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3 years ago

Archimedes drained the water in his tub.

Mathematics

1 answer:

frosja888 [35]3 years ago

5 0

Answer:

a) 1/4 minute

Step-by-step explanation:

You can find the time using a proportion. It took 5 minutes to drain the entire 360 liters, so we can write the proportion as ...

time/volume = (5 min)/(360 L) = t/(18 L)

Multiplying by 18 L gives ...

t = (18/360)(5 min) = (5/20) min = 1/4 min

It took 1/4 minute to drain each 18 liters.

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Which method would you use to prove that the two triangles are congruent?

Alona [7]

Answer:- AAS postulate

Explanation:-

AAS postulate tells that if two angles and a non-included side of a triangle to equal to the two angles and a non-included side of another triangle then the two triangles are said to be congruent.

Given:- One angle and one side of a triangle is equal to the one angle and one side of the other triangle.

We see there is one more pair of equal angles as they are vertically opposite angles . [See the attachment]

⇒ there is a triangle where two angles and a non-included side of a triangle to equal to the two angles and a non-included side of another triangle then the two triangles are said to be congruent.

⇒ The triangles are congruent [ by ASA postulate]

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4 years ago

The volume of a cylinder is 176 π cm and its height is 11 π cm.

Liula [17]

Answer:

r = sqrt(16/pi)

Step-by-step explanation:

Cylinder formula = r^2 x pi x height

176 pi/11pi = 16

16 = r^2 x pi

16/ pi = r^2

r = sqrt(16/pi)

6 0

2 years ago

Use linear approximation to approximate √25.3 as follows.

Sophie [7]

The idea is to use the tangent line to $f(x)=\sqrt x$ at $x=25$ in order to approximate $f(25.3)=\sqrt{25.3}$ .

We have

$f(x)=\sqrt x\implies f(25)=\sqrt{25}=5$

$f'(x)=\dfrac1{2\sqrt x}\implies f'(25)=\dfrac1{10}$

so the linear approximation to $f(x)$ is

$L(x)=f(5)+f'(5)(x-5)=5+\dfrac{x-5}{10}=\dfrac x{10}+\dfrac92$

Hence $m=\frac1{10}$ and $b=\frac92$ .

Then

$f(25.3)\approx L(25.3)=\dfrac{25.3}{10}+\dfrac92=\boxed{7.03}$

4 0

3 years ago

Which equation has a slope of 3?

monitta

Answer:

the correct answer is C

Step-by-step explanation:

mx+b

5 0

3 years ago

Read 2 more answers

What is the result of substituting for y in the bottom equation y=x+3 y=x^2+2x-4

8_murik_8 [283]

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

Solution:

Given that,

$y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4 ----- eqn 2$

We have to substitute eqn 1 in eqn 2

$x + 3 = x^2 + 2x - 4$

$\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0$

$\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}$