MATHEMATICS HIGH SCHOOL

An arch is 630 ft high and has 580=ft base. It can be modeled by the parabola =630\left [ 1-\left ( x/290 \right )^2 \right ]. Find the average height of the arch above the ground.The average height of the arch is __??? ft above the ground.

Answers

Answer 1

Answer:

Answer:

420 ft

Step-by-step explanation:

The given equation of a parabola is

$y=630[1-\left((x)/(290)\right)^(2)]$

An arch is 630 ft high and has 580=ft base.

Find zeroes of the given function.

$y=0$

$630[1-\left((x)/(290)\right)^(2)]=0$

$1-\left((x)/(290)\right)^(2)=0$

$\left((x)/(290)\right)^(2)=1$

$(x)/(290)=\pm 1$

$x=\pm 290$

It means function is above the ground from -290 to 290.

Formula for the average height:

$\text{Average height}=(1)/(b-a)\int\limits^b_a f(x) dx$

where, a is lower limit and b is upper limit.

For the given problem a=-290 and b=290.

The average height of the arch is

$\text{Average height}=(1)/(290-(-290))\int\limits^(290)_(-290) 630[1-\left((x)/(290)\right)^(2)]dx$

$\text{Average height}=(630)/(580)[\int\limits^(290)_(-290) 1dx -\int\limits^(290)_(-290) \left((x)/(290)\right)^(2)dx]$

$\text{Average height}=(63)/(58)[[x]^(290)_(-290)-(1)/(84100)\left[(x^3)/(3)\right]^(290)_(-290)]$

Substitute the limits.

$\text{Average height}=(63)/(58)\left(580-(580)/(3)\right)$

$\text{Average height}=(63)/(58)((1160)/(3))$

$\text{Average height}=420$

Therefore, the average height of the arch is 420 ft above the ground.

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Answers

Answer: C = b7 + bc

Step-by-step explanation:

The volume of a box with a rectangular base is 3 072cm3.the length of the sides are in the ratio 1:2:3. Calculate the length of the shortest side.

Answers

(1) The volume of a box with a rectangular base is 3072 cm³...

X x Y x Z = 3072 cm³

(2) The length of the sides are in the ratio 1:2:3

This means that:

(X)*(2X)*(3X) = 3072 cm³

It also means that:

Y=2X

Z=3X

(3) Calculate the length of the shortest side...

(X)*(2X)*(3X) = 3072 cm³

6X³ = 3072 cm³

X³ = (3072 cm³)/6

X³ = 512 cm³

X = ∛(512 cm³)

X = 8 cm

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Answers:

Length of the shortest side (X): 8 cm

Length of the side (Y): 16 cm

Length of the side (Z): 24 cm

Consider the quadratic equation y = –3x2 – 2x + 4. A. Find the value of the discriminant. B. How many real roots does the equation have? C. Does the vertex of the graph of the equation lie above, on, or below the x-axis?

Answers

A. discriminant = 52;
B. 2, because 52 > 0
C. - discrminant / 4a = -52 / -12 = 6 > 0 => the vertex of the graph of the equation lie above the x-axis.

What is the value for ƒ(x) = 42x - 100 when x = 2 ?

Answers

f(2)=42(2)-100
f(2)=84-100
f(2)=-16

Answer:

-16

Step-by-step explanation:

We are given that a function

$f(x)=42x-100$

We have to find the value of given function at x=2

To find the value of function at x=2 we will substitute x=2 in given function.

Substitute x=2 in given function

Then, we get

$f(2)=42(2)-100$

$f(2)=84-100$

Using multiplication property of integer

$f(2)=-16$

Subtraction property of integers

Hence, the value of function at x=2 =-16

What is .31 as a fraction

Answers

0.31 = 31%
% is out of 100 so 31% is 31 out of 100 which is 31/100 :)

If u know how to do this plz help cause I missed class and I don’t understand anything :/

Answers

Answer:

Step-by-step explanation:

sum of angles in a triangle is 180

(26x - 2) + 70 + 60 = 180

26x -2 = 180 - 70 - 60

26x - 2 = 50

26x = 52

x = 2

hope this helped

Answer:

D) 2

Step-by-step explanation: The interior angles of triangles will ALWAYS add up to 180 degrees. In this case 2 angles are already provided, 70 and 60, so adding those together (130) the remaining angle must be 50 (180-130=50). In 26x-2=50, x=2 is the only possible answer. (Feel free to ask any questions if you don't understand anything I said!)

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