Mathematics, 24.08.2020 04:01 surfergirlmymy

Just making sure my answers are right. Please show the steps clearly. Thank you so much

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Answer from: mandilynn22

See below

Step-by-step explanation:

Let's split the integral into two parts, by the Sum Rule.

$\int\limits {x-4x^3} \, dx$ [split into 2 integrals]

$\int\limits {x} \, dx -\int\limits {4x^3} \, dx$ [solve integral for each part]

$\frac{1}{2} x^2-x^4+C$ [Remember, we need to add C for constant]

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$\int\limits {\frac{1+x}{\sqrt{x} } } \, dx$ [expand into 2 integrals]

$\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\frac{x}{\sqrt{x} } } \, dx$ [simplify second integral]

$\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\sqrt{x} } \, dx$ [solve integral for each part]

$2\sqrt{x} +\frac{2}{3}x^3^/^2+C$

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$\int\limits^4_0 {z(z^1^/^2-z^-^1^/^2)} \, dz$ [distribute]

$\int\limits^4_0 {z^3^/^2-z^1^/^2} \, dz$ [split into 2 integrals]

$\int\limits^4_0 {z^3^/^2} \, dz -\int\limits^4_0 {z^1^/^2} \, dxz$ [solve integral for each part]

$\frac{64}{5} -\frac{16}{3}$ [solve]

$\frac{112}{15}$

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D. *Note: I can't put -1 for the interval, but know that the 1 on the bottom is supposed to be -1.

$\int\limits^1_1 {(1+u)(1-u)} \, du$ [expand]

$\int\limits^1_1 {1-u^2} \, du$ [split into 2 integrals]

$\int\limits^1_1 {1} \, du-\int\limits^1_1 {u^2} \, du$ [solve integral for each part]

$2-\frac{2}{3}$ [solve]

$\frac{4}{3}$

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

Answer from: Quest

answer: finding the extract measurements and knowing the points

step-by-step explanation:

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Just making sure my answers are right. Please show the steps clearly. Thank you so much
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