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2 years ago

A cylinder has a volume of 200 mm3 and a height of 17 mm.

Mathematics

1 answer:

Gnoma [55]2 years ago

4 0

Answer:

The radius of the cylinder is 1.93mm.

Step-by-step explanation:

1) Formula to find the missing radius : V= pi r^2 (h)

( V= volume, pi=3.14 r=radius, h= height)

2) Plug all the give variables into the formula: 200=pi r^2 (17)

3) Multiply pi with 17 and then round it to the nearest hundredth which you get 53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2

4) Next you want to isolate the r^2 by dividing both sides by 53.41

200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74) ---> 3.74=r^2

5) Now you have to square both sides to get rid of that exponent : squared 3.74 = squared r^2

6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)

7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.

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Consider the system of linear equations. x + y = 9.0 0.50 x + 0.20 y = 4.05 Find the values of x and y .

mixas84 [53]

Answer:

x=7.5

y=1.5

Step-by-step explanation:

$x + y = 9.0$

subtract x from both sides

$y=9-x$

$0.50x + 0.20y= 4.05$

$0.50 x +0.20(9-x)= 4.05$

$0.50x+1.8-0.2x= 4.05$

combine like terms

$0.30x+1.8= 4.05$

subtract 1.8 from both sides

$0.30x=2.25$

divide both sides by 0.3

x=7.5

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$y=9-7.5$

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2 years ago

Converting 4.9 kilograms would give you 11 of which US customary system unit? A. Pounds B. Stones C. Teaspoons D. Ounces Mark fo

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Kilograms is a type of measurement for weight, and so the converted measure should also be weight (which leaves only oz. and lbs.)

The converting ratio of kilograms to pounds is: 1 = 2.2

The converting ratio of kilograms to ounces is: 1 = 35.274

This means that pounds, or (B) is your closest answer

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2 years ago

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Scarlet and Paula are on a vacation. They went to a store to buy some souvenirs for their friends back home. Scarlet bought thre

snow_lady [41]

Answer:

Step-by-step explanation:

1. Choose a person.

2. Substitute the numbers into the correct values.

105 - 15 = ?/5 = 18

105 - 18 = ?/5 = 3.48

105 - 12 = ?/5 = 18.6

105 - 23 = ?/5 = 16.4

It is A because it is the only one in which the answer is equivalent to the cost.

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2 years ago

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Ella completed the following work to test the equivalence of two expressions.

MrRa [10]

Answer:

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Step-by-step explanation:

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Two algebraic expressions are said to be equivalent if their values obtained by substituting any values of the variables are same.

Two expressions 3f+2.6 and 2f+2.6 are not equivalent, because when f=1,

3f + 2.6 = 3.1 + 2.6 = 3 + 2.6 = 5.6

2f + 2.6 = 2.1 + 2.6 = 2 + 2.6 = 4.6

5.6 = 4.6

Method of substitution can only help her to decide the expresssions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.

3f + 2.6 = 2f + 2.6

3f = 2f

3f - 2f = 0

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This is true only when f=0.

Hence,

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

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2 years ago

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In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

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Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .