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3 years ago

(please explain clearly, I am very tired) Find the surface area of the composite figure.

Mathematics

1 answer:

Y_Kistochka [10]3 years ago

8 0

Answer:

644

Step-by-step explanation:

SA=[2×(5×20 + 5×6 + 20×6)] +

[2×(4×12 + 4×6 + 12×6)] -

[ 2× 12×6]

= [2×(250)]+[2×(144)] - [144]

= 500+288-144

= 644 cm²

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

4 0

3 years ago

How do you compare 36.782 or 37.762

Ber [7]

Answer:

36.782 < 37.762

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3 years ago

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babunello [35]

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3 years ago

Ivan and Kate live 40 miles apart. Ivan leaves his house at 8:00 a.m.

Triss [41]

Answer: Time at which the meet = 10:17:24 am

Step-by-step explanation: Speed of Ivan = 12 mph

Speed of Kate = 16 mph

Total distance traveled = Initial separation = 40 miles

Ivan leaves his house at 8:00 a.m and Kate leaves her house at 9:30 a.m

If t is the time of catch up after Ivan starting, time taken by Kate is t - 1.5,

We have

Distance = Speed x Time

Total distance traveled = Distance traveled by Kate + Distance traveled by Ivan

40 = t x 12 + (t-1.5) x 16

40 = 28t - 24

28t = 64

t = 2.29 hours

So after 2.29 hours of Ivan's starting they meet,

Time = 8:00 am + 2.29 hours = 10:00 am + 0.29 x 60 minutes = 10:17am + 0.4 x 60 seconds = 10:17:24 am

Time at which the meet = 10:17:24 am

6 0

2 years ago

Pls help trig question!!

s2008m [1.1K]

$4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\$

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5 0

2 years ago