Please help i need it as fast as possible

A basketball is thrown, and its height above ground is represented by the function f(x)=-3x^2+10x+4. At the same time, a drone t

JulijaS [17]

Answer:

The drone takes 2.25 seconds to be higher than the basketball.

Step-by-step explanation:

Based on the definitions given on statement and the image attached below, the red line represents the height of the basketball and the blue line represents the height of the drone, respectively. The height of the drone is higher than the height of the basketball when the y-value of the former is higher than the y-value of the latter. The time is contained in the +x semiaxis.

According to the figure, the drone takes 2.25 seconds to be higher than the basketball.

5 0

3 years ago

Which quotient is reasonable? Do not perform the division. 7315 ÷ 12 A. 6 R 9 B. 60 R 9 C. 609 D. 6,009

ANTONII [103]

Answer:

C. 609

Step-by-step explanation:

In the question, 4-digits number were given to be divided by a 2-digits number. Without performing the division, it is only reasonable to say that the quotient will be a 3-digits number.

In the given options, the only 3-digits number is 609

Also, you can multiply 609 by 12 to check how reasonable your guess is.

⇒ 609 x 12 = 7308

The difference between 7315 and 7308 is 7.

The remaining number (7) is not up to 12 and when 7 is divided by 12 it will not give a whole number digit.

Therefore, the only reasonable quotient in the given options is 609.

5 0

3 years ago

1/3x−2= 3 What must the value of this number be?

Simora [160]

Answer: 15

Step-by-step explanation:

1/3x - 2 = 3

1/3x = 5

x = 15

6 0

3 years ago

X According to a survey, 60 sixth grade students at Madison Middle School attended a summer camp. This is 30% of the entire sixt

Liula [17]

Answer: total is 200

Step-by-step explanation:

30% = 60

10% = 60/3 = 20

100% = 200

7 0

3 years ago

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

7 0

3 years ago