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3 years ago

11

Javiers grandmother lives 120 miles away. It takes 1 hour to travel 40 miles by train. If Javier leaves at 7am it is reasonable

to say he will arrive in his grandmother city by 9am

2 answers:

nordsb [41]3 years ago

7 0

It would be 10 am 40 x 3 =120

Ksenya-84 [330]3 years ago

5 0

Yes because one hundred-twenty divided by 40 is thirty and that is two hours

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Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

<u>Using Pythagoras Theorem</u>

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

<u>First derivative</u>

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

<u>apply chain rule</u>

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

<u>Equate the first derivative to zero, that is V'(x) = 0</u>

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$ <u />

<u>maximum volume:</u> <u>when h = 40/3</u>

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

<u>minimum volume:</u> <u>when h = 0</u>

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

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bearhunter [10]

Answer:

Step-by-step explanation: Can you ask your teacher? Or no?

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Daria makes and sells stuffed toys. She uses special fabric to cover a foam cube to make a number cube. How much fabric did Dari

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Answer:294

Step-by-step explanation: you’re trying to find the surface area of the cube to find out how much material Daria needs. To do so find the area of 1 face of the cube (which is a square). The problem gives us 1 side of the square as 7cm. A square has the same length for its 4 sides, so to find the area of that 1 face do 7 x 7=49. The question also gives the hint that a cube has 6 faces so you would multiply the 49 by 6 to get the total surface area of the cube. 49 x 6=294.

Not sure if this is right but hope it helps.

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A rectangle measures 3 feet by 24 inches. Find the area of the rectangle in square feet.

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I'm begging, please-

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Answer: Hope this one helps :)

Part A: The length of each side is units long.

Part B: The dimensions are 5x-4 and 5x+4 units long.

Step-by-step explanation:

Part A:

-->

--> Multiply 9 times 4 to see the factors of that product

--> 9 times4 = 36

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Use the factor 6 and make it negative so -6

add another -6

Keep in mind that it is -6x

--> 9x^2-6x-6x+4

Separate the four terms into two different binomials

--> 9x^2-6x and -6x+4

Factor the binomials

With 9x^2-6x you can factor a 3x

So it will 3x(3x-2)

Do the same thing with -6x+4

You can factor out a -2

-2(3x-2)

The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)

Take the two numbers that you factored and put them to make an expression so (3x-2)

--> (3x-2)(3x-2) or (3x-2)^2

3x-2 is the length of each side so it is 3x-2 units long

Part B:

-->25x^2-16y^2

Use the difference of squares

take the square root of 25x^2

that is 5x

take the square root of 16y^2

that is 4y

write it in this way (5x+4y)(5x-4y)

These are the dimensions of the rectangle

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3 years ago