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2 years ago

Plss help I need this for my algebra class and have no idea what to do

Mathematics

1 answer:

Salsk061 [2.6K]2 years ago

7 0

Answer:

30t if t ≤ 2

25(t-2) + 60 if 2 < t ≤ 6

160 if 6 < t ≤ 10

Step-by-step explanation:

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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

2 years ago

In a group of 60 students, 12 students take Algebra I, 18 students take Algebra II, and 8 students take both subjects. How many

vodomira [7]

Since 8 students take both, that leaves only 4 students who take Algebra I alone.
Likewise since 8 students take both, that leaves 10 who only take Algebra 2
So out of the 60, twenty two are taking either Alg I Alg Ii or both.

That leaves 38 people who are not taking either.
b. 38

You can set this up using a 2 circle venn diagram. Just be sure to put the 8 who take both in first.

4 0

2 years ago

Read 2 more answers

The sales tax for a certain state can be found by multiplying the purchase price by 1/20 . What is the sales tax on an item that

Nuetrik [128]

The answer is $1.28 sale tax
Step-by-step explanation:
Multiply the cost of the item times 0.05 to get the amount of the sales tax:
25.60 * 0.05 = $1.28 sales tax

5 0

2 years ago

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f(x)=4 hallar el dominio, codominio, ceros o raices, vertices, asintotas, tabla de valores, graficas, identificar el tipo de fun

nekit [7.7K]

Answer:

Tipo de función: Función Constante o Función Polinómica de Orden Cero

Dominio: $Dom \{f(x)\} = \mathbb{R}$

Codominio: $Ran \{f(x)\} = 4$

Asíntota: $y = 4$

Raíces: No tiene.

Vértices: No tiene.

La tabla de valores y el gráfico se encuentran adjuntos al fondo.

Step-by-step explanation:

Sea $f(x) = 4$ , el cual representa a una Función Constante o Función Polinómica de Orden Cero, cuyos dominio y codominio son $Dom \{f(x)\} = \mathbb{R}$ y $Ran \{f(x)\} = 4$ . No tiene vértices. Esta función tiene una asíntota horizontal coincidente con la función ( $y = 4$ ) y carece de raíces al ser $f(x) \ne 0$ para todo $x\in \mathbb{R}$ .