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3 years ago

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Mathematics

1 answer:

DochEvi [55]3 years ago

4 0

Tides move around Earth as bulges in the ocean. As the ocean bulges toward the moon, a high tide is created. The high tide on the side of Earth facing the moon is called the high high tide. The high tide caused by the bulge on the opposite side of Earth is called the low high tide.

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the length of an arc of a circle is 1/5 of its circumference. if the area of the circle is346.5cm²,find the angle subtended by t

dexar [7]

Answer:

72°

Step-by-step explanation:

From the question,

Area of the circle = πr²

A = πr²................. Equation 1

Where r = radius of the circle.

⇒ r = √(A/π)............. Equation 2

Given: A = 346.5 cm², π = 3.14

r = √(346.5/3.14)

r = √(110.35)

r = 10.5 cm.

Therefore,

circumference of the circle = 2πr = 2×3.14×10.5

circumference = 65.94 m

If the length of the arc(s) is 1/5 of its circumference.

Therefore, length of arc (s) = 13.188

⇒ length of arc/circumference = 13.188/65.94 = 1/5

s/2πr = θ/360

Where θ = angle substends at the center of the circle

1/5 = θ/360

θ = 360/5

θ = 72°

3 0

3 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

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

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

3 years ago

when mary and jack bought their house their property taxes were 3,630 annually after 8 years their property taxes are now 4,065.

Umnica [9.8K]

Answer:

jsjfjjrrifirkeiwiiieiriiwkfkfifiwjre

6 0

3 years ago

Write the coordinate of the intercept

Basile [38]

Answer:

m = 2/3

y-intercept: 2

Explanation:

First convert this equation into standard form by distributing the 6y and -4x from the coefficient of 2, and then putting the variables in order.

This equation should be in the form: Ax + By = C (Standard form)

y = -Ax/B + C/B : y = mx + b (Slope intercept form)

2(6y - 4x) = 24 → 12y - 8x = 24

→ -8x + 12y = 24 → -8x = -12y + 24 → 8x = 12y - 24 → 8x - 12y = -24

8x - 12y = -24

| | |

A B C

Once you have standard form, you are ready to convert this into slope intercept by isolating the y completely.

8x - 12y = -24

-8x -8x

(First through the subtraction property of equality, remove 8x from both sides so that -12y is by itself on the left)

-12y = -8x - 24

×-1 ×-1 ×-1

(Through the identity property of negative 1, remove the negative sign from all of the numbers because a negative times a negative is a positive)

12y = 8x + 24

(Lastly, through the division property of equality, divide all sides by 12 because it is the coefficient of y, which will solve for the variable)

8 0

3 years ago

The sum of two numbers is seventeen. One number is thirteen more than the other. Find the numbers.

AlexFokin [52]

Answer:

the second number is 4

Step-by-step explanation:

13+x=17

x=4

6 0

3 years ago