areas of all six sides. Compare the SAs of the two boxes.

Ratio: SA of the large box is ___ times the SA of the small box

2. Compare the volumes (V) of the two boxes, measured in cubic inches. Pretend that you are filling the boxes with 1-inch cubes. The volume of each cube is 1 cubic inch (cu. in.).

Small box ____ cubes fill one layer, and ___ layers fill the box. The box holds ___ 1-inch cubes. Volume= ____ cu. in. Large box ___ cubes fill one layer, and ___ layers fill the box The box holds ____ 1-inch cubes. Volume= ___ cu. in. Ratio: The volume of the large box is ___ times the volume of the small box.

3. Show your work to compare a 3inch cube with a I-inch cube.

Think about this: 1. Look at your estimate for the amount of thatch for the kibo Art Gallery. Do you agree with it? Explain.

2. Two cylinders (cans) have similar shapes. One has four times the dimensions of the other. Show how you can compare their surface areas and volumes without the use of formulas. What conclusions do you expect? Use another sheet, if necessary.

Weekly production schedules are needed for the manufacture of two products X and Y. Each unit of X uses one component made in the factory, while each unit of Y uses two of the components, and the factory has a maximum output of 80 components a week. Each unit of X and Y requires 10 hours of subcontracted work and agreements have been signed with subcontractors for a minimum weekly usage of 200 hours and a maximum weekly usage of 600 hours. The marketing department says that all production of Y can be sold but there is a maximum demand of 50 units of X, despite a long-term contract to supply 10 units of X to one customer. The net profit on each unit of X and Y is $200 and $300 respectively.

Linnear Programming step by step, show work manually without using excel, Include a graph, and corner. I would like to try to understand how the question is done step by step. Thank you so much

Prove that the sum of angles of a hyperbolic triangle is less than 180.

Detailed Proof

Solve each compound inequality, write its solution set in interval notation, and graph the solution set on a number line.

5) -3 < 4 p - 3 ? 13

WHY DO I NEED TO STUDY POLYNOMIALS? HAVE I EVER GOING TO USE IT? JOBS THAT USE POLYNOMIALS Visit the following site, read and give an example of your understanding use of polynomials in your job or any example you have. https://careertrend.com/list-6330381-jobs-use-polynomials.htm (Links to an external site.)Links to an external site.l

A massive oil spill in the gulf unleashes approximately 20,311 barrels of oil into the Gulf each hour. This creates an expanding circular layer of oil on the water’s surface about 1/16 inches thick with the center being the source of the spill. Letting R(t) represent the radius (in miles) t hours after 6:00pm, the growing radius of this oil spill can be modeled by the formula: R(t)=1/2 √(t+1) A.) What time did this spill start? (When was the radius zero?) B.) Fill in the table below: (round your answer to 2 decimal places) Table 1 t hours 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 R(t) miles C.) If left unchecked, how long will it take this oil spill to reach a 2 mile radius? The nearest containment crew is on the Louisiana coast 50 miles away. At 6:00 pm, containment vessels instantly head towards the center of this spill, but the fastest these containment ships can travel is only 15 mph. D.) Write an equation that represents the distance D(t) in miles that the containment vessel is from the center of the spill t hours after 6:00 pm. E.) Fill in the table below: Table 2 t hours 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 D(t) miles F.) When will the containment vessels reach the center of spill? G.) By observing the two tables above, in which 30 minute interval will the containment vessels reach the outer edge of the spill? H.) Algebraically find exactly (to the nearest minute) when the containment vessels will reach the outer edge of the oil spill. You should get two answers…explain them. I.) What is the radius of the oil spill at this time? J.) To manage the spill, one containment vessel is needed every 800 feet around the outer circumference of the spill. How many vessels do they need? (5280 ft. = 1 mile)