What is the area of a circle that has a diameter of 10 feet? (Use 3.14 for pi.)

The graphs of f(x) and g(x) are shown below:

rosijanka [135]

<h2>Answer:</h2>

Option: C is the correct answer.

C.) x = −3.8, 3

<h2>Step-by-step explanation:</h2>

The function f(x) is given by:

$f(x)=x^2-x-12$

and the function g(x) is given by:

$g(x)=-1.8x-0.6$

Now, we are asked to find the solution of the equation:

$f(x)=g(x)$

i.e. we have to find the value of x such that both the functions are equal i.e.

$x^2-x-12=-1.8x-0.6\\\\i.e.\\\\x^2-x+1.8x-12+0.6=0\\\\i.e.\\\\x^2+0.8x-11.4=0\\\\i.e.\\\\10x^2+8x-114=0\\\\i.e.\\\\5x^2+4x-57=0$

Now, on solving the equation using the quadratic formula i.e. the solution of the equation:

$ax^2+bx+c=0$

is given by:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here we have:

$a=5,\ b=4\ and\ c=-57$

Hence, the solution is given by:

$x=\dfrac{-4\pm \sqrt{4^2-4\times 5\times (-57)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{-4\pm \sqrt{16+1140}}{10}\\\\i.e.\\\\x=-3.8\ and\ x=3$

6 0

3 years ago

A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. find the height and radius of the cup that will use the

alekssr [168]

The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm

6 0

3 years ago

How do you factor out the coefficient of the variable

murzikaleks [220]

Factor out the GCF. Do not forget to include the GCF as part of your final answer. In this case, the three terms have a 3x in common, which leaves: Step 3: Multiply the leading coefficient and the constant, that is multiply the first and last numbers together.

4 0

2 years ago

Using the properties of inequalities, write down the inequality that you will get if you: add the number –5; 2.7; 7; to both sid

puteri [66]

Answer:

See below

Step-by-step explanation:

1..........................

18 >−7

Add –5; 2.7; 7 to both sides

18 -5 > -7 - 5 ⇒ 13 > -12
18 + 2.7 > - 7 + 2.7 ⇒ 20.7 > - 43
18 + 7 > -7 + 7 ⇒ 25 > 0

2..........................

5 > -3

Subtract 2; 12; -5 from both sides

5 - 2 > -3 -2 ⇒ 3 > - 5
5 - 12 > -3 - 12 ⇒ -7 > -15
5 -(-5) > -3 - (-5) ⇒ 10 > 2

3..........................

- 9 < -6

Multiply both sides by 3; −3; −1

<em>When multiplying both sides of inequality by positive number the sign stays as is, when multiplying both sides of inequality by negative number the sign reverses</em>

-9 *3 < -6*3 ⇒ -27 < - 18
-9*(-3) > -6*(-3) ⇒ 27 > 18
-9*(-1) > -6*(-1) ⇒ 9 > 6

7 0

3 years ago

Read 2 more answers

Approximate the change in the volume of a sphere when its radius changes from r = 30 ft to r=10.1 ft [v(r)=4/3Ï€r^3]. When r cha

ella [17]

Answer: ∆V for r = 10.1 to 10ft

∆V = 40πft^3 = 125.7ft^3

Approximate the change in the volume of a sphere When r changes from 10 ft to 10.1 ft, Î”V=_________

[v(r)=4/3Ï€r^3].

Step-by-step explanation:

Volume of a sphere is given by;

V = 4/3πr^3

Where r is the radius.

Change in Volume with respect to change in radius of a sphere is given by;

dV/dr = 4πr^2

V'(r) = 4πr^2

V'(10) = 400π

V'(10.1) - V'(10) ~= 0.1(400π) = 40π

Therefore change in Volume from r = 10 to 10.1 is

= 40πft^3

Of by direct substitution

∆V = 4/3π(R^3 - r^3)

Where R = 10.1ft and r = 10ft

∆V = 4/3π(10.1^3 - 10^3)

∆V = 40.4π ~= 40πft^3

And for R = 30ft to r = 10.1ft

∆V = 4/3π(30^3 - 10.1^3)

∆V = 34626.3πft^3

3 0

3 years ago