Taylor took 6 hours to drive home from college for Thanksgiving break, a total distance of 290 miles.

Mathematics

1 answer:

vredina [299]3 years ago

7 0

Answer: at 50 mph, she drove for 4 hours.

at 45 mph, she drove for 2 hours.

Step-by-step explanation:

Let t represent the time that she spent driving at 50 miles per hour.

Taylor took 6 hours to drive home from college for Thanksgiving break. This means that the time that she spent driving at 45 miles per hour is (6 - t) hours.

Distance = speed × time

Distance covered while driving 50 miles per hour is

50t

Distance covered while driving 45 miles per hour is

45(6 - t)

Since the total distance that she drove is 290 miles, it means that

50t + 45(6 - t) = 290

50t + 270 - 45t = 290

50t - 45t = 290 - 270

5t = 20

t = 20/5 = 4

At 45 miles per hour, she drove at

6 - 4 = 2 hours

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soldier1979 [14.2K]

Answer:

78.5%

Step-by-step explanation:

The area of the square is equal to diameter squared

i.e 4 in × 4 in = 16 square inches

The area of the circle is π × r²

i.e π × 2² = 12.56637061

The percent of the time the point will be in the circle = (Area of the circle) ÷ (Area of the square) × 100

i.e $\frac{12.56637061}{16}$ × 100 = 78.53981631%

And is equal to 78.5% (rounded up to the nearest tenth of a percent)

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3 years ago

Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,

Lina20 [59]

The shortest distance between the tip of the cone and its rim exits 51.11cm.

<h3>What is the shortest distance between the tip of the cone and its rim?</h3>

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

$$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x$