If f(a)=b and g(b)=c are functions then domain and range of fog and gof equals to

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

Solve for x and y simultaneously: X-2y=3 4xsquared-5xy+6y=3

Mkey [24]

X - 2y = 3
4x^2 - 5xy + 6y = 3
lets solve for x the first and substitute in the second:
x = 3 + 2y
4(3 + 2y)^2 - 5(3 + 2y)y + 6y = 3
4(9 + 12y + 4y^2) - 15y - 10y^2 = 3
36 + 48y +16y^2 - 15y - 10y^2 = 3
6y^2 + 33y + 33 = 0
we can solve using the general quadratic formula:
y = (-33 +- √(33^2 - 4*6*33))/12
y = (-33 +- √(297))/12
so there are 2 solutions for y:
y1 = (-33 + √(297))/12
y2 = (-33 - √(297))/12
pick one and then substitute the y value in the first equation to find x

4 0

4 years ago

Read 2 more answers

673 grams round to nearest 10 grams

natima [27]

673 grams is closer to 670 than 680.
so 673 is rounded to 670 grams.

8 0

3 years ago

Read 2 more answers

if Alex buys a 16 ounce bag of hot cheetos from ingles for $4.80. When Brad was at Dollar General he noticed they were on sale,

sveticcg [70]

Answer: