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College
Calculus and Analysis
Integral Calculus

How do I find the directrix of the parabola whose equation is $y = \frac{x^{2}}{32}$ ?

beyondthegametcm 2022-02-12

The function:
$f (x) = e^{x + 1} - 2$
a) Domain
b) Range
c) x, y-intercepts
d) Sketch a graph of f
e) What transformations happened to $y = e^{x}$ to get $f (x) ?$

legurl083ra 2022-02-12

What are Bezier curves?

Marlee Yates 2022-02-12

$L^{- 1} [\frac{s}{{(s + 3)}^{2} + 9}]$

Racetovb4j 2022-02-12

Find the Laplace Transform of the following
$f (8 t - 13)$

Fastage6bk 2022-02-12

Invariance of $d s^{2}$ and transformation properties of ${d x}^{i}$
Invariance of $d s^{2}$ and transformation properties of ${d x}^{i}$
$d s^{^{'} 2} = d s^{2}$
$g_{i j}^{^{'}} {d x}^{^{'} i} {d x}^{^{'} j} = g_{i j}^{^{'}} \frac{\partial x^{^{'} j}}{\partial x^{k}} {d x}^{k} \frac{\partial x^{^{'} j}}{\partial x^{l}} {d x}^{l}$
$= g_{i j}^{^{'}} \frac{\partial x^{^{'} i}}{\partial x^{k}} \frac{\partial x^{^{'} j}}{{d x}^{l}} {d x}^{k} {d x}^{l}$
$= g_{k l} {d x}^{k} {d x}^{l}$
where $g_{i j}$ is metric tensor
1) I want to ask that idea behind this transformation is because distance remains invariant under transformation to different coordinate system
2) How this new variable k,l are introduced the text i am reading is physics pages

Pegov1 2022-02-12

Linear transformation with special properties
Linear transformation $f : R^{10} \to R^{7}$ has an attribute that every vector v for which is true that $f (v) = 0$ is in linear span ${(1, 2, \dots, 10)}^{T}, {(1, 1 \dots, 1)}^{T} >$ . Create such transformation or prove that it doesn't exists.

Jessica Collier 2022-02-12

Examine transformation properties of functions under symmetry operations
I need help learn how to examine transformation of a functions under a symmetry operation. For example, applying reflection in x axis on a vector (x,y)
$(x, y) . [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}] = (x, - y)$
from which we know how x and y transform under reflection. My question is how to examine what happens to other functions such as $x^{2}, x y, x^{2} + y^{2}$ .. etc, under the same operation? Also, how to find matrix representations of the operation for these functions?

Dillan Gibbs 2022-02-12

How do you name the curve given by the conic $r = \frac{4}{1 + 2 \sin θ}$ ?

Pegov1 2022-02-12

How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{14.4}{2 - 4.8 \cos θ}$ ?

kaibaloveyou3cj 2022-02-12

How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{0.8}{1 - 0.8 \sin θ}$ ?

Kai Ashley 2022-02-12

How do you find the points of intersection of the curves with polar equations $r = 6 \cos θ and r = 2 + 2 \cos θ$ ?

Dalia Morales 2022-02-11

How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{10}{2 - 2 \sin θ}$ ?

snajat3l 2022-02-11

Write the integral as a sum of integrals without absolute values and evaluate:
$\int_{- 6}^{3} {| x |}^{3} d x$

Belen Jones 2022-02-10

How do you name the curve given by the conic $r = \frac{6}{2 + \sin θ}$ ?

cyrsvab 2022-02-10

How do I find the directrix of the parabola $y = 2 x^{2}$ ?

simsek6li 2022-02-10

How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{8}{4 - 1.6 \sin θ}$ ?

Malaki Aguilar 2022-02-10

How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{2}{1 + 2 \cos θ}$ ?

Sage Rodgers 2022-02-10

Where is the vertical directrix of a conic if the denominator of its polar equation has the form $1 - e \cos q$ ?

dohtarjev510 2022-02-10

How do you name the curve given by the conic $r = 6$ ?

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