1. The answer is C. cos180=-1, sin180=0. 2*(cos180+i*sin180)=2*(-1+0)=-2. Check every other answer, none of which gets -2.
2. The answer is C. cos270=0, sin270=-1. (You can draw out these angles to see). 2*(cos270+i*sin270)=2*(0-i)=-2i, as desired. Other choices don't work.
3. Answer A. Modulus of z is \sqrt(6^2+(-6)^2)=6*\sqrt(2). <span>The </span>angle<span> of the </span>point<span> on the complex </span>plane<span> is the </span>inverse tangent<span> of the complex portion over the real portion. Theta=arctan(-6/6), and arctan(-1)=-pi/4, so theta=-pi/4=-pi/4+2pi=7pi/4. So A is the correct answer.
4. The answer is A. As above, cos270=0, sin270=-1. 3(cos270+sin270*i)=3*(0-i)=-3i. This problem is similar to question 2.
5. </span>z1 = 7(cos 40° + i sin 40°), and z2 = 6(cos 145° + i sin 145°). z1*z2=7*6*(cos 40° + i sin 40°)*(cos 145° + i sin 145°)=42*(cos40*cos145-sin40*sin145+i*sin40*cos145+i*sin145*cos40). Use formula for sum/difference formula of cosines, cos40*cos145-sin40*sin145=cos(40+145)=cos185. Again, sin40*cos145+sin145*cos40=sin(40+145)=sin185. The answer is <span>42(cos 185° + i sin 185°).</span>
To determine the cost of the mail, we simply substitute the mass of the package to the given function. Mathematical functions are used to relate two variables, observing how changing one variable affects the other variable. For this case, the cost of a mail and the weight of the package are related by the function <span>y = 0.7x2 –2.5x + 3 where x represents the mass in units of pounds (lb) and y is the cost in units of dollars ($). We calculate cost as follows:
</span><span>y = 0.7x^2 –2.5x + 3
</span><span>y = 0.7(5)^2 –2.5(5)+ 3
y = 8 dollars
Therefore, the cost of mailing a 5 lb package would be 8 dollars.</span>
Answer:
The minimum sample size required is 207.
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population mean <em>μ</em> is:
The margin of error of this confidence interval is:
Given:
*Use a <em>z</em>-table for the critical value.
Compute the value of <em>n</em> as follows:
![MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207](https://tex.z-dn.net/?f=MOE%3Dz_%7B%5Calpha%20%2F2%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C3%3D2.576%5Ctimes%20%5Cfrac%7B29%7D%7B%5Csqrt%7Bn%7D%7D%20%5C%5Cn%3D%5B%5Cfrac%7B2.576%5Ctimes29%7D%7B3%7D%20%5D%5E%7B2%7D%5C%5C%3D206.69%5C%5C%5Capprox207)
Thus, the minimum sample size required is 207.
y = (x - 2)(x + 5) First I would multiply (x - 2) and (x + 5) together
y = x² + 5x - 2x - 10
y = x² + 3x - 10
Next I would plug in a number for x to find its y value. I will plug in 0
y = 0² + 3(0) - 10
y = -10
(0, -10) [this is the y-intercept (the y value when x = 0)]
Your answer is Graph A because the y-intercept is (0,-10)
Answer:
y=-(4x/3) -1
Step-by-step explanation:
Slope=m= -4/3
y intercept = c = -1
now using equation;
y= mx+c
y= (-4/3)x+(-1)
y=-(4x/3) -1
