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2 years ago

What is the unite rate for 42 laps in 6 races?

2 answers:

5 0

In 6 races = 42 laps,
Then it would be: 1 race = 6 laps.

So, in 1 race there would be 6 laps & that is your unit rate.

So, your final answer is 6

Nitella [24]2 years ago

3 0

42/6 = 7 laps per race

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Laura invests $2,000 in a bank account which pays a compound interest rate of 6.4%. To the nearest cent, what amount is in the a

EastWind [94]

Answer:

9,000

Step-by-step explanation:

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2 years ago

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

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2 years ago

Angle 2 is 60. Find angle 8. Options: 140 100 40 60

pav-90 [236]

Angle 8 is 60 too
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2 years ago

Please help, i'm horrible @ math :)

katovenus [111]

$\displaystyle\\
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1 \frac{2}{5} = \frac{1\times 5+2}{5}=\boxed{\frac{7}{5}} \\ \\ 
-5 \frac{1}{2} =-5 -\frac{1}{2} = \frac{-5\times2-1}{2} =\frac{-10-1}{2}=\frac{-11}{2}= \boxed{-\frac{11}{2} }\\ \\ \texttt{OR} \\ \\ 
-5 \frac{1}{2} = -\Big(5 \frac{1}{2} \Big)= -\Big( \frac{5\times2+1}{2} \Big)=-\Big( \frac{11}{2} \Big)= \boxed{-\frac{11}{2} }$

$\displaystyle\\
\Longrightarrow ~~1 \frac{2}{5} +\Big(-5 \frac{1}{2} \Big) =\frac{7}{5} -\frac{11}{2} = \frac{7\times 2}{5\times 2} -\frac{11\times 5}{2\times 5} = \\ \\ 
= \frac{14}{10} -\frac{55}{10} = \frac{14-55}{10} =\frac{-41}{10} = -\frac{41}{10}=-\frac{40+1}{10}=\boxed{\boxed{-4\frac{1}{10}}}$

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3 years ago

The area of the surface of a pool table is 24 square feet. The perimeter is 22 feet. What are the dimensions of the pool table?

trasher [3.6K]

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Step-by-step explanation:

So 8*3=24 which corresponds with the formula for area l*w= Area

And perimeter means we add up all 4 sides so

8+8+3+3= 22

So the dimensions are 8 and 3

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2 years ago