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2 years ago

6

Can u solve this puzzle?

1 answer:

finlep [7]2 years ago

4 0

Answer:

i dont think so sorry

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

2 years ago

6: REDUCE to simplest term. 4/1 + 15/2

vovangra [49]

Answer:

$\frac{4}{15}+\:\frac{1}{2}$ in the simplest term is:

$\frac{4}{15}+\frac{1}{2}=\frac{23}{30}$

Step-by-step explanation:

Given the expression

$\frac{4}{15}+\:\frac{1}{2}$

Thus, solving to reduce to the simplest term

$\frac{4}{15}+\frac{1}{2}$

LCM of 15, 2: 30

Adjusting fraction based on the LCM

so the expression becomes

$\frac{4}{15}+\:\frac{1}{2}=\frac{8}{30}+\frac{15}{30}$

Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

$=\frac{8+15}{30}$

Add the numbers: 8+15 = 23

$=\frac{23}{30}$

Therefore, $\frac{4}{15}+\:\frac{1}{2}$ in the simplest term is:

$\frac{4}{15}+\frac{1}{2}=\frac{23}{30}$

4 0

2 years ago

Help me to solve thisssss

m_a_m_a [10]

Answer:

(a + 3)

Step-by-step explanation:

a³ - 9a = a(a² - 9) = a(a + 3)(a - 3)

a² + a - 6 = (a - 2)(a + 3)

a⁴ + 27a = a(a³ + 27) = a(a - 3)(a² + 6a + 9) = a(a - 3)(a + 3)(a + 3)

HCF = (a + 3)

Hope it helps.

;)

<3

7 0

2 years ago

Kona wants to bake 30 loaves of bananas bread and nut bread one is 2.50 and other is 2.75 she wants to make are lasts 44$ write

kykrilka [37]

Answer:$79.25

Step-by-step explanation:

6 0

2 years ago

Please help me asap! I will give brainly!

NemiM [27]

Answer:

Figure 4 : 9 by 4 rectangle

17 red squares is figure 8

51 yellow squares

The pattern is +2 for the length, and the width stays the same. Hope this helped. :)

7 0

2 years ago

Read 2 more answers