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3 years ago

Solving a word problem involving rates and time conversion

Mathematics

1 answer:

Grace [21]3 years ago

6 0

Answer:

3.5 minutes

Step-by-step explanation:

32x=112

112/32

x=3.5 minutes

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Try to find x & y. I need it so much please

kumpel [21]

Answer:

x = 3

y = 5

Step-by-step explanation:

Using theorem of similar triangles, we have,

(6 + x)/6 = (7 + 3.5)/7

(6 + x)/6 = 10.5/7

Cross multiply

7(6 + x) = 10.5(6)

42 + 7x = 63

7x = 63 - 42

7x = 21

x = 21/7

x = 3

Thus:

7.5/y = (7 + 3.5)/7

7.5/y = 10.5/7

Cross multiply

7.5*7 = 10.5*y

52.5 = 10.5*y

Divide both sides by 10.5

52.5/10.5 = y

y = 5

3 0

2 years ago

Amanda, Boris, and Jose sent a total of 124 text messages during the weekend. Amanda sent 8 fewer messages than Jose

GrogVix [38]

Answer:

Amanda= 14

Boris = 88

Jose= 22

Step-by-step explanation:

Amanda= jose-8

Boris = 4×jose

Jose= Jose

total all = 124

(jose-8)+(jose×4)+(jose)= 124

so we substitute jose with X .

(X-8)+(4X)+(X)=124

6X-8= 124.

6X=124+8

X=132/6

X= 22.

so that total jose is 22, minus 8 we get Amanda, times 4 we get Boris.

7 0

2 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

3 years ago

Can you kindly help me out please?!

Mila [183]

Answer:

32h^7

Step-by-step explanation:

(4h^4)3=64h^12

64h^12/2h^5=

32h^12/2h^5=32h^7

Hope this helps :)

5 0

2 years ago

Please help me this is very important

Virty [35]

Answer:

a. 24.5 $

b. 10.5 $

c. 7/10

Step-by-step explanation:

Given the original price of the sweater is: $ 35.

a) If you pay only $\frac{7}{10}$ of the price, then the actual amount paid is: $\frac{7}{10} \times 35 = \frac{49}{2}$ = 24.5 $.

b) Total amount Saved = Actual price - Price you paid

$\implies$ Total Amount Saved = $35 - \frac{49}{2}$

$= \frac{21}{2}$ = 10.5 $.

c) Fraction of the original price saved = Total amount Spent/Actual Price

$\implies$ Total amount Saved = $\frac{49}{2(35)}$

$= \frac{49}{70}$ = $\frac{7}{10}$

3 0

2 years ago