agrejas0hxpx
2022-05-18
Answered

Find the value of x such that 22x-8=-12.

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Braeden Shannon

Answered 2022-05-19
Author has **13** answers

Move all terms not containing $x$ to the right side of the equation.

$22x=-4$

Divide each term in $22x=-4$ by $22$ and simplify.

$x=-\frac{2}{11}$

The result can be shown in multiple forms.

Exact Form:

$x=-\frac{2}{11}$

asked 2021-05-13

A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing a rope attached to a chandelier, heswings down to grapple with the movie's villian (mass 70.0 kg), whois standing directly under the chandelier.(assume that thestuntman's center of mass moves downward 5.0 m. He releasesthe rope just as he reaches the villian).

a) with what speed do the entwined foes start to slide acrossthe floor?

b) if the coefficient of kinetic friction of their bodies withthe floor is 0.250, how far do they slide?

asked 2020-10-18

Find a least squares solution of Ax=b by constructing and solving the normal equations.

$A=\left[\begin{array}{cc}3& 1\\ 1& 1\\ 1& 4\end{array}\right],b\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

$\stackrel{\u2015}{x}=$ ?

asked 2021-03-07

The article “Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 654.1 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

a) Find a$95\mathrm{\%}$ confidence interval for the improvement in traffic flow due to the new system.

b) Find a$98\mathrm{\%}$ confidence interval for the improvement in traffic flow due to the new system.

c) A traffic engineer states that the mean improvement is between 581.6 and 726.6 vehicles per hour. With what level of confidence can this statement be made?

d) Approximately what sample size is needed so that a$95\mathrm{\%}$

confidence interval will specify the mean to within$\pm \text{}50$ vehicles per hour?

e) Approximately what sample size is needed so that a$98\mathrm{\%}$ confidence

interval will specify the mean to within$\pm \text{}50$ vehicles per hour?

a) Find a

b) Find a

c) A traffic engineer states that the mean improvement is between 581.6 and 726.6 vehicles per hour. With what level of confidence can this statement be made?

d) Approximately what sample size is needed so that a

confidence interval will specify the mean to within

e) Approximately what sample size is needed so that a

interval will specify the mean to within

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How do you write in standard form an equation of the line passing through the given point (-3,3) with the given slope 1?

asked 2022-06-21

Confusion regarding the Logarithmic function change of base formula

My textbook seems to be making a big leap when trying to prove the change of base formula for logarithms. If someone could help clear this up it would be very appreciated.

It starts with:

${b}^{x{\mathrm{log}}_{b}(a)}$

and uses the power rule to get:

${b}^{x{\mathrm{log}}_{b}(a)}={b}^{{\mathrm{log}}_{b}({a}^{x})}$

And it equates all this to:

${b}^{x{\mathrm{log}}_{b}(a)}={b}^{{\mathrm{log}}_{b}({a}^{x})}={a}^{x}$

Okay, I get it up to here, but then for me it leaps from that to this:

${\mathrm{log}}_{a}(x)\cdot {\mathrm{log}}_{b}(a)={\mathrm{log}}_{b}({a}^{{\mathrm{log}}_{a}(x)})={\mathrm{log}}_{b}(x)$

And it says that divide through by ${\mathrm{log}}_{b}(a)$ to get the result.

What precisely has happened here? Could someone walk me through this step-by-step?

Thank you.

My textbook seems to be making a big leap when trying to prove the change of base formula for logarithms. If someone could help clear this up it would be very appreciated.

It starts with:

${b}^{x{\mathrm{log}}_{b}(a)}$

and uses the power rule to get:

${b}^{x{\mathrm{log}}_{b}(a)}={b}^{{\mathrm{log}}_{b}({a}^{x})}$

And it equates all this to:

${b}^{x{\mathrm{log}}_{b}(a)}={b}^{{\mathrm{log}}_{b}({a}^{x})}={a}^{x}$

Okay, I get it up to here, but then for me it leaps from that to this:

${\mathrm{log}}_{a}(x)\cdot {\mathrm{log}}_{b}(a)={\mathrm{log}}_{b}({a}^{{\mathrm{log}}_{a}(x)})={\mathrm{log}}_{b}(x)$

And it says that divide through by ${\mathrm{log}}_{b}(a)$ to get the result.

What precisely has happened here? Could someone walk me through this step-by-step?

Thank you.

asked 2022-05-02

What is 16 divided by 2?

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Given the tangent functions of $y=1\u20133\mathrm{tan}\left(\frac{2x-\pi}{4}\right)$ , find the Equation of all of its vertical asymptotes.