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3 years ago

The points (-5, -22) and (4, r) lie on a line with slope 3. Find the missing coordinate r.

Mathematics

1 answer:

lara [203]3 years ago

5 0

Step-by-step explanation:

here,

x1= -5. x2=4

y1= -22. y2=r

slope(m)=3

now we have,

m=(y2-y1)/(x2-x1)

or,3=(r-(-22))/(4-(-5))

or,3=(r+22)/(4+5)

or,3=(r+22)/9

or,27=r+22

or,r=27-22

or,r=5

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Write the integral that gives the length of the curve y = f (x) = ∫0 to 4.5x sin t dt on the interval [0,π].

Troyanec [42]

Answer:

Arc length $=\int_0^{\pi} \sqrt{1+[(4.5sin(4.5x))]^2}\ dx$

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Step-by-step explanation:

The arc length of the curve is given by $\int_a^b \sqrt{1+[f'(x)]^2}\ dx$

Here, $f(x)=\int_0^{4.5x}sin(t) \ dt$ interval $[0, \pi]$

Now, $f'(x)=\frac{\mathrm{d} }{\mathrm{d} x} \int_0^{4.5x}sin(t) \ dt$

$f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left ( [-cos(t)]_0^{4.5x} \right )$

$f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left ( -cos(4.5x)+1 \right )$

$f'(x)=4.5sin(4.5x)$

Now, the arc length is $\int_0^{\pi} \sqrt{1+[f'(x)]^2}\ dx$

$\int_0^{\pi} \sqrt{1+[(4.5sin(4.5x))]^2}\ dx$

After solving, Arc length $=9.75053$

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3 years ago

Need help solving this

DedPeter [7]

Answer:

x = (√21)/2

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. That means the middle-length side is (√3)/2 times the length of the longest side.

x = (√3)/2·√7

$\boxed{x=\dfrac{\sqrt{21}}{2}}$

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