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sergey [27]
3 years ago
8

how many pieces of string that are 2/7 of an inch long can be cut from a piece of string that are 7/8 of an inch long

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
6 0

namely, how many times does 2/7 go into 7/8?

\bf \cfrac{7}{8}\div\cfrac{2}{7}\implies \cfrac{7}{8}\cdot \cfrac{7}{2}\implies \cfrac{49}{16}\implies 3\frac{1}{16}\impliedby \textit{3 whole times}

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2 years ago
On a morning of a day when the sun will pass directly​ overhead, the shadow of a 60​-ft building on level ground is 25 ft long.
AysviL [449]

Answer:

The shadow is decreasing at the rate of 3.55 inch/min

Step-by-step explanation:

The height of the building = 60ft

The shadow of the building on the level ground is 25ft long

Ѳ is increasing at the rate of 0.24°/min

Using SOHCAHTOA,

Tan Ѳ = opposite/ adjacent

= height of the building / length of the shadow

Tan Ѳ = h/x

X= h/tan Ѳ

Recall that tan Ѳ = sin Ѳ/cos Ѳ

X= h/x (sin Ѳ/cos Ѳ)

Differentiate with respect to t

dx/dt = (-h/sin²Ѳ)dѲ/dt

When x= 25ft

tanѲ = h/x

= 60/25

Ѳ= tan^-1(60/25)

= 67.38°

dѲ/dt= 0.24°/min

Convert the height in ft to inches

1 ft = 12 inches

Therefore, 60ft = 60*12

= 720 inches

Convert degree/min to radian/min

1°= 0.0175radian

Therefore, 0.24° = 0.24 * 0.0175

= 0.0042 radian/min

Recall that

dx/dt = (-h/sin²Ѳ)dѲ/dt

= (-720/sin²(67.38))*0.0042

= (-720/0.8521)*0.0042

-3.55 inch/min

Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min

8 0
3 years ago
Victoria filled up her car with gas before embarking on a road trip across the country. The car uses 1.75 gallons of gas for eve
lozanna [386]

Answer:

G = 14 - 1.75(t)

Where G is the number of gallons of gas remaining;

14 represents the amount of gas in gallons in the full gas tank of the vehicle

t is the number of hours

Step-by-step explanation:

Here, we want to write an equation.

We are told that the car uses 1.75 gallons of gas every hour and after 4 hours 7 gallons were left

In the 4 hours, the amount of fuel used will be 1.75 * 4 = 7 gallons

So therefore since we have 7 gallons left, the amount of gallons in the full tank of the vehicle will be 7 + 7 = 14 gallons

Hence, the equation we want to write will be;

G = 14 - 1.75(t)

6 0
3 years ago
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