A lawn fertilizer company is working on different formulas for lawn fertilizer. They want to examine the difference between their "Original Formula" and their "Improved Formula".

Answer:

[tex]b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}[/tex]

Step-by-step explanation:

Given - The circumference of the ellipse approximated by [tex]C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }[/tex]where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

[tex]C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }[/tex]

Squaring Both sides, we get

[tex][\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }[/tex]

[tex]\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b[/tex]

∴ we get

[tex]b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}[/tex]

Answer:

f(-4) is basically just saying that you need to use the function given while x = -4.

The function given:

f(x) = -8(5-x)

We see that f(-4) means that x has to be -4, so we can substitute it in:

f(-4) = -8(5-(-4))

f(-4) = -8(9)

f(-4) = -72

Therefore, f(-4) is -72.

Answer:

Option A

Step-by-step explanation:

From the question given in the picture attached,

Directrix of the parabola → y = 2

Focus of the parabola → (-5, 0)

Since, focus is below the directrix, parabola will open open downwards.

Equation of the parabola will be in the form of,

y - k = -4p(x - h)²

Here, (h, k) is the vertex of the parabola

p = Distance between vertex and focus or distance between vertex and directrix

Since, distance between vertex and focus = Distance between vertex and directrix

Therefore, vertex of the parabola → (-5, 1)

Now distance (p) between vertex (-5, 0) and focus (-5, 1) = 1 unit

By substituting these values in the equation,

y - 1 = -4(1)[x - (-5)]²

y - 1 = -4(x + 5)²

y = -4(x + 5)² + 1

Option A will be the answer.

I think the answer is 2 percent

hope this is answer

Wait… what lesson? I am confused :/

Answer:

C = 43.96 miles

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

C = 2 * 3.14 * 7

C = 43.96 miles

Answer:

6.25

Step-by-step explanation:

Step-by-step explanation:

The formula for probability is favourable outcome/ Total outcome. So the answer might be 7/30.

Answer:

It's D I believe because y is the total cost . $2.50 is being added per pound of berries they pick which represents x. Then you add the $3 payed to enter the farm. Hopefully it's righttt :)

Let's take a look at our table here in order to solve the problem. We need to know what g(0) and g(4) are to be able to solve.

Since we are plugging in x-values and looking for y-values, we simply need to find 0 and 4 on the left side of the table (the x side), and then find their corresponding g(x), or y, values.

g(0) = -5

g(4) = -4

Now, all that's left to do is add these two values.

-5 + -4

-9

Hope this helps!! :)

Answer:

- 9

Step-by-step explanation:

g(0) = - 5 ← value of g(x) when x = 0

g(4) = - 4 ← value of g(x) when x = 4

Then

g(0) + g(4) = - 5 + (- 4) = - 5 - 4 = - 9

Answer:

3 to the power 9 is the answer

Answer:

[tex] 3^9 [/tex]

Step-by-step explanation:

[tex] 3^8 \times 3 = 3^8 \times 3^1 = 3^{8 + 1} = 3^9 [/tex]

Answer:

its 6th grade math but the answer is 36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

when you have an exponent of 2. you times/multiply the number by itself

Answer:

Step-by-step explanation:

Roots:  set y = x^2 + 8x + 12 = 0 and solve for x:  x + 6 = 0, so x = -6 is one root.  The other is x = -2.  The corresponding points are (-6, 0) and (-2, 0).

y-intercept:  Let x = 0.  Then y = 12.  The y-intercept is (0, 12).

Axis of symmetry:  x = -b / (2a) => x = -8/(2*1) = -4:  x = -4

Vertex y-value:  evaluate y at x = - 4:  (-4)^2 + 8(-4) + 12 = -4:    (-4, -4)

Arbitrarily chosen x value:  x = 1 => 1^2 + 8(1) + 12 = 21:     (1, 21)

The five points are:  (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21).  The vertex is (-4, -4).  The parabolic graph opens UP.

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² + 8x + 12

Conver the equation into a vertex form. Then we have

y = x² + 8x + 12

y = x² + 8x + 16 - 16 + 12

y = (x + 4)² - 4

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

The graph is given below.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

#SPJ2

Step-by-step explanation:

TSA = 3543.72 hope its helpfull

Answer:

$12

Step-by-step explanation:

Given data

Radius= 2in

cost = $4

New jaw breaker radius= 6in

cost=???

If 2 in jaw breaker cost $4

6in jaw breaker will cost x

cross multiply

6*4= 2*x

24= 2x

x= 24/2

x= $12

Hence the 6 in jawbreaker will cost $12

Answer:

Land slide

Step-by-step explanation:

I think you can see how, its litteraly land that is sliding

Answer:

3.26 hours

Step-by-step explanation:

speed = distance / time

595 = 1940 / t

t = 1940 / 595  = 3.26 hours

or

The length of the ramp is 6.91 feet

Given data:

To determine the length of the ramp, we can use trigonometry. So, use the sine function, which relates the angle of the ramp to the ratio of the opposite side (length of the ramp) to the hypotenuse (the distance the ramp covers).

Given that the angle of the ramp is 24°, set up the equation:

sin(24°) = opposite/hypotenuse

The opposite side is the length of the ramp and the hypotenuse is the distance it covers, which is 17 feet.

sin(24°) = length of the ramp / 17

To find the length of the ramp, rearrange the equation:

The length of the ramp = sin(24°) * 17

L ≈ 6.91 feet

Hence, the length of the ramp is approximately 6.91 feet.

To learn more about trigonometric relations, refer:

https://brainly.com/question/14746686

#SPJ4

Answer:

83.05

Step-by-step explanation:

The two measures of the center are 82.5 and 83.6

The value of the median can be calculated a follows

= 82.5 + 83.6/2

= 166.1/2

= 83.05

Hence the value of the media is 83.05

Answer:

well im pretty sure its ( 1,1,3)

Step-by-step explanation:

21-1-2

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

2 + 2 = 4

5 + 5 = 5

4/5

Add :

→ (√5 + 2√2) & (√2 - 5√3)

→ (√5 + 2√2) + (√2 - 5√3)

Removing the brackets.

→ √5 + 2√2 + √2 - 5√3

→ √5 + (2 + 1)√2 - 5√3

→ √5 + 3√2 - 5√3

Therefore, the required answer is √5 + 3√2 - 5√3.

Answer:

hi

Step-by-step explanation:

To round a number to the nearest hundredth , look at the next place value to the right (the thousandths this time). Same deal: If it's 4 or less, just remove all the digits to the right. If it's 5 or greater, add 1 to the digit in the hundredths place, and then remove all the digits to the right.

Answer:

Step-by-step explanation:

let the missing angle be x

take 65 degree as reference angle

use tan rule

tan 65=opposite/adjacent

2.14=x/7

2.14*7=x

14.98=x

Answer: A  Rhombus has 4 congruent sides .

Answer:

10 inches

Step-by-step explanation:

Answer:

[tex]x\geq 2[/tex]

Step-by-step explanation:

The parent function, [tex]y=\sqrt{x}[/tex], has a domain of [tex]x\geq 0[/tex] or [tex][0, \infty)[/tex], because the value under the radical cannot be less than 0 (we cannot take the square root of a negative number). Thus, by setting everything inside the radical to 0, we can find the domain of this function:

[tex]x-2\geq 0,\\x\geq 2[/tex]

Thus this domain of this function is:

As an inequality: [tex]x\geq 2[/tex] (desired in problem)

In interval notation: [tex][2, \infty)[/tex]