Questions asked
One of the most important adaptations for reptiles to surpass amphibians and fully inhabit the land was: The development of legs The development of a closed circulatory system The development of the amniotic egg The development of lungs
A ballistic pendulum is used to measure the speed of a bullet shot from a gun. The mass of the bullet is 50.0 g, and the mass of the block is 20.0 kg. When the bullet strikes the block, the combined mass rises a vertical distance of 5.00 cm. What was the speed of the bullet as it struck the block?
After conducting the signal speed experiment a student has recorded the following data. L2 (m) dt (ns) 1.5 6.50 3 13.72 4.5 21.02 8 38.10 15 72.20 30 145.42 L2 is the length of the longer cable in meters and dt is the measured time delay in nanoseconds. The student neglected to record L1, the length of the shorter cable. After speaking with their instructor, they learn all is not lost. They know the speed of the signal can be calculated based on the distance traveled divided by the time. However, the recorded times measure how much longer the signal had to travel in L2 compared to L1. A little bit of thought convinces them (correctly) that $v = \frac{L_2 - L_1}{dt}$ with v the signal speed. The student makes a plot of dt (vertical axis) vs L2 (horizontal axis) and finds a signal speed. What speed do they find in the units of meters per nanosecond?
Question 23 Which of the following best represents the electronic configuration of Sc ($^{21}Sc_{44.96}$)? A 1s$^2$2s$^2$2p$^6$3s$^2$3p$^6$4s$^2$3d$^2$ B 1s$^2$2s$^2$2p$^5$3s$^2$3p$^6$4s$^2$3d$^1$ C 1s$^2$2s$^2$2p$^6$3s$^2$3p$^6$3d$^3$ D 1s$^2$2s$^2$2p$^6$3s$^2$3p$^6$4s$^2$4p$^1$ E 1s$^2$2s$^2$2p$^6$3s$^2$3p$^6$4s$^2$3d$^1$
(1) (15 points) Determine if the integral below converges or diverges. Justify your answer clearly. \( \int_{7}^{\infty} \frac{x + 20 - 3 \cos(x)}{\sqrt{x + x^3}} dx \)
Find all scalars $c_1$, $c_2$ and $c_3$ such that $c_1(1, -1, 0) + c_2(4, 3, 1) + c_3(0, 1, 2) = (-6, -2, -3)$
In Problems 7-16, obtain the general solution to the equation. 7. \frac{dy}{dx} - y - e^{3x} = 0 8. \frac{dy}{dx} = \frac{y}{x} + 2x + 1 9. \frac{dr}{d\theta} + r \tan \theta = \sec \theta 10. x\frac{dy}{dx} + 2y = x^{-3} 11. (t + y + 1)dt - dy = 0 12. \frac{dy}{dx} = x^2e^{-4x} - 4y 13. y\frac{dx}{dy} + 2x = 5y^3 14. x\frac{dy}{dx} + 3(y + x^2) = \frac{\sin x}{x} 15. (x^2 + 1)\frac{dy}{dx} + xy - x = 0 16. (1 - x^2)\frac{dy}{dx} - x^2y = (1 + x)\sqrt{1 - x^2}
A block with a weight of 150 N is sitting on an elevator, which is initially moving downward with a constant velocity of 2 m/s. If the elevator takes .5 sec to come to rest at the next floor, what is the normal force on the block while the elevator is slowing down? (Assume the elevator is slowing with a constant acceleration) A) 155 N B) 167 N C) 196 N D) 211 N E) 230 N
III) Pick three from the following choices that are mostly considered as the Owner's Equity. (3 c. retained earning a. Contributed capital, b. cash investment in growing crops d. accounts payable e. accounts receivable f. accrued expenses g. income and social security taxes h. inventories, i. Farm debt j. market gain 3. Choose one from: increase/decrease/stays the same for the following(i-iv). (7 If the cash receivable amount increases, the cash flow of a business will ____ (increase/decrease/stays the same). i) If the Accounts Payable decreases, the cash flow of a business will ____ (increase/decrease/stays the same). ii) If a business increases its' Inventories, the cash flow will ____ (increase/decrease/stays the same.) iii) If a business increases in selling common stocks, the cash flow will ____ (increases/decreases/stays the same) iv) Business delivered services on credit, the cash flow will ____ (increases/decreases/stays the same) v)
Given $f(x) = x^3$ (a) Find the linearization of $f$ at $x = 8$. Be sure to enter an equation in the form $y = mx + b$ (b) Using this, we find our approximation for $(8.4)^3$ is (c) Find the absolute value of the error between $f(8.4)$ and its estimated value $L(8.4)$ $|error| = $ (d) Find the relative error for $f(8.4)$ and its estimated value $L(8.4)$. Express your answer as a percentage and round to three decimals. Relative error $= \frac{|error|}{|f(8.4)|} = $ %
