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3 years ago

Convert y=-(x-3)^2+11 to standard form

Mathematics

1 answer:

Citrus2011 [14]3 years ago

8 0

Y=−x2+6x+2 is the standard form of the equation you provided.

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15) g(n) = 2n + 5 f(n) = -4n-1 Find g(f(n))

Lisa [10]

Answer:

g[f(n)] = -8n+3

Step-by-step explanation:

Given,

g(n) = 2n + 5 , f(n) = -4n-1

Find g(f(n)),

Solutions,

g[f(n)] = g[-4n-1]

= 2(-4n-1) + 5

= -8n–2+5

g[f(n)] = -8n+3

Final Answer = g[f(n)] = -8n+3.

6 0

3 years ago

What is the surface area of the triangular prism?

SCORPION-xisa [38]

Answer:

300yd²

Step-by-step explanation:

Surface Area = area of triangles *2 + area of thhe 3 rectangles

SA= 2*( 9*4/2) + 5*12 + 8*12 + 9*12= 2*18 +5*12 + 8*12 + 9*12 =

36+60+96+108 = 300

3 0

3 years ago

How do you find the length of the curve x=3t−t3x=3t-t^3, y=3t2y=3t^2, where 0≤t≤3√0<=t<=sqrt(3) ?

taurus [48]

It's simple, you just have to do this:

$L=\int\limits_{a}^{b}\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}~dt$

$x=3t-t^3$

$\frac{dx}{dt}=3-3t^2$

$y=3t^2$

$\frac{dy}{dt}=6t$

replacing

$L=\int\limits_{0}^{\sqrt{3}}\sqrt{\left(3-3t^2\right)^2+\left(6t\right)^2}~dt$

$L=\int\limits_{0}^{\sqrt{3}}\sqrt{9-18t^2+9t^4+36t^2}~dt$

$L=\int\limits_{0}^{\sqrt{3}}\sqrt{9+9t^4+18t^2}~dt$

$L=\int\limits_{0}^{\sqrt{3}}\sqrt{(3t^2+3)^2}~dt$

$L=\int\limits_{0}^{\sqrt{3}}(3t^2+3)~dt$

$L=t^3+3t|_0^{\sqrt{3}}$

$\boxed{\boxed{L=3\sqrt{3}+3\sqrt{3}=6\sqrt{3}}}$

8 0

3 years ago

Annual fixed costs for a product are $75,000. The product itself sells for $6 and it costs $2 in variable costs to make each pro

rusak2 [61]

Given

Annual fixed costs for a product are $75,000.

The product i sells for $6

it costs $2 in variable costs to make each product.

the variable cost per unit goes up to $2.50

find out how many units will the annual break-even point for the product change .

To proof

FORMULA

Break even = Fixed cost ÷ Contribution margin per unit

where

Contribution margin per unit = sale price - variable price

Take two cases

Case first

fixed costs for a product = $75,000

product itself sells = $6

variable costs = $2

put all the value in the above equation

we get

Contribution margin per unit = 6 - 2

= 4

$Break even (say B1 ) = \frac{75000}{4}$

= 18750 units

CASE SECOND

the variable cost per unit goes up to $2.50

put value inthe formula

Contribution margin per unit = 6 - 2.50

= 3.5

$Break even (say B2 ) = \frac{75000}{3.5}$

we get

Breakeven (sayB2) = 21428.6 unit

change in the break even product = B2- B1

= 21428.6 - 18750

= 2678.6 unit

Hence proved

4 0

3 years ago

Soccer balls go on sale for $7.50 each. The store also sells footballs and the manager wants to earn a daily profit of $400 from

Tasya [4]

At $7.50 per soccer ball, they earn a daily profit of $232.50.
The store needs to earn a daily profit of $400 – $232.50 = $167.50 from footballs.
Solve 167.50 = –4x2 + 80x – 150 to find the price for footballs: x = $5.46 and $14.54.

5 0

3 years ago

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