A rectangular metal sheet of length 44 cm and breadth 11 cm is folded by breadth side to form a cylinder.find its volume.

Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is

Mamont248 [21]

Answer:

1)The rocket hit the ground at $x = \frac{5}{4}$

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

Step(i):-

Given equation

y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

$\frac{dy}{dx} = -2( 2x) +5(1) = -4x +5$

Equating zero

$\frac{dy}{dx} = 0$

⇒ -4 x +5 =0

⇒ -4 x = -5

⇒ $x = \frac{5}{4}$

The rocket hit the ground at $x = \frac{5}{4}$

Step(ii):-

$\frac{dy}{dx} = -4x +5$ ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

$\frac{d^{2} y}{dx^{2} } = - 4(1)$

The maximum height at x = $\frac{-5}{4}$

y = -2 x² + 5 x + 7

$y = -2 (\frac{5}{4})^{2} + 5 (\frac{5}{4} ) + 7$

$y = \frac{-2(25)+ 25 (16)+7(64)}{64}$

$y = \frac{798}{64} = 12.468 feet$

The maximum height of the rocket = 12.468 feet

4 0

3 years ago

"A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the vol

Darya [45]

Answer:

$w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}$

Step-by-step explanation:

We are given the following in the question:

Volume of cake = 351 cubic inches

Let x inches be the width of cake.

Width of cake, w =

$x\text{ inches}$

Then, length of cake,l =

$(x + 4)\text{ inches}$

Height of cake,h =

$\dfrac{x}{3}\text{ inches}$

Volume of cake = Volume of cuboid

$V = lwh$

Putting values, we get:

$351 = x(x+4)(\dfrac{x}{3})\\\\1053 = x^3 + 4x\\x^3+4x^2-1053= 0\\\\\text{For x = 9}\\(9)^3+4(9)^2-1053= 0$

Thus, dimensions of cake are:

$w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}$

3 0

3 years ago

the value y varies directly with x. which function represents the relationship between x and y if y=20/3 when x=30?

joja [24]

If y varies directly with x, means that they can be modeled by a linear equation, lets choose a line with 0 y intercept, that is:
y = mx + b
y = mx
where m is the slope of the line, now we plug in the data we have:
y = mx
20/3 = m(30)
solving for m:
m = (20/3)(1/30)
m = 20/90
m = 2/9
so the line equation, or function modeling the y and x relationship is:
y = (2/9)x

6 0

3 years ago

!!HELP!!

Anna11 [10]

Answer:

Just leave it and tell your teacher about it, Desmos did that to me before as well and she told me just to leave it

7 0

2 years ago

Read 2 more answers

Use substitution to solve the system. X= 2y-5 4x+3y=-9

sergey [27]

Step-by-step explanation:

x=2y-5 - equation 1

4x+3y=-9 -equation 2

Replace equation 1 in equation 2

4(2y-5)+3y=-9

8y-20+3y=-9

11y=-9+20

11y=11

y=11/11

y=1

If y=1, therefore x=2(1)-5=-3

x=-3,y=1

6 0

3 years ago