Find the volume of the described solid. A cap of a sphere with radius and height h

Caelan
2021-05-28
Answered

Find the volume of the described solid. A cap of a sphere with radius and height h

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falhiblesw

Answered 2021-05-29
Author has **97** answers

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Find the point on the line

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Find all solutions to the following system of linear congruences: $x\equiv 1\text{mod}2,x\equiv 2\text{mod}3,x\equiv 3\text{mod}5,x\equiv 4\text{mod}7,x\equiv 5\text{mod}11$ .

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Let L :$:{P}_{2}\to {P}_{3}$ be a linear transformation for which we

know that$L:\left(1\right)=1,L\left(t\right)={t}^{2},L\left({t}^{2}\right)={t}^{3}=t.$

(a) Find$L(2{t}^{2}-5t=3).$

(b) Find$L(a{t}^{2}-bt+c).$

know that

(a) Find

(b) Find

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For the following statement, either prove that they are true or provide a counterexample:

Let a, b, m,$n\in Z$ such that m, n > 1 and $n\mid m$ . If $a\equiv b\left(\text{mod}m\right)$ , then

$a\equiv b\left(\text{mod}n\right)$

Let a, b, m,

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Distance between (7,3,4) and (5,2,9)?

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$K\in {\mathbb{R}}_{+}$ and $z\in [0,x]\cap [0,K]$ $\gamma >0$ one defines

$\begin{array}{r}\varphi (z)=(K-z){\left(\frac{z}{x}\right)}^{\gamma}\end{array}$

The maximum is attained at $z=\frac{\gamma K}{\gamma +1}$. Question: Why is for $x\le \frac{\gamma K}{\gamma +1}$:

$\begin{array}{r}\underset{z}{max}\varphi (z)=K-x\end{array}$

And for $x>\frac{\gamma K}{\gamma +1}$

$\begin{array}{r}\underset{z}{max}\varphi (z)=\varphi \left(\frac{\gamma K}{\gamma +1}\right)\text{?}\end{array}$

Best regards.

$\begin{array}{r}\varphi (z)=(K-z){\left(\frac{z}{x}\right)}^{\gamma}\end{array}$

The maximum is attained at $z=\frac{\gamma K}{\gamma +1}$. Question: Why is for $x\le \frac{\gamma K}{\gamma +1}$:

$\begin{array}{r}\underset{z}{max}\varphi (z)=K-x\end{array}$

And for $x>\frac{\gamma K}{\gamma +1}$

$\begin{array}{r}\underset{z}{max}\varphi (z)=\varphi \left(\frac{\gamma K}{\gamma +1}\right)\text{?}\end{array}$

Best regards.