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pychu [463]
3 years ago
15

4x-10+1.5x-4x+11=8.5-6

Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0

Answer:

x=1

Step-by-step explanation:

4x-10+1.5x-4x+11=8.5-6

Combine like terms

1.5x+1=2.5

Subtract 1 from each side

1.5x+1-1=2.5-1

1.5x = 1.5

Divide by 1.5

1.5x/1.5 = 1.5/1.5

x=1

statuscvo [17]3 years ago
7 0

Answer:

x=1

Step-by-step explanation:

Given :

4x-10+1.5x-4x+11=8.5-6

4x+1.5x-4x=8.5-6-11+10

1.5x=1.5

x=1

Value of x=1

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3 years ago
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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
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The rate of change of the height is 0.021 meters per minute

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From the formula

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\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)

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

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

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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.

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