On a number line, numbers always increase to the right and decrease to the left. Numbers to the right are greater than numbers to the left and numbers to the left are less than numbers to the right.

6 0

3 years ago

Any highly recommended math word problem solving app.... please

serg [7]

Owl Hat is a tutor and next-level math solver at your fingertips.

8 0

3 years ago

Rationalize the denominator and simplify. 5/4-√3

Yakvenalex [24]

I assume the denominator is (4-√3)
Multiple both top and bottom by (4+√3)
[5(4+√3)]/[(4-√3)(4+√3)]
=[20+5√3]/[4²-(√3)²]
=[20+5√3]/13

4 0

3 years ago

Carlos is filling a spherical balloon with water. if he increases the volume of the balloon from 4,188.79 cubic centimeters to 1

Harrizon [31]

We know that the volume of a sphere of radius r is given by

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

Now, we have been given the initial volume was 4,188.79 cubic centimeters. Let us find the radius at this time.

Substituting the value of volume in the above equation, we get

$4,188.79=\frac{4}{3}\pi r^3\\
\\
4\pi r^3=4,188.79 \times 3\\
\\
r^3=\frac{4188.79 \times 3}{4\pi}\\
\\
r^3=1000\\
\\
r=10$

Now, the final volume is given by 14,137.167 cubic centimeters. Thus, we have

$14137.167 =\frac{4}{3}\pi r^3\\
\\
4\pi r^3=14137.167 \times 3\\
\\
r^3=\frac{14137.167\times 3}{4\pi}\\
\\
r^3=3375\\
\\
r=15$

Now, let us find the surface areas for these two radii.

For $r=10$

Surface area is given by

$S=4\pi r^2\\
\\
S=4\times 3.14 \times (10)^2\\
\\
S=1256 \text{ square centimeters}$

Similarly, for

$r=15\\
\\
S=4\times 3.14\times (15)^2\\
\\
S=2826 \text{ square centimeters}$

Therefore, the increase in the surface area is given by

$\Delta S= 2826-1256= 1570 \text{ square centimeters}$

Hence, the average rate at which the surface area is changing is given by

$\frac{1570}{12}=130.8$

Therefore, the average rate at which the surface area is changing is given by 130.8 square centimeters per second.

7 0

4 years ago