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kolbaska11 [484]

3 years ago

9

Simplify: 5(x-12x^2)+3(4x+7x^2)

2 answers:

VladimirAG [237]3 years ago

7 0

Answer:

-39x^2 + 17x

Step-by-step explanation:

= 5x - 60x^2 + 3 (4x+7x^2)

= 5x - 60x^2 + 12x + 21x^2

= -39x^2 + 17x

photoshop1234 [79]3 years ago

7 0

Answer:

-39x^2 + 17x is correct

Step-by-step explanation:

I checked it

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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

3 years ago

The distance between the points (12,9) and (0,4) is A) 14 units B) 13 units C) 15 units D) 16 units

Juliette [100K]

Answer:

Option B 13 units is correct.

Step-by-step explanation:

The formula used to find distance between 2 points is:

$d(P1,P2)=\sqrt{(x_{2} -x_{1})^2 + (y_{2} -y_{1})^2 }$

x₁ = 12 x₂ = 0 y₁= 9 and y₂=4

Putting values in the formula:

$=\sqrt{(0-12)^2+(4-9)^2}\\=\sqrt{(-12)^2+(-5)^2}\\=\sqrt{144+25} \\=\sqrt{169} \\=13$

So, Option B 13 units is correct.

6 0

3 years ago

Read 2 more answers

Write the equation of the function that<br> can be modeled by this table?

Alika [10]

Answer:

<em>y = 3x + 5</em>

Step-by-step explanation:

y = mx + b (slope-intercept form)

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

Slope m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

y - $y_{1}$ = m( x - $x_{1}$ ) (point-slope form of linear equation)

~~~~~~~~~~~~~~~

3 0

2 years ago

EASY MATH PLEASE HELP

topjm [15]

Answer:

C

Step-by-step explanation:

My Apologies if Wrong!

4 0

3 years ago

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Simplify each expression by combining like terms <br> 3x^-1 - 10x^-1

Dmitry_Shevchenko [17]

Answer:

-7/x

Step-by-step explanation:

first, you combine the terms together to get -7x^-1. you cant have negative exponents in the numerator so you move the x^-1 to the denominator. once it move its becomes positive then.

7 0

3 years ago