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4 years ago

Simplify the expression below: 4+2×[(3+1)×5] (show work please need it for review)

Mathematics

1 answer:

____ [38]4 years ago

5 0

Answer:

Step-by-step explanation:

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

First we need to do the work inside the parenthesis that are in the boxed parenthesis

3 + 1 = 4

4 * 5 = 20

Now we multiply

20 * 2 = 40

Now we add

40 + 4 = 44

Best Of Luck,

- I.A. -

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Answer:

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Step-by-step explanation:

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4 years ago

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A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed

N76 [4]

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

$\dfrac{AD}{AB} = \dfrac{DE}{BC}$

$\dfrac{8}{12} = \dfrac{2}{y}$

8y = 24

y = 24/8

y = 3 meters

Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x

∴

$\dfrac{12-x}{12}=\dfrac{2}{y}$

$1- \dfrac{1}{12}x = 2* \dfrac{1}{y}$

To find the derivatives of both sides ;we have:

$- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy$

$- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}$

During that time ;

$\dfrac{dx}{dt }= 1.4 \ m/s$ and y = 3

So; replacing the value into above ; we have:

$-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}$

$\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}$

$\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}$

$\dfrac{dy}{dt} =0.525 \ m/s$

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

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3 years ago

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Answer:

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Step-by-step explanation:

Considering she waters her plants with 25 1/2 gallons i.e 51/2

and with the new system, she does it with 19 3/4 i.e 79/4

taking the difference:

$\frac{51}{2} - \frac{70}{4}$ = $\frac{23}{4}$ gallons per day

For 30 days:

30 x $\frac{23}{4}$ = 172.5 or $172\frac{1}{2}$ gallons

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Answer:

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