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3 years ago

Nick has 189 trading cards. Kyle has 198 trading cards. Who has fewer cards ?

Mathematics

2 answers:

Darya [45]3 years ago

7 0

Nick has fewer trading cards. 189 < 198; there is a difference of 9.

HACTEHA [7]3 years ago

6 0

Nick has fewer cards Kyle 198- 189 that Nick has = Nick has 9 less trading cards

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

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2 years ago

Write the explicit formula for the geometric sequence.<br><br> 64, 32, 16, 8, ...

Setler [38]

Answer:

aₙ = 1/2 x aₙ₋₁ n≥2

Step-by-step explanation:

aₙ = 1/2 x aₙ₋₁ n≥2

a₁ = 64

a₂ = 1/2 x 64 = 32

a₃ = 1/2 x 32 = 16

7 0

2 years ago

What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4? f(x) = one fourth (x − 3)2 + 1 f(x)

mina [271]

Let point (x, y) be any point on the graph, than the distance between (x, y) and the focus (3, 6) is sqrt((x - 3)^2 + (y - 6)^2) and the distance between (x, y) and the directrix, y = 4 is |y - 4|

Thus sqrt((x - 3)^2 + (y - 6)^2) = |y - 4|
(x - 3)^2 + (y - 6)^2 = (y - 4)^2
x^2 - 6x + 9 + y^2 - 12y + 36 = y^2 - 8y + 16
x^2 - 6x + 29 = -8y + 12y = 4y
(x - 3)^2 + 20 = 4y
y = 1/4(x - 3)^2 + 5

Required answer is f(x) = one fourth (x - 3)^2 + 5

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2 years ago

How many 0.2 liter glasses of water are contained in a 3.6 liter pitcher

PIT_PIT [208]

3.6 / 0.2 = 18 liter glasses :))

4 0

2 years ago

The circumference of a circle is 23π m. What is the area, in square meters? Express your answer in terms of \piπ

LenaWriter [7]

Answer:

Area of the circle = $\frac{529}{4}$ π m² or 132.25 π m²

Step-by-step explanation:

To find the area, we will follow the steps below.

First write down the formular for the circumference of a circle, then use the formula to find the radius of the circle after which you can now find the area of the circle.

That is;

C = 2πr

where c is the circumference of the circle and r is the radius of the circle

From the question given, circumference C = 23π

23π = 2π r

Divide both-side of the equation by 2π

23π/2π = 2πr/2π

23/2 = r

radius = $\frac{23}{2}$ m

Formula for calculating the area of a circle is given by;

A = πr²

where A= area of the circle and r is the radius of the circle

A = π ( $\frac{23}{2}$ )²

A = $\frac{529}{4}$ π m² or 132.25 π m²

Area of the circle = $\frac{529}{4}$ π m² or 132.25 π m²

6 0

2 years ago