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jarptica [38.1K]

3 years ago

15

The water from an outdoor fountain follows a path that is shaped like a parabola. The arch created by the water is 32 inches wid

e and 27 inches high.
Use the description of the fountain to label the three points on the graph, modeling the path of the water

1 answer:

exis [7]3 years ago

6 0

Answer:

i dont understand

Step-by-step explanation:

oh wait... (0,0) (16,28) (0,33)

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F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0

3 years ago

The winning 5K race time was less than 22 minutes.

Vladimir79 [104]

Answer:

im not entirely sure how to help you

Step-by-step explanation:

can you be more specific?

4 0

3 years ago

What is the y-intercept of the function, represented by the table of values

AleksandrR [38]

Answer:

9

Step-by-step explanation:

The table is given below

$\left|\begin{array}{c|cc}x&y\\--&--\\-2&15\\1&6\\2&3\\4&-3\\7&-12\end{array}\right|$

We can see that the table represents a linear function since by checking its slope.

Using:

Points (-2,15) and (1,6)
Points (1,6) and (2,3)

$Slope =\dfrac{6-15}{1-(-2)} =\dfrac{3-6}{2-1}=-3$

Therefore, the values represent a linear function.

A linear equation is of the form y=mx+b

Therefore:

y=-3x+b

Using the points (7,-12)

$-12=-3(7)+b\\-12=-21+b\\b=-12+21\\b=9$

Therefore, the y-intercept of the function, represented by the table of values is 9.

6 0

3 years ago

Heeeeeeeeelppp ppppppppppppppppppppppppplllllassss

SVETLANKA909090 [29]

Answer:

AC= 20

Step-by-step explanation:

since the two figures are similar, CB Is congruent to FD

since image/preimage, 12/3 =4

The dilation is 4.

AC is congruent to EF

EF=5

4 x 5 = 20

AC=20

someone correct me if im wrong :)

8 0

2 years ago

On a skiing trip there are five people but only three pairs of skis how many different groups of three could ski

____ [38]

10 different groups can ski.

This is a combination of 5 items taken 3 at a time:
$_5C_3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{120}{12}=10$

3 0

3 years ago