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2 years ago

13

Determine the stopping distance of a car with an initial speed of 29.97 m/s, a human reaction time of 1s, and an acceleration of

-4 m/s^2.

2 answers:

Rudik [331]2 years ago

8 0

Answer:

5/18 m/s?

Step-by-step explanation:

deff fn [24]2 years ago

6 0

Answer:

Step-by-step explanation:

is that the qustion

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Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

During first semester the ratio of the number of students in art class to the number of students in gym class was 2:7. However t

elena-s [515]

5/4 = 75/g....cross multiply because this is a proportion
5g = 300
g = 300/5
g = 60
so in 2nd semester, there were 75 students in art class and 60 students in gym class....for a total of 135 students.

1st semester....ratio was 2:7...added = 9
art : 2/9(135) = 270/9 = 30 <=== art class had 30
gym: 7/9(135) = 945/9 = 105 <=== gym class had 105

4 0

2 years ago

Classify this triangle by its sides and angles.

larisa [96]

Answer:

Right and isosceles

Step-by-step explanation:

Classification by sides: Isosceles because two sides are equal.

Classification by angles : Right angled triangle because one angle is 90°.

6 0

2 years ago

Read 2 more answers

I need help please with this math problem

Arada [10]

When the dilation is centered on the origin, you can multiply each of the individual coordinates by the scale factor.

All the coordinates are ±5 and the scale factor is 1/5. Multiplying those gives ±1. The only selection with all coordinates being ±1 is
.. Selection A.

You can check to see if the signs agree in detail. (They do.)

8 0

2 years ago

F(x) 3x^2+x-3 g(x)=x^2-5x+1 find f(x)-g(x)

wel

Answer:

2x² + 6x - 4

Step-by-step explanation:

f(x) - g(x)

= 3x² + x - 3 - (x² - 5x + 1) ← distribute

= 3x² + x - 3 - x² + 5x - 1 ← collect like terms

= 2x² + 6x - 4

5 0

3 years ago

Read 2 more answers