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2 years ago

PLSSS HELP

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

4 0

The correct standard form of the equation of the parabola is:

$(x+3)^{2}$ = 4(y - 3).

<h3 /><h3>What is a parabola?</h3>

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.

For the given question,

Vertex of parabola is (-3,3)

Thus, the equation of the parabola is:

$(x-h)^{2}=4(y-k)$

$(x+3)^{2}$ = 4(y-3)

Learn more about parabolas here:

brainly.com/question/64712

#SPJ1

You might be interested in

An angle measures 26.9 degrees. What is its complement?

Degger [83]

Answer:

63.1°

Step-by-step explanation:

Complementary angles sum 90°

90 - 26.9 = 63.1°

8 0

2 years ago

Consider the transformation T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v

irina1246 [14]

Answer:

Step-by-step explanation:

$T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v$

$\frac{d(x,y)}{d(u,v)} =\left|\begin{array}{ccc}x_u&x_v\\y_u&y_v\end{array}\right|$

$=(\frac{56}{65} )^2+(\frac{33}{65} )^2\\\\=\frac{(56)^2+(33)^2}{(65)^2} \\\\=\frac{4225}{4225} \\\\=1$

B )

$S:-65 \leq u \leq 65, -65 \leq v \leq 65$

$T(65,65)=(x=\frac{56}{65} (65)-\frac{33}{65} (65),\ \ y =\frac{33}{65} (65)+\frac{56}{65} (65)\\\\=(23,89)$

$T(-65,65)=(-56-33,\ \ -33+56)\\\\=(-89,23)$

$T(-65,-65) = (-56+33,-33-56)\\\\=(-23,-89)$

$T(65,-65)=(56+33, 33-56)\\\\=(89,-23)$

$\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}$

$=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(x^2+y^2)(\frac{d(x,y)}{d(u,v)} du\ \ dv$

Now

$x^2+y^2=(\frac{56}{65} u-\frac{33}{65} v)^2+(\frac{33}{65} u+\frac{56}{65} v)^2$

$[(\frac{56}{65} )^2+(\frac{33}{65}) ^2]u^2+[(\frac{33}{65} )^2+(\frac{56}{65}) ^2]v^2$

$=\frac{(65)^2}{(65)^2} u^2+\frac{(65)^2}{(65)^2} v^2=u^2+v^2$

$\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}$

$=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(u^2+v^2) du\ \ dv$

$=\int\limits^{65}_{-65}\int\limits^{65}_{-65}u^2du \ \ dv+\int\limits^{65}_{-65}\int\limits^{65}_{-65}v^2du \ \ dv$

By symmetry of the region

$=4\int\limits^{65}_0 \int\limits^{65}_0u^2 du \ \ dv + u\int\limits^{65}_0 \int\limits^{65}_0v^2 du \ \ dv$

$= 4(\frac{u^3}{3} )^{65}_{0}(v)_0^{65}+(\frac{v^3}{3} )^{65}_{0}(u)_0^{65}\\\\=4[\frac{(65)^4}{3} +\frac{(65)^4}{3} ]$

$=\frac{8}{3} (65)^4$

8 0

3 years ago

The number of new visits to a website is decreasing exponentially. It can be modeled by the function h(d)=2170(0.92)^d, where h

In-s [12.5K]

Answer:

2) -141 hits/da

Step-by-step explanation:

Calculate the values of h(2) and h(4)

h(2) = 2170(0.92)² = 2170 × 0.8464 = 1837

h(4) = 2170(0.92)⁴ = 2170 × 0.7164 = 1555

Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = (1555 -1837)/(4 - 2) = -282/2 = -141 hits/da

The average rate of change is -141 hits/da.

In the figure below, the red curve represents the function h(d), while the green dashed line represents the average rate of change over the interval 2 ≤ d ≤4.

8 0

3 years ago

Find the circumference and area of a circle with a diameter of 14 inches. Leave your answers in terms of pi. (4 points)

kobusy [5.1K]

Given:
diameter = 14 inches
radius = 14 inches / 2 = 7 inches

Circumference of a circle = 2 π r = 2 * π * 7inches = 14 inches * π

Area of a circle = π r² = π * (7in)² = π * 49in²

C = 14π and A = 49π

4 0

4 years ago

Read 2 more answers

PLEASE HELP ASAP!!!!!!!!<br><br> Find the value of the variables.

Korvikt [17]

Answer:

g=79

h=55

j=75

Step-by-step explanation:

1. When a transversal intersects two parallel lines corresponding angles, angles that are located in the same relative position an intersection of transversal and two or more straight lines, are congruent. Therefore g=79.

2. Since the two lines are parallel same side interior angles are supplementary. This means they add up to 180. So to find h solve the equation h+125=180. Once solved you get 55.

3. Like question 2, these angles are same side interior and therefore supplementary. To find j solve the equation j+105=180, which gets j=75.

3 0

3 years ago