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alexgriva [62]
3 years ago
6

What is 372 rounded to the nearest 100

Mathematics
2 answers:
Xelga [282]3 years ago
7 0
372

The number 3 is in the hundreds place.

Look to the number immediately to the right.

We know that 7 is bigger than 3.

So, we add 1 to 3 and the rest become 0.

Answer: 400
NeX [460]3 years ago
4 0
372 rounded to the nearest hundred would be 400.
The answer is 400 because 372 is closer to 400 than 300.

Hope this helped :).
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A volleyball reaches its maximum of 13 feet, 3 seconds after it is served. What quadratic formula could model the height of the
Katena32 [7]

Answer:

H=-(t-3)^2+13

Step-by-step explanation:

The path covered by the volleyball will be a downward parabola with the vertex being the highest point of the ball.

A general form of a downward parabola is given as:

y=-a(x-h)^2+k

Where (h,k) is the vertex of the parabola and 'a' is a constant.

Now, let 'h' be the vertical height and 't' be the time taken.

So, the equation would be of the form:

H=-a(t-h)^2+k

Now, as per question:

h = 2 seconds, k = 13 feet.

H=-a(t-3)^2+13

Now, taking a = 1. So, the formula that can be used is:

H=-(t-3)^2+13

7 0
3 years ago
Write a system of inequalities using the given graph
ziro4ka [17]

For dark line

  • (0,1)
  • (-1,-4)

Slope

  • m=-4-1/-1=5

Equation in point slope form

  • y-1=5x
  • y=5x+1

Put (0,0)

  • 0<1

As line is dark sign is ≤

The inequality

  • y≤5x+1

For dashed line

  • (2,0)
  • (0,-2)

Equation in intercept form

  • x/2-y/2=1
  • x-y=2
  • y=x-2

Put (0,0)

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Symbol is >

Inequality is

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7 0
2 years ago
Y=x^2-6x-16 in vertex form
satela [25.4K]

Answer:

y=(x-3)^{2} -25

Step-by-step explanation:

The standard form of a quadratic equation is y=ax^{2} +bx+c

The vertex form of a quadratic equation is y=a(x-h)^{2} +k

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

h=\frac{-b}{2a}

In this case, our quadratic equation is y=x^{2} -6x-16. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

h=\frac{-b}{2a} ⇒ h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is y=x^{2} -6x-16

y=x^{2} -6x-16 ⇒ y=(3)^{2} -6(3)-16 ⇒ y=9-18-16 ⇒ y=-25

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: y=a(x-h)^{2} +k

a: 1

h: 3

k: -25

y=(x-3)^{2} -25

Hope this helps!

3 0
3 years ago
Hello people ~
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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2 years ago
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