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3 years ago

180 red marbles to 145 blue marbles

Mathematics

1 answer:

bezimeni [28]3 years ago

5 0

Answer:

36/29

Step-by-step explanation:

for every 36 red marbles there is 29 blue marbles

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Step-by-step explanation:

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2 years ago

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4 years ago

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Angle 1 and Angle 2 are supplementary angles. Find x and the measure of Angle 1.

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3 years ago

Kevin and monica lead visitor tours at a museum. Last month, both kevin and monica led the same number of vistors. Kevin lead 15

kiruha [24]

Answer:

Number of students in each group = 8

Step-by-step explanation:

kevin and monica led the same number of vistors.

Let x = number of students in each group

Kevin lead 150 adults, plus 6 student groups.

150 + 6x

Monica led 134 adults, plus 8 student groups.

134 + 8x

Equate both equations

150 + 6x = 134 + 8x

Collect like terms

150 - 134 = 8x - 6x

16 = 2x

Divide both sides by 2

x = 16 / 2

= 8

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Number of students in each group = 8

3 0

3 years ago

A silo is to be built by attaching a hemisphere roof onto a circular cylinder. The hemisphere part of the silo is constructed by

crimeas [40]

The radius and height, in two decimal places are mathematically given as

r=10.60

<h3>What is the radius and height, in two decimal places?</h3>

Generally, the equation for the volume is mathematically given as

$V=\pi r^{2} h+\frac{2}{3} \pi r^{3}$

Therefore

$5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}$

$V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\$

$\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle$

Using Lagrange method

$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$

$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$

$$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\$

$400 \pi r-300 \pi r=150 \pi h$

$$160 \pi r=150 \pi h \quad \\\\\\$

with

$h=\frac{2}{3} r $$

$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$

$\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$$

$$\frac{4 \pi \gamma^{3}}{3}=5000 \quad$

$r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$$

r=10.60

In conclusion, the radius and height, in two decimal places is

r=10.60