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2 years ago

Round 97.081 to the nearest tenth. A : 97 B : 97.1 C : 97.8 D : 97.08

Mathematics

2 answers:

marishachu [46]2 years ago

6 0

B 97.1
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SCORPION-xisa [38]2 years ago

6 0

Answer:

Step-by-step explanation:

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The sum of two positive numbers is 12. what two numbers will maximize the product g

son4ous [18]

Given two numbers x and y such that:

x + y = 12 ... (1)

<span>two numbers will maximize the product g</span>

from equation (1)

y = 12 - x

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

2x = 12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

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3 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

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2 years ago

Marie has 5 apples, Toby takes 2 away. How many does he have less?

Natali [406]

Answer:

2less apples

Step-by-step explanation:

5-2=3. 3+2=5

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3 years ago

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Hannah buys 3 pairs of shoes for $x each. She uses a $10 off coupon. She

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Answer:

$15 per pair

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We know that the total amount of money she spent on the shoes (without discount) is 3x. Since she used a $10 off coupon, the money she spent is 3x - 10, since $10 off means - 10. And this amount equals $35:

$3x - 10 = 35\\3x = 45\\x = 45/3 \\x = 15$

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