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3 years ago

8

Round off 0.065 to one significant figure

2 answers:

Alexeev081 [22]3 years ago

8 0

So the significant figure is 0

Dmitrij [34]3 years ago

5 0

I think what you are wanting id 0.1 is that rounded to one significant figure

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How to solve for x and y?

BlackZzzverrR [31]

(2x-y)+(3y-x) = 2y+X = 25
25 = 2:1 = 2Y:X
25/3 = 25/3
25/3 * 2 = 50/3 = 2y

x = 25/3
y = 25/3

Hope this helps! :)

4 0

3 years ago

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

(c) Simplify fully<br> exexexf<br> ————<br> exex fxf

Dvinal [7]

Could u be more specific

3 0

3 years ago

Read 2 more answers

Let y=(3x + f(4 − x^2))^3. Find dy/dx for x=1, given that f(3)= -6 and f'(3)= 4

Shkiper50 [21]

Answer:

correct

Step-by-step explanation:

4 0

3 years ago

Simplify 7j-6k-5j+4k which explanation please:)

Phantasy [73]

Step 1. <span>Gather like terms

</span> $(7j-5j)+(-6k+4k)$
<span>
Step 2. </span><span>Simplify

</span> $2j-2k$
<span>
Done! Hope this helps :)</span>

4 0

3 years ago

Read 2 more answers