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3 years ago

-8x + 2x – 16 < -5x + 7x

Mathematics

1 answer:

lana [24]3 years ago

5 0

Answer:

x > 2

Step-by-step explanation:

Given

- 8x + 2x - 16 < - 5x + 7x ← simplify both sides

- 6x - 16 < 2x ( subtract 2x from both sides )

- 8x - 16 < 0 ( add 16 to both sides )

- 8x < - 16 ( divide both sides by - 8 )

Remembering to reverse the symbol as a consequence of dividing by a negative value.

x > 2

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find the surface areas of the larger cone and the smaller cone in terms of pi. compare the surface areas using a percent. (the m

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ANSWER :

Surface area of larger cone : 24π units^2

Surface area of smaller cone : 6π units^2

The surface area of the smaller cone is 25% of that of the larger cone.

EXPLANATION :

From the given problem,

AB = 3 is the radius of the larger cone and the slanted height is BC = 5

DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5

Recall the surface area of the cone :

$A=\pi r^2+\pi rL$

where r = radius and L = slanted height.

For the larger cone, r = 3 and L = 5

$\begin{gathered} A=\pi(3)^2+\pi(3)(5) \\ A=24\pi \end{gathered}$

For the smaller cone, r = 1.5 and L = 2.5

$\begin{gathered} A=\pi(1.5)^2+\pi(1.5)(2.5) \\ A=6\pi \end{gathered}$

Comparing the surface areas :

The area of the smaller cone compared to the larger cone is :

$\begin{gathered} \frac{smaller}{larger}\times100=\frac{6\pi}{24\pi}\times100 \\ \\ =25\% \end{gathered}$

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1 year ago

The students at your school are taking a field trip to a science museum 154 miles away. If the school bus traveled 154 miles in

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The school but would have been driving at about 81 miles per hour.

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3 years ago

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The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

a) H'(5) is approximately -2.6 degrees Celsius per minute.

b) Yes

c) The equation for the line tangent is y = -3.6·t + 90.8
The approximate value of C(5) is 72.8 °C

d) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

$\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}$

Which gives;

$\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}$

Therefore, H'(5) = -2.6°C per minute

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

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Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of C is, $C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}$

At t = 3, we have;

$The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1$

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

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The equation for the tangent is; y = -3.6·x + 90.8

The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

C(5) ≈ 72.8°

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is -3.6 degrees per minute.

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Step-by-step explanation:

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