2 x4 + 14x² + x² – 21x – 6<br> 2x²

Solve. 4x + 10= 2x – 14

hammer [34]

Answer:

x = -12

Step-by-step explanation:

Step 1: Subtract 2x from both sides

2x + 10 = -14

Step 2: Subtract 10 from both sides

2x = -24

Step 3: Divide both sides by 2

x = -12

8 0

3 years ago

Read 2 more answers

A 10 foot ladder is leaning against a wall. Call x the distance from the top of the ladder to the ground, and call y the distanc

liq [111]

$-5.3\:\text{ft/s}$

Step-by-step explanation:

We start by applying the Pythagorean theorem to the ladder, with its length L as the hypotenuse:

$L^2 = 100\:\text{ft}^2 = x^2 + y^2$

where x is the vertical distance from the top of the ladder to the ground and y is the horizontal distance from the bottom of the ladder to the wall. Taking the derivative of the above expression with respect to time, we get

$0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}$

Solving for dx/dt, we get

$\dfrac{dx}{dt} = -\left(\dfrac{y}{x}\right)\dfrac{dy}{dt} = -\left(\dfrac{\sqrt{L^2 - x^2}}{x}\right)\dfrac{dy}{dt}$

We know that

$\dfrac{dy}{dt} = 4\:\text{ft/s}$

when x = 6 ft. So the rate at which the top of the ladder is going down is

$\dfrac{dx}{dt} = -\left(\dfrac{\sqrt{100\:\text{ft}^2 - (6\:\text{ft})^2}}{6\:\text{ft}}\right)(4\:\text{ft/s})$

$\:\:\:\:\:\:\:= -5.3\:\text{ft/s}$

The negative sign means that the distance x is decreasing as y is increasing.

5 0

3 years ago

Let p: A number is greater than 25 Let q: A number is less than 35 If p ^ q is true, then what could the number be? Select two o

luda_lava [24]

Answer:

28,32

Step-by-step explanation:

8 0

3 years ago

A parcel delivery service will deliver a package only if the length plus girth (distance around) does not exceed 84 in. What are

Lesechka [4]

Answer:

a) $\frac{28}{\pi}$ in

b) 28 in

c) 784 in²

Step-by-step explanation:

Let the length be 'L'

and the radius be 'r'

Thus, according to the question

L + 2πr = 84 in

L = 84 - 2πr ............(1)

Volume of the cylinder, V = πr²L

substituting the value of L from 1, we get

V = πr²(84 - 2πr)

or

V = 84πr² - 2π²r³

for points of maxima, differentiating the above equation and equating it to zero

$\frac{dV}{dr}=\frac{d(84\pi r^2-2\pi^2 r^3))}{dr}$

or

2(84)πr - 3(2)π²r² = 0

or

2πr(84 - 3πr) = 0

or

r = 0 and 84 - 3πr = 0

or

⇒ 3πr = 84

or

⇒ r = $\frac{28}{\pi}$ in

since, the radius cannot be zero therefore, r = 0 is neglected

Therefore,

a) The radius of the largest cylindrical package = $\frac{28}{\pi}$ in

b) from (2)

L = 84 - 2πr

or

⇒ L = $84 - 2\pi\times\frac{28}{\pi}$

or

⇒ L = 84 - 56 = 28 in

The length of the largest cylindrical package = 28 in

c ) The volume of the largest cylindrical package ,V = πr²L

= $\pi\times\frac{28}{\pi}\times28$

= 784 in²

7 0

3 years ago

What is m<4+ m<5+ m<6?<br> 180°<br> 270°<br> 300°

pickupchik [31]

I really think it is 180

8 0

3 years ago

2 x4 + 14x² + x² – 21x – 6 2x² – 3