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Aleksandr [31]
3 years ago
5

How to solve question one ?

Mathematics
1 answer:
viva [34]3 years ago
6 0
-30-5x=-4x-6(5+4x)

First, you need to use the distributive property on the right to get -30-5x=-4x-30-24x

Then, you can add like terms to get -30-5x=-30-28x

Then, you can add 30 to both sides and add 5x to both sides to get 0=-23x

Finally, you divide both sides by -23 to get 0=x
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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
Which of the following is a valid probability distribution? A 2-column table labeled Probability Distribution A has 4 rows. The
Ksenya-84 [330]

Answer:

i think its D on edg

Step-by-step explanation:

8 0
4 years ago
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Water flows at a rate of 8000 cubic inches per minute into a cylindrical tank. The tank has a diameter of 128 inches and a heigh
beks73 [17]

Answer:

The height of the water = 6.2 in. to the nearest tenth

Step-by-step explanation:

∵ The rate of flows of water into the tank = 8000 in.³/min.

∴ The volume of the water in the tank after 10 min. = 8000 × 10 = 80000 in.³

∵ The water take the shape of the tank

∴ The height of the water = volume of water ÷ Area of the base of the tank

∵ The tank is cylinder with diameter 128 in. and height 72 in.

∴ The area of the base of the tank = π(128/2)²

∴ The height of the water = \frac{80000}{\pi(64)^{2}}=6.2169899

∴ The height of the water = 6.2 in. to the nearest tenth

 

5 0
3 years ago
6 (x + 2) = 4 (x − 5) pleaze help
nexus9112 [7]

Answer:

x=-16

Step-by-step explanation:

6x+12=4x-20

2x=-32

x=-16

8 0
3 years ago
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Simplify the exponential problem<br> 7b^5/b^4
Norma-Jean [14]

Solution:

If the <u>numerator</u> and the <u>denominator</u> have like bases in exponents, then the <u>exponents</u> subtract.

  • \frac{7b^5}{b^4} = 7b^5^{-4}
  • => 7b

Thus, 7b is the simplified expression.

5 0
3 years ago
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