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3 years ago

10

Multiply the sum of 7/8 and 3/4 by the differences of 5/36 from 11/13

1 answer:

Anni [7]3 years ago

4 0

Answer:

$=-\frac{331}{288}=-1.14930\dots$

Step-by-step explanation:

$(\frac{7}{8} + \frac{3}{4} )\times (\frac{5}{36} - \frac{11}{13} )\\\\\mathrm{Join}\:\frac{7}{8}+\frac{3}{4}:\quad \frac{13}{8}\\\\=\frac{13}{8}\left(\frac{5}{36}-\frac{11}{13}\right)\\\\\mathrm{Join}\:\frac{5}{36}-\frac{11}{13}:\quad -\frac{331}{468}\\\\=\frac{13}{8}\left(-\frac{331}{468}\right)\\\\=-\frac{13}{8}\times\frac{331}{468}\\\\\mathrm{Cross-cancel\:common\:factor:}\:13\\=\frac{1}{8}\times\frac{331}{36}\\\\=-\frac{1\cdot \:331}{8\times\:36}\\\\=-\frac{331}{288}$

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The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

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3 years ago

I need help with this fast

AnnZ [28]

Answer:

l( longer side ) = 12cm

S (shorter side) =9cm

D's( distance between the shorter side). ( It is also the height. I hope you got the clue…)

Anyway,

Area=9X8=72cm^2

Distance of the longer sides is

Area/the length of the longer side

72/12=6cm…

Distance between the longer sides is 6cm

Hope this helps…

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posledela

Answer:

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Step-by-step explanation:

4x² - 400 = 0

Add 400 to both sides

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