63 as a fraction in simplest form.

A circular garden has a circumference of 138 yards. Lars is digging a straight line along a diameter of the garden at a rate of

PilotLPTM [1.2K]

Answer:

4 hours

Step-by-step explanation:

Circumference formula:

C = πd

Use the given value and find the diameter:

138 = 3.14d
r = 138/3.14
r = 43.94 ≈ 44 yards

Time required to dig across the garden:

44/11 = 4 hours

6 0

2 years ago

Read 2 more answers

Find the distance from the point (1,4) to the line y = 1/3x - 3

Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

$d=\sqrt{(1-x)^2+(4-y)^2}$

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

$d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 }$ and simplify:

$d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }$

. No we'll expand each binomial by squaring:

$d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2) }$

. Combining like terms gives us

$d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50 }$

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

$\frac{20}{9}x-\frac{20}{3}$

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

$d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50 }$

which simplifies down, finally, to

x ≈ 6.325 units

8 0

3 years ago

The surface area of a cone is 54 square inches. What is the surface area of a similar cone that is three times as large?

12345 [234]

Given:

Given that the surface area of the cone is 54 square inches.

We need to determine the surface area of the cone that is similar to the cone three times large.

Surface area of the similar cone:

Let us determine the surface area of the similar cone.

The surface area of the similar cone can be determined by multiplying the surface area of the cone by 3. Because it is given that the similar cone is three times large.

Thus, we have;

$SA = 3 \times 54$