Which is the ratio 4 to 48 expressed as a fraction in lowest terms?

Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm thick to a hemispherical dome

pogonyaev

The amount of paint is the volume of paint needed.

The amount of paint needed is 0.065312 cubic meters

<h3>How to determine the amount of paint needed</h3>

The volume of a hemisphere is:

$V = \frac 23\pi r^3$

Differentiate the above equation

$V' = 2\pi r^2 r'$

The above equation represents the estimate of the amount of paint needed.

Where:

r represents the radius (r = 52/2 m)
r' represents the thickness (r' = 0.04 cm)

So, we have:

$V' = 2\pi r^2 r'$

$V' = 2 * 3.14 * (52/2\ m)^2 * (0.04cm)$

$V' = 2 * 3.14 * (26\ m)^2 * (0.04cm)$

Express cm as m

$V' = 2 * 3.14 * (26\ m)^2 * (0.0004m)$

$V' = 0.065312 m^3$

Hence, the amount of paint needed is 0.065312 cubic meters

Read more about volumes at:

brainly.com/question/10171109

3 0

2 years ago

An average American child aged 0-2 years old has about 915 minutes of screen time in 5 days. 6 times the difference between a ch

Alborosie

Answer:

For children ages 2 to 5, limit screen time to one hour a day of high-quality programming. As your child grows, a one-size-fits-all approach doesn't work as well. You'll need to decide how much media to let your child use each day and what's appropriate.

Step-by-step explanation:

For kids aged 2 to 5, screen time should be limited to 1 hour per day, and parents should watch the programs with their child. Also, parents should have times when screens are turned off, and bedrooms should be media-free.

7 0

2 years ago

Mark's cell phone provider charges a monthly fee of $24.95 and $0.10 per each text message (t) sent or received. The total month

enot [183]

Answer:

Step-by-step explanation:

the answer is 25.00 hope this helps

6 0

2 years ago

Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral

Stella [2.4K]

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

$l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}$

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

$l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}$

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

$l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}$

The length of side DA, with D = (-1, -1) and A = (1,4) gives;

$l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}$

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Therefore;

$Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1$

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

$Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1$

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

5 0

2 years ago

What is the median of the following 9 numbers 23,15,32,27,19,22

Travka [436]

22.5 i think but i have no idea good luck

7 0

2 years ago