How do you factor 18-12?

1) If y = x3 + 2x and dx/ dt = 5, find dy/dt when x = 2. Give only the numerical answer. For example, if dy, dt = 3, type only 3

Semenov [28]

Answer:

a) 70

b) 10π ft²/ft

c) 0.24 ft/sec

Step-by-step explanation:

1) y = x³ + 2x

$\frac{dy}{dt}=\frac{d(x^3+2x)}{dt}$

or

$\frac{dy}{dt}$ = $3x^2\frac{dx}{dt}+2\frac{dx}{dt}$

at $\frac{dx}{dt}=5$ and x = 2

$\frac{dy}{dt}$ = $3(2)^2\times(5)+2\times(5)$

or

$\frac{dy}{dt}$ = 60 + 10 = 70

2) A = πr² ft²

$\frac{dA}{dr}=\frac{d(\pi r^2)}{dr}$

or

$\frac{dA}{dr}$ = 2(πr)

at r = 5 ft

$\frac{dA}{dr}$ = 2(π × 5) ft²/ft

or

$\frac{dA}{dr}$ = 10π ft²/ft

3) From Pythagoras theorem

Base² + Perpendicular² = Hypotenuse²

Thus,

B² + P² = H² .............(1)

here, H = length of the ladder

P is the height of the wall

B is the distance from the wall at bottom

or

B² + P² = 25² ...........(1)

at B = 20 ft

20² + P² = 25²

or

P² = 625 - 400

or

P = √225

or

P = 15 ft

differentiating (1) with respect to time, we get

$2B\frac{dB}{dt}+2P\frac{dP}{dt}=0$

at B = 20 ft, $\frac{dB}{dt} = 0.18$ and P = 15 ft

⇒ 2(20)(0.18) + $2(15)\frac{dP}{dt}$ = 0

or

$30\frac{dP}{dt}$ = - 7.2

or

$\frac{dP}{dt}$ = - 0.24 ft/sec (Here negative sign depicts the ladder slides down)

7 0

4 years ago

find the area of the triangle given a = 24, b=40, and C= 55°. Round your answer to the nearest tenth.

prohojiy [21]

Answer: 393.2 units²

<u>Step-by-step explanation:</u>

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

$A=\dfrac{1}{2}ab \sin C$

Given: a = 24, b = 40, C = 55°

$A=\dfrac{1}{2}(24)(40) \sin 55^o\\\\.\quad =480\sin 55^o\\\\.\quad =393.2$

4 0

4 years ago

Read 2 more answers

On his last birthday, Arnie was 144 centimeters tall. Since that time, he has grown h centimeters. Which expression tells Arnie'

telo118 [61]

Answer:

H(M) = (1)M + 10

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

THIS IS A QUESTION FOR WOLLFGIRL Write out 2-4 sentences about which advertisement would give you the "best deal"

ratelena [41]

Answer:

answers are highlighted below! I hope this helps! please do not copy my work! ^-^ :)

Step-by-step explanation:

okay, on the first one we are told we have 15% off of $729.99

which then takes off about $109.50

after we subtract the $109.50 from the $729.99 we are left with $620.49, that's not including tax

sales ax is 8.25% or $51.19 that comes out to equal $671.69

so we can conclude that the big tv sale at the big box store is equal to the amount of $671.69

on the second one, its normally $699.99

we have the coupon for $100 off of that price so that leaves us with $599.99

but we have the $50 charge for delivery. so now its at $649.99

now we need to determine the price after tax. the price of tax is $53.62

add the tax amount to $649.99 to get $703.61

$703.61

the initial price of the tv is $734.95

$150 in rebate (refund)

$734.95 - $150 = $584.95

now we need to find the price including the delivery cost

$584.95 + $35 = $619.95

now lets find the tax price

$51.15

After Tax Price: $671.10

The TV from the Electronic Warehouse is the best option. You pay only $671.10! The prices from the two other stores are $703.61 and $671.69.

We are paying .59 cents less than one of the TV's, and we are also paying $32.51 less than the other TV! So the best option would be the TV from the Big Box store!

7 0

3 years ago

How do I factor x^2+4x+20

icang [17]

Its like x² + 4x +20 = 0,
x = [-4 + √[(4²) - (4*1*20)]]/(2*1) = [-4 + √(16-80)]/2 = [-4 + √(-64)]/2 = [-4 + 8√(-1)]/2 = -2 + 4i,
x = [-4 - √[(4²) - (4*1*20)]]/(2*1) = [-4 - √(16-80)]/2 = [-4 - √(-64)]/2 = [-4 - 8√(-1)]/2 = -2 - 4i,
here i = √(-1), its a complex number.
so solution is a complex number,
x = -2 - 4i & -2 + 4i.

8 0

3 years ago