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vredina [299]
3 years ago
9

Write the first six nonzero multiples of 5

Mathematics
1 answer:
iragen [17]3 years ago
6 0
The first multiples of 5 without a zero are
5,15,25,35,45,55, we must elimitate the 10's because it has a zero
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1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.
xxTIMURxx [149]

First, rewrite the equation so that <em>y</em> is a function of <em>x</em> :

x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}

(If you were to plot the actual curve, you would have both y=x^{2/3} and y=-x^{2/3}, but one curve is a reflection of the other, so the arc length for 1 ≤ <em>x</em> ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx

We have

y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}

Then in the integral,

\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx

Substitute

u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx

This transforms the integral to

\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du

and computing it is trivial:

\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)

We can simplify this further to

\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}

7 0
3 years ago
PLEASE HELP! ( no random links )
yawa3891 [41]

Answer:

This is not a statistical question

Step-by-step explanation:

A statistical question is a question the gathers varying data

7 0
3 years ago
The formula for voltage (in volts) is given by V = IR, where I is the current in amperes, and R is the resistance in ohms.
svlad2 [7]
R = V/I
R = 1.8/0.4 = 4.5 . . . ohms
8 0
3 years ago
Convert 320% to an equivalent decimal.​
lapo4ka [179]

Answer:

Answer is 3.2

Step-by-step explanation: you can take any percent and divide it by 100. So in this example you would divide 320/100 and it will give you 3.2

6 0
3 years ago
Pls I need help not the best at this.
Mazyrski [523]

Answer:

B

Step-by-step explanation:

because I did the math and had my mom check it :)

7 0
3 years ago
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