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3 years ago

Which function has x-intercepts of 3 and 8 and contains the point (–1, –2)?

1 answer:

6 0

This is how you do it.

y = a(x - 3)(x - 8)
-2 = a(-1 - 3)(-1 - 8) 
-2 = 36a 
- 1 / 18 = a 
y = ( - 1 / 18)(x^2 - 11x + 24) 
y = (- 1 / 18)x^2 + (11 / 18)x - (3 / 2)

If this doesn't explain it enough, please, ask questions.

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What is the value of x in this triangle?

Sedaia [141]

Since it's a right triangle, we can use SOH-CAH-TOA. So tan(x) = opposite/adjacent = 5/20
tan(x) = 1/4 = 0.25
x = arc-tan (0.25) = 14.04°

8 0

3 years ago

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,

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

6 0

3 years ago

The formula f= 1.8 + 32 is used to convert temputure from degrees celsius ºC to degrees

Svetach [21]

Answer:

The Formula F=1.8C+32 gives the temperature in degrees Celsius (C). There is one temperature for which a number of degrees Fahrenheit is equal to the number of degrees Celsius.

Step-by-step explanation:

20ºC = 68ºF i think this is equation.;-;

3 0

3 years ago

3. Carla opened a retirement account that pays P percent interest compounded

8090 [49]

Answer:

y=x + p

Step-by-step explanation:

3 0

3 years ago

HELP NEEDED!!! WILL GIVE 5 STARS!

Jlenok [28]

270=2b + a
420=2a + 3c (you have to use trial and error for this)

B = 120
A = 30
C = 120

Just to check
270 = (2x120) + 30
420 = (2x30) + (3x120)

3 0

3 years ago