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3 years ago

The sum of 10 and one third of a number is equal to 13 what is the number

Mathematics

1 answer:

kherson [118]3 years ago

4 0

the answer is 9.

10+x=13

subtract 10 from both sides.

x=3

since this is one third of the number we need to find,you do reverse operations.

multiply 3 by 3.

the answer is 9.

hope this helped. god bless. :D

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the perimeter of the circular base of a cone is 132 cm and its vertical height is 28 cm find the curved surface area total surfa

Elden [556K]

Answer:

i. Curved surface area = 2310 $cm^{2}$

ii. Total surface area = 3696 $cm^{2}$

iii. volume = 12936 $cm^{3}$

Step-by-step explanation:

Perimeter of the circular base = circumference of the circle = 132 cm

circumference of a circle = 2 $\pi$ r

132 = 2 $\pi$ r

r = $\frac{132}{2\pi }$

= $\frac{66}{\pi }$

r = 66 x $\frac{7}{22}$

= 3 x 7

= 21

radius = 21 cm

vertical height, h = 28 cm

Thus applying the Pythagoras theorem,

$l^{2}$ = $h^{2}$ + $r^{2}$

= $28^{2}$ + $21^{2}$

= 784 + 441

= 1225

l = $\sqrt{1225}$

l = 35 cm

The slant height is 35 cm.

i. Curved surface area = $\pi$ rl

= $\frac{22}{7}$ x 21 x 35

= 22 x 3 x 35

= 2310

curved surface area of the cone is 2310 $cm^{2}$ .

ii. Total surface area = $\pi r^{2}$ + $\pi$ rl

= $\pi$ r(r + l)

= $\frac{22}{7}$ x 21 (21 + 35)

= 22 x 3 x 56

= 3696

The total surface area of the cone is 3696 $cm^{2}$ .

iii. volume of a cone = $\frac{1}{3}$ $\pi r^{2}$ h

= $\frac{1}{3}$ x $\frac{22}{7}$ x $21^{2}$ x 28

= 12936

The volume of the cone is 12936 $cm^{3}$

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3 years ago

What will be the scale factor of the dilation below? k = 1/2

Brut [27]

Answer?

Step-by-step explanation:

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Multiply: (- 12 / 25) (-10 / 16) -3/10 3/10 -5/6 5/6

spayn [35]

3/10.................

7 0

4 years ago

Read 2 more answers

Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, Stav, Zeke, and Georgia are

anastassius [24]

And this problem, we're trying to figure out the probability that Xerxes arrives first and Regina arrives last. Now, the first thing to note is that there are nine people. So if we list off nine different spaces, there's nine spaces and now the order in which they arrive could be any order. So for the first spot there are nine different ways that someone can show up, Anyone can show up first and then once someone has shown up first, the person who arrives second, there are eight different ways to choose that person. Similarly, the person who arrives third, there are seven people remaining, so there's seven ways to choose that and so on. And so there are actually nine factorial ways that the people can arrive to the party. Now if xerxes needs to be in the first spot and Regina needs to be in the last spot than in these remaining seven spaces, we can put any people, so there can be any ordering between xerxes and Regina. So there is seven factorial ways to order the people between xerxes and Regina. So the probability that we end up with is seven factorial divided by nine factorial. So that is seven factorial. And remember that nine factorial can be written as nine times eight times seven factorial. The seven factorial are going to cancel. We get 1/7 times eight which is equal 1/72 which is equal to approximately zero point 014 and that's it

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3 years ago

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outermost r

Andrews [41]

Solution-

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.

The radius of the outer ripple is given by r(t)= 0.6t,

where t is the time in seconds after the pebble strikes the water.

The area of the circle is given by the function $a(r) = \pi r^2$

(a ◦ r)(t) = a(r(t)) ( ∵ Using function composition / plugging in the second function into the first function)

⇒ $a(r(t))=a[0.6t]=(\pi)(0.6t)^2=0.36 \pi t^2$

∴ This is the expression for area of circle of outermost ripple, at time t after the pebble strikes the water.

8 0

3 years ago