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3 years ago

9

Mr. Lim and Mr. Tay had $31 090 at first.Mr. Lim donated $2390 of his money and Mr. Tay spent half of his money on a holiday tri

p. As a result, Mr. Lim had 3 times as much money as Mr. Tay. How much money did Mr. Lim have at first?

2 answers:

hjlf3 years ago

7 0

Answer:

Mr.Lim had 19,610 dollars, and Mr.Tay had 1,1480 dollars at first.

andriy [413]3 years ago

3 0

Answer:

Mr.Lim had 19610 dollars, and Mr.Tay had 11480 dollars at first.

Step-by-step explanation:

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A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

3 years ago

-3/7, -8/3 and -5/2,-2 slope

Alja [10]

So the points are (-3/7,-8/3) and (-5/2,-2)
to find the slope do
(y2-y1)/(x2-x1)
(x,y)
x1=-3/7
y1=-8/3
x2=-5/2
y2=-2

subsitute
$\frac{-2-( \frac{-8}{3} )}{ \frac{-5}{2} - \frac{-3}{7} }$
simplify by finding similar denomenators
$\frac{\frac{-6}{3}-( \frac{-8}{3} )}{ \frac{-35}{14} - \frac{-6}{14} }$
$\frac{\frac{-6}{3}( \frac{8}{3} )}{ \frac{-35}{14} + \frac{6}{14} }$
add
$\frac{\frac{2}{3}}{ \frac{-29}{14}}$
multiply top and bottom by $\frac{-14}{29$
$\frac{\frac{-28}{87}}{1}$
$\frac{-28}{87}$
answer is
slope= $\frac{-28}{87}$

8 0

3 years ago

Help pls, thank you !!

nikdorinn [45]

Answer:

the first one is a lie

Step-by-step explanation:

caf is more 45 degrees than 25

7 0

2 years ago

The quadrilaterals ABCD and JKLM are similar.

Paha777 [63]

Answer: 4.8

Step-by-step explanation:

Corresponding sides of similar figures are proportional, so

$\frac{x}[4}=\frac{6}[5}\\\\x=4\left(\frac{6}{5} \right)=\boxed{4.8}$

7 0

2 years ago

An inscribed triangle with the hypotenuse being the diameter of the circle has angle A be 42 degrees. Angle C is 90 degrees. The

eduard

Answer:

The Radius of circle is 7.15 cm

Step-by-step explanation:

Given as :

A Triangle is inscribed into circle

The center of circle is O

The Diameter of circle = AK = d

The hypotenuse of triangle being the diameter of circle

The Area of triangle = 50 cm²

Let The radius of circle = r cm

The Triangle is right angle at c

So , ∠ACK = 90°

∠CAK = 42°

∠AKC = 180° - (90° + 42°)

So, ∠AKC = 48°

Now, ∵ Area of triangle ACK = 50 cm²

So, $\dfrac{1}{2}$ × AC × CK = 50

Or, AC × CK = 50 × 2

i.e , AC × CK = 100 ..........1

From figure

Sin 48° = $\dfrac{AC}{AK}$

Or, 0.74 = $\dfrac{AC}{d}$

∴ AC = 0.74 d ..........2

<u>Similarly</u>

Sin 42° = $\dfrac{CK}{AK}$

Or, 0.66 = $\dfrac{CK}{d}$

∴ CK = 0.66 d .............3

<u>Putting eq 2 and 3 value into eq 1</u>

i.e AC × CK = 100

Or, 0.74 d × 0.66 d = 100

Or, 0.4884 × d² = 100

∴ d² = $\dfrac{100}{0.4884}$

Or, d² = 204.75

Or, d = $\sqrt{204.75}$

Or, d = 14.30

So, The diameter of circle = d = 14.30 cm

Now, Radius of circle = $\dfrac{\textrm diameter}{2}$

Or, r = $\dfrac{\textrm 14.30 cm}{2}$

i.e r = 7.15 cm

So, The Radius of circle = r = 7.15 cm

Hence, The Radius of circle is 7.15 cm Answer

7 0

3 years ago