Solve real word problems involving comparing and ordering integers

The volume of a cylinder is 4 pi x3 cubic units and its height is x units.

Rzqust [24]

Answer:

$2x$

Step-by-step explanation:

The volume of a cylinder, $V$ is given by the formula,

$V=\pi r^{2}h$

Where, $r$ is the radius and $h$ is the height of the cylinder.

Here, $V=4\pi x^{3}$ , $h=x$ . Plug in these values and solve for radius, $r$ .

This gives,

$V=\pi r^{2}h\\4\pi x^{3}=\pi r^{2}x\\r^{2}=\frac{4\pi x^{3}}{\pi x}\\r^{2}=4x^{2}\\$

Taking square root both sides, we get

$\sqrt{r^{2}}=\sqrt{4x^{2}}\\r=2x$

Therefore, the radius of the cylinder can be expressed as $2x$ .

6 0

2 years ago

What is the formula to find the area of a triangle? choose all that apply

Nana76 [90]

Answer:

the second and thrid one :)

Step-by-step explanation:

3 0

2 years ago

Find the equation of the line through (0,4) perpendicular to the line y = 3x

Rufina [12.5K]

Answer:

$y = - \frac{1}{3} x + 4$

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

The product of the gradients of perpendicular lines is -1.

Gradient of given line= 3.

(Gradient of line)(3)= -1

3m= -1

m= $- \frac{1}{3}$

subst. m= $- \frac{1}{3}$ into the equation:

$y = - \frac{1}{3} x + c$

To find the value of c, substitute a coordinate.

When x=0, y=4,

$4 = - \frac{1}{ 3} (0) + c \\ 4 = c \\ c = 4$

Thus the equation of the line is $y = -\frac{1}{3} x + 4$ .

3 0

3 years ago

Solve the system of equations by elimination.<br> 2x - y + 3z=-1<br> x + 2y - 4z=-1<br> y – 2z=0

MrRa [10]

Answer:

x = -1, y = 2 and z = 1

Step-by-step explanation:

The given system of equations are :

2x - y + 3z= -1 ....(1)

x + 2y - 4z = -1 ......(2)

y – 2z = 0 .....(3)

Equation (3) can be written as :

y = 2z

Use y = 2z in equation (2)

x + 2(2z) - 4z = -1

x + 4z - 4z = -1

x = -1

Put the value of x in equation (1) :

-2 -y +3z = -1

-y+3z = 1 ....(4)

Adding equation (3) and (4)

y-2z+(-y+3z)=1

z = 1

Now put z = 1 in equation (4)

-y+3=1

-y = -2

y = 2

Hence, the values of x,y and z are -1, 2 and 1 respectively.

6 0

2 years ago

Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slop

OLEGan [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is $y = -4 x$

Step-by-step explanation:

From the question we are told that

The line is $y = \frac{1}{4} x + 8$

The point is P(0,0 )

Generally the equation for a line is $yn = mx + c$

Now comparing this with the given equation we see that

$m =\frac{1}{4} = slope$

$C =8 = intercept$

Generally the slope of the perpendicular to the given line is mathematically evaluated as

$m_1 = - \frac{1}{m}$

=> $m_1 = - \frac{1}{ \frac{1}{4}}$

=> $m_1 = -4$

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and $m_1 = -4$ is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

$y = -4 x$

8 0

2 years ago