Question Jack plants a magic beanstalk that is 3 feet tall. The height of the magic beanstalk increases exponentially, doubling each day. Write a function f that determines the height of the beanstalk (in feet) in terms of the number of days t since the beanstalk was planted. f(t)= If the moon is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the moon? (The moon is 238,900 miles from the earth, and there are 5,280 feet in 1 mile.) days If the sun is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the sun? (The sun is 92,960,000 miles from the earth, and there are 5,280 feet in 1 mile.) days

I had a meeting with a herbicide specialist set up by owner Sabbling. Edgar said we could build a greenhouse for $2,222 to protect trees from insects and disease. He showed me a bunch of additional figures, enough to convince me. Our company can only commit $4,225 to this project without going into debt. Also, since the greenhouse can only hold so many trees, we need to make sure that we’re spending no more than $100 per tree, otherwise we’ll operate at a loss. Edgar assured me this was possible — he even showed me how to do it — but he took most of his notes with him, and I’m no mathematical genius. Here’s how the expenses add up: First, the cost of the greenhouse. Then, for each tree in the greenhouse you need $5 for a proper planter. But the more trees there are the easier it is to spread infection between them, so the cost of disinfecting a tree rises as the number of trees increases. Specifically, disinfecting each tree costs the total number of trees in the greenhouse. The one example Edgar shared that I managed to save goes like this: Suppose we plant 10 trees. Then we’d spend $2,222 for the greenhouse, plus $50 for planters, plus $10 to disinfect each of the 10 trees (meaning $100 for disinfecting the whole greenhouse). The total cost would be $2,372. So far so good. But unfortunately, this comes to more than $237 per tree — that’s bad. I tried figuring out what happens if we increase the number of trees, say to 100. In that case, the cost per tree improves but still is not acceptable at $127. The total cost would be an exorbitant $12,722. Although I’m not even sure these figures are correct. I’m hoping you can tell me. When I showed these figures to Sabbling she threw a fit — swore I’m going to wreck the company. Can you help me figure out the math that will meet this challenge?

Part A The post is made of Douglas fir and has a diameter of 100 mm (Figure 1) It is subjected to the load of 20 kN and the soil provides a frictional resistance distributed around the post that is triangular along its sides that is, it varies from w=0 kN/mat y=0 m to w= 15 kN/m at y = 2 m. Neglect the weight of the post Determine the force at its bottom needed for equilibrium Express your answer to three significant figures and include appropriate units. HÅ ? Value Units Submit Request Answer Figure 1 of 1 Part B 20KN What is the displacement of the top of the post with respect to a bottom B? Express your answer to three significant figures and include appropriato unito, ? 2 m 0 = Value Units 12 kN/m Submit Request Answer

a hockey puck moving at 7.0 m/s coasts to a halt in 75m on a smooth ice surface. What is the coefficient of friction between the ice and the puck?

​​​​​​​ The bar has a cross-sectional area of \( 1900 \mathrm{~mm}^{2} \) and \( E=250 \mathrm{GPa} \). (Figure 1) Determine the displacement of its end \( A \) when it is subjected to the distributed loading. Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of contraction and positive value in the case of elongation. Figure 1 of 1 X Incorrect; Try Again; 4 attempts remaining

      please solve all tasks A car rental company owns five types of cars: Small, Economy, Standard, Family, Exclusive. The prices for per day rent for each type of the cars aregiven in British pounds by the \( 1 \times 5 \) matrix \[ \mathbf{p}=\left(\begin{array}{lllll} 15 & 19 & 21 & 28 & 37 \end{array}\right) \] The care demand for five days of a week ahead is given by the matrix \[ \mathbf{A}=\left(\begin{array}{ccccc} 2 & 4 & 3 & 1 & 3 \\ 4 & 3 & 3 & 5 & 3 \\ 10 & 11 & 8 & 6 & 9 \\ 4 & 3 & 2 & 3 & 4 \\ 2 & 1 & 3 & 2 & 1 \end{array}\right) \] Calculate the total income in British pounds of the company for this week. a. 10500 b. 3420 C. 2242 d. 4520 Consider the clockwise rotation \( T \) of \( \mathbb{R}^{2} \) by the angle of \( 30^{\circ} \). Mark only correct statements. a. The matrix of \( T \) is \( \left(\begin{array}{cc}-\frac{\sqrt{3}}{2} & \frac{1}{2} \\ \frac{1}{2} & -\frac{\sqrt{3}}{2}\end{array}\right) \) b. The matrix of \( T \) is symmetric. c. The matrix of \( T \) is \( \left(\begin{array}{rr}\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) d. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) e. The matrix of \( T \) is \( \left(\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right) \) A company manufactures three types of perfume-refreshing \( (R) \), standard \( (S) \), and exclusive \( (E) \), in four factories in different countries \( A \), B, C, D. The distributions of costs in producing a single piece of perfume are given in the left table below. The number of pieces of perfume produced in one month at the four locations are given in the right table. a. Location A materials: \( \$ 4500 \) b. Location B: labor \( \$ 8000 \) c. Location A: labor \( \$ 14000 \) d. Location D: materials \( \$ 25000 \) e. Location C: overheads \( \$ 16000 \)

A car rental company owns five types of cars: Small,Economy, Standard, Family, Exclusive. The prices for per day rent for eachtype of the cars are given in British pounds by the1×5matrix