The area of a square is given by A=x2, where x is the side length. The differential of this equation is dA=2x dx. You can use this differential to approximate the error of the area of the square, if for dx you take the error of the side length
measurement. With your numbers you get dA≈2(12)(1/64)...
The angle of diffraction is directly related to the wavelength of the wave: longer waves are diffracted (bent around obstacles) more than shorter waves. Among electromagnetic waves, radio waves are diffracted more than visible light, since radio waves
have wavelengths of a few meters or kilometers,...
CaS (aq) + Co(NO3)2 (aq) → Ca(NO3)2 (aq) + CoS (aq)
You do not need to calculate the lattice energies in order to rank them. You just need to recognize that the lattice energy of ionic compounds becomes larger (more negative) as the charge on the ions becomes larger.
The ionization equations for your three compounds are:
"Decreasing by 6.5% per year" means decreasing to (100-6.5)%=93.5%, or .935, of the previous year's value.
After two years, the acreage will have decreased to .9352 of the original value (10,500,000 acres), and after 15 years it will have decreased to .93515 of its original value, namely...
The population increases from 200 to 3000 in 1 hour, i.e. by a factor of 3000/200=15.
Since the growth is exponential, in 3 hours it will increase by a factor of 153=3,375, to 200*3,375=675,000.
You want to fail to reject H0 at the 5%-level, so the P-value needs to be at least 0.05.
Therefore, we want the sample means
x such that z0=(x-60)/(4.8/√36) results in a probability
P(z≥z0) = 0.05
Use invNorm(0.95) and get z0≤1.64.
We know the population standard deviation σ, so use the z-test:
z = (2.9-2.5)/(0.7/√35) = 3.381
P = 3.617*10-4
Since P<0.05, the result is significant at the 0.05-level, so reject H0.
I'm assuming you mean the function f(x) = kx for 0≤x≤2, 0 otherwise.
For f(x) to be a probability density function (pdf) it has to be non-negative and normalized to 1:
∫-∞∞ f(x) dx = 1
In this case
∫-∞∞ f(x) dx =∫02 (kx) dx =2k = 1, which implies k=1/2.
The phase shift is pi/6.
By phase, we mean the entire quantity inside the trigonometric function, in this case (2/3)x-pi/6. The
phase shift is the value of the phase at x=0. You get -pi/6, where the minus sign indicates the trigonometric function is shifted pi/6 radians to the right...
First find the probability that one car has an efficiency exceeding 32 mpg. Assuming a normal distribution, you do this by finding the corresponding z-score:
Now use a table or calculator to find the probability P(z≥1.667):
Now for the...
The answer depends on how the points are located relative to each other. If all 39 of them are colinear (i.e., already on a straight line), we can draw only one line through them. This is is the minimum.
Now for the maximum number. Suppose no three of them are colinear. Then they form...
Use the definition of logarithm:
y = logax ⇔ ay=x (a>0, x>0)
Now solve for a:
a = x1/y
Now use the definition of logarithm again:
a = x1/y ⇔ 1/y = logxa, or y= 1/logxa
logax = 1/logxa.
Total revenue: TR=5Q
Total cost: TC = 20,000 +2Q
Break even when TR=TC ⇒ 5Q = 20,000+2Q ⇒ Q =20,000/3=6,667
We know for the n=400 sample, x=45.4 and s=8, but we do not know σ, the standard deviation of the population. Therefore, we must use the t-test.
Use a calculator to get t=3.5, P=5.18*10-4.
Since P<0.05, the result is significant at the 5%-level (even...
Cramer's rule and the chain rule are entirely unrelated.
The chain rule is a rule in calculus that lets you take the derivative of a composite function, such as h(x)=g(f(x)). It says that h'(x)=g'(f(x))*f'(x), or "outside derivative times inside derivative".
Cramer's rule is...
This is an interesting question, since logarithms have been around for much longer than calculators!
Before calculators were around, people used tables to calculate anything that went beyond the basic arithmetic operations of addition, subtraction, multiplication, and division...
The distance between a line ax+by+c=0 and a point (x0,y0) not on the line is given by
Find the equation of your line from its slope and y-intercept version and get 4x-3y+26=0, and the point is (3,-4), so that a=4, b=-3, c=26, x0=3, and y0=-4. Therefore,
The distance between two parallel lines y1=mx+b1 and y2=mx+b2 is given by
With m=3, b1=4, and b2=-6, you get
d= |-6-4|/sqrt(32+1) = 10/√10 = √10.
(a) Draw the feed tank, the pump, and the overhead tank, a horizontal 3-inch pipe from the feed tank to the pump, and a vertical 2-inch discharge pipe from the pump to the overhead tank 50 ft above.
1. You will need the cross-sectional areas of both pipes; calculate them from A=pi*d²/4...