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3 years ago

On a road trip, Maura drove at a speed of 60 miles per hour for the first two hours. She then

Mathematics

1 answer:

choli [55]3 years ago

5 0

She must be tired , I can't drive that long :(

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Two towns are 80km apart. Sylvia wants to drive from one town to the other in exactly one hour. For the first 30minutes she driv

Varvara68 [4.7K]

Answer:

100 km/hr

Step-by-step explanation:

First Leg:

Speed = 60 km/h

Time = 30 min = 0.5 h

1st leg distance = speed x time = 60 km/hr x 0.5hr = 30 km

Second Leg:

Distance remaining = 80 km - 30 km = 50 km

Time = 30 min = 0.5 h

speed = distance / time = 50 / 0.5 = 100 km/hr

5 0

3 years ago

Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

What is the volume of this rectangular prism?

photoshop1234 [79]

Answer:

$\frac{64}{27} cm^3$

Step-by-step explanation:

V = L*W*H

V= (4/3)*(4/3)*(4/3)

Volume = $\frac{64}{27} cm^3$

8 0

3 years ago

the volume of a cylinder is 411π in^3. The height of the cylinder is 9 in. Calculate the diameter of the cylinder to the nearest

EleoNora [17]

Answer:

13.5 in, or 34.3 cm.

Step-by-step explanation:

First, use the formula volume = pi * r^2 * height- you have the volume, so just solve the equation 411pi = pi * 9 * r^2 for r, and you get that r = 6.75. Since diameter is equal to 2r, multiply 6.75 by 2 to get your answer of 13.5 inches. The questions asks for the diameter in centimeters though, which makes it 34.3 cm.

Hopefully this helps- let me know if you have any questions!

8 0

2 years ago

Someone help me please

iren [92.7K]

Answer: I dont need your help hmmmp

Explanation: i dont know why

3 0

3 years ago