i need help with this

Question 1. Solve the following exponential equations. Show your work. a) 2 +1 = 24 b) 33x-1 _ 32x c) 16*+2 = 43(x+1)Question 2. Below is a drawing of the floor plan ofa basement. A painter would like to paint the floor of the rectangular shaped room in blue and the floor of the two triangular shaped rooms in green. How much will it cost to paint the basement floor if the blue paint costs $5 per meter square (m2) and the green paint costs $7 per meter square (m2) ? Show your work and round your answer to the nearest tenth. 50 30M- Question 3. A scientist is performing an experiment to find the heightUz) in meters of a ball alter a certain number of bounces (n). The scientist was able to come up with the following algebraic expression: 3 (0.6)3" (0.6)3" 4:: (0.6)" (0.6)3 3 h: a) Simplify the algebraic expression above. Show your work. b) At what height was the ball dropped? Show your work. (Note: this question can be answered even if you are unabie to simpiii'j/ the aigebraic expression). c) Find the height of the ball after 2 bounces. Show your work. (Note: this question can be answered even if you are unabie to simplify the algebraic expression] d) The scientist found that the height (H) of another ball based on the number of bounces can be expressed by the following equation: H : 3(036)3 + 0'25\" . The scientist thinks that both balls will have the same height aer four bounces. Is the scientist right? If the scientist is right, show why the scientist has the correct answer and if the scientist is wrong then nd the right answer. Show your work. Question 4. The volume of a cone with a radius r and a height h is given by the formula below. Note: You may use 3J4 as the value of 1210 answer the following questions. Cl) V _ :rrzh cone _ 3 What is the volume of a cone with a radius of? m and a height 5 m '5' Show your work and round your answer to the nearest tenth. What is the height ofa cone that has a radius of 2 m and a volume of1000 m3 ? Show your work and round your answer to the nearest tenth. What is the radius of a cone that has a height of 5 m and a volume of 300 m3 ? Show your work and round your answer to the nearest tenth. In front ofyou is a cone with a height of10 m and a sphere that both have the same radius. What is the length of the radius of the cone and the sphere if you want them to both have the same volume? The formula for a sphere is given below. Show your work and round your answer to the nearest tenth. 4Jrr3 sphere - 3