Will85237

The formula for the resistivity of a wire is shown below.

\(𝜌=\frac{RA}{L}\)

Where 𝜌 is resistivity, R is resisitance, A is cross-sectional area, and L is length. Simply plug the values you were given into the equation, and solve for R. Make sure that they are all in SI units.

\(1.72\times{10}^{-8}=\frac{0.000016R}{1000}\)

\(R=1.075\Omega\)

sin^-1(4/9)

It's easiest to solve questions like these just by plugging them in a calculator.

= 26.4°

Divide the total number of jars by the number of jars Bob needs to eat to get diabetes.

1,000,000 / 17.5

= 57,143

Bob will get diabetes roughly 57,100 times, if that were possible...

Total number of minutes of movie made by Spielberg = 3910 + 90 * number of "new" movies

Total number of minutes of movie made by Jackson = 2890 + 150 * number of "new" movies

Put the total number of minutes of movie made by each director equal to each other and solve for the number of new movies.

3910 + 90n = 2890 + 150n

1020 + 90n = 150n

1020 = 60n

17 = n

It will take 7 years for them to have produced the same number of minutes of film.

The way to calculate this is to work backwards, knowing that we can calculate the percentage of a number by multiplying it by the percentage and dividing by 100.

\(1970.67=x*16/100\)

By rearranging, we can find x as shown.

\(x=1970.67/0.16\)

\(x=12316.69\)

Therefore, 1,970.67 is 16% of 12,316.69.

A reflex angle is an angle which is more than 180°.

The easiest way to solve this is to graph it. I've used https://www.desmos.com/calculator to make the graph below.

Although you can't see the exact values of the roots on this picture, the roots are x = -3.849, -0.672, 0.659, 2.085 because these are the values of x where the line crosses the x-axis.

Use the following trigonometric identity.

\(sin^2(\theta )+cos^2(\theta )=1 \)

Rearrange it in terms of cos.

\(cos(\theta )=\sqrt{1-sin^2(\theta )}\)

Substitute in your value of sine of theta, 0.4.

\(cos(\theta )=\sqrt{1-0.4^2}\)

Solve.

\(cos(\theta )=\sqrt{1-0.16}\)

\(cos(\theta )=\sqrt{0.84}\)

As an approximation.

\(cos(\theta )=0.92\)

You can treat the ">" as an equal sign, and then apply algebra.

\(-(1-x)>2x-1\)

Expand the brackets on the left side.

\(-1+x>2x-1\)

Add 1 to each side.

\(x>2x\)

Minus x from each side.

\(0>x\)

x must be less than 0

Just apply the rules of algebra.

\(-6(6x+3)+2(6x+4)=38\)

Expand the brackets by multiplying.

\(-36x-18+12x+8=38 \)

Add and subract the like terms together.

\(-24x=48 \)

Divide each side by -24.

\(x=-2 \)