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3 years ago

What is the slope of Y = -3x + 12?

Mathematics

2 answers:

GrogVix [38]3 years ago

8 0

Answer:

-3

Step-by-step explanation:

Karolina [17]3 years ago

3 0

-3
That’s the answer

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The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

$S(r)=4\pi r^2$

and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

4 0

3 years ago

4x − 1 < 11 solve for x

kvv77 [185]

Answer:

$\huge \boxed{x < 3}$

Step-by-step explanation:

4x - 1 < 11

Add 1 on both sides.

4x - 1 + 1 < 11 + 1

4x < 12

Divide both sides by 4.

(4x)/4 < 12/4

x < 3

8 0

3 years ago

What is the measurement of the missing angle?

RSB [31]

Answer:

Step-by-step explanation:

180-40+20=120

180-120+39=?

99=?

6 0

3 years ago

Complete the pattern

romanna [79]

1.) 376.2
2.) 37620
3.)376200.
3.) 3762000

hope that helped

7 0

3 years ago

Please help!! I’m stuck on this

beks73 [17]

Answer:

B. $x = -4\,\lor \,x = -1$

Step-by-step explanation:

Let $\sqrt{-4-5\cdot x} = x$ , we solve for $x$ by algebraic means.

1) $\sqrt{-4-5\cdot x} = x$ Given

2) $-4-5\cdot x = x^{2}$ Definition of power/Symmetry of equality

3) $x^{2}+5\cdot x + 4 = 0$ Compatibility with addition/Commutative and associative properties/Existence of additive inverse/Modulative property

4) $(x+4)\cdot (x+1) = 0$ $x^{2}+(a+b)\cdot x +a\cdot b = (x + a)\cdot (x+b)$

5) $x = -4\,\lor \,x = -1$ Result

Hence, the correct answer is B.

7 0

3 years ago