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3 years ago

14

The area of a square is decreasing at a rate of 43 square inches per second. At the time when the side length of the square is 7

, what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).

1 answer:

Sergio039 [100]3 years ago

8 0

Answer:

26.230 Inches per second.

Step-by-step explanation:

Since, Area of square is decreasing at the rate of 43 square inches per second And area is directly proportional to square of the side , So

Its side will be decreasing at the rate of $\sqrt{43}$ inches per second .

Now,

Perimeter of square is directly proportional to 4 times of the side of the square.

so Perimeter of square will be decreasing at the rate of 4× $\sqrt{43}$

After rounding off to three decimal places we will get 26.230 Inches per second.

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Write the equation for a circle that satisfies the given conditions.

Alisiya [41]

The standard form of a circle is:

$(x-a)^2+(y-b)^2=r^2$

Your center is $(-10, -6)$ and your radius is $9$

Plug them into the equation and you get

$(x-(-10))+(y-(-6)) = 9^2$

$(x+10)^2 + (y+6)^2=81$

The correct answer is D.

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3 years ago

What is the solution? 2/3(x-7)= -2

koban [17]

Answer:

x =4

Step-by-step explanation:

2/3(x-7)= -2

Multiply each side by 3/2 to clear the fractions

3/2 * 2/3(x-7)= -2 *3/2

x-7 = -3

Add 7 to each side

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3 years ago

Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

I need help with this!!!!

Ira Lisetskai [31]

Answer:

D: 2/4

Step-by-step explanation:

Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:

BC : CD = 2 : 2 = 1 : 1

Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.

__

None of the segments is 3 units long, so neither of answer choices A or B makes any sense.

While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.

There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.

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3 years ago

For the following right triangle find the side length x

sertanlavr [38]

Since there is a right angle, you can use Pythagoras' Theorem:

So x = √(24² + 7²) = 25

---------------------------------------------------------

Answer:

25

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3 years ago