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2 years ago

Simplify the expression (65 points)

Mathematics

2 answers:

Fantom [35]2 years ago

8 0

Answer:

11+2x

Step-by-step explanation:

You can combine like terms to simplify expressions:

6+5=11

-2x+4x=2x

Let me know if you need any other clarification

Llana [10]2 years ago

8 0

Solution:

Step-1: Combine like terms.

$6 - 2x + 5 + 4x$

$\rightarrow x(-2 + 4) + (6 + 5)$

Step-2: Simplify.

$\rightarrow x(2) + (11)$

$\rightarrow \bold{2x + 11}$

Hence, the simplified expression is $\bold{2x + 11}.$

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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

Shaded areas please help guys ❤❤❤

pentagon [3]

Answer:

77cm

Step-by-step explanation:

Area of a rectangle=L×B

7×11=77cm

3 0

3 years ago

Read 2 more answers

Please help me. It’s geometry

Verizon [17]

Option 3:

m∠ABC = 66°

Solution:

Given $\overline {F A D} \| \overline {E H C}$ and ABH is a transversal line.

m∠FAB = 48° and m∠ECB = 18°

m∠ECB = m∠HCB = 18°

Property of parallel lines:

If two parallel lines cut by a transversal, then the alternate interior angles are equal.

m∠FAB = m∠BHC

48° = m∠BHC

m∠BHC = 48°

Exterior angle of a triangle theorem:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

m∠ABC = m∠BHC + m∠HCB

m∠ABC = 48° + 18°

m∠ABC = 66°

Option 3 is the correct answer.

4 0

3 years ago

15 times as much as 1 fifth of 12

Ann [662]

1) Work out what 1/5 of 12 is
To do this, we divide 12 by 5
12/5 = 2.4

2) Multiply 2.4 by 15
2.4 x 15 = 36

If you don't like decimals, you can also do it this way...

This can be rewritten as 15 x 1/5 x 12
Multiplications alone can be performed in any order

1) Work out what 1/5 of 15 is
1/5 of 15
15/5 = 3

2) 3 multiplied by 12
3 x 12 = 36

8 0

3 years ago

Read 2 more answers

Suppose y = sqrt 2x+1, where x and y are functions of t.

frutty [35]

If y = √(2x + 1), then differentiating both sides implicitly with respect to t gives

dy/dt = 1/2 • 1/√(2x + 1) • 2 • dx/dt = 1/√(2x + 1) • dx/dt

(a) If dx/dt = 9 and x = 4, then

dy/dt = 1/√(2•4 + 1) • 9

dy/dt = 1/√(8 + 1) • 9

dy/dt = 1/√9 • 9

dy/dt = 9/3

dy/dt = 3

(b) If dy/dt = 3 and x = 40, then

3 = 1/√(2•40 + 1) • dx/dt

3 = 1/√(80 + 1) • dx/dt

3 = 1/√81 • dx/dt

3 = 1/9 • dx/dt

dx/dt = 27

5 0

2 years ago