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2 years ago

In a circle with a radius of 8 ft, an arc is intercepted by a central angle of 3π4 radians.

2 answers:

8 0

We know that

the length of a circumference=2*pi*r
for r=8 ft
the length of a circumference=2*pi*8---------> 16π ft

if 2π radians (full circle)-------------------> has a length of 16π ft
3π/4 radians-------------------------------> X
X=3π/4*16π/2π-------------> X=6π<span> ft

the answer is
6</span>π ft

frez [133]2 years ago

7 0

Answer:

Step-by-step explanation:

It is given that In a circle with a radius of 8 ft, an arc is intercepted by a central angle of $\frac{3\pi}{4}$ radians. Then the length of the arc is given by:

Length of the arc=radius×angle in radians

⇒Length of the arc= $8{\times}\frac{3\pi}{4}$

⇒Length of the arc= $6{\pi}ft$

Therefore, the length of the arc is $6{\pi}ft$ .

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STatiana [176]

First you solve for the area of the unshaded triangle. Use the formula of area of triangle which is 1/2bh to find. 1/2(9)(4) = 18 cm^2. The area of the unshaded triangle is 18cm^2. Now we need to find the area of the rectangle. We can find that by using the formula for area of rectangle which is (b)(h). 12*4 = 48 cm ^2. Now that we have the area of the triangle and the area of the rectangle, we just need to subtract the area of the triangle from the area of the rectangle to get the area of the shaded region. 48 cm^2 - 18 cm^2 = 30 cm^2.

So our answer is: The area of the shaded region is 30 cm^2. In this case it’s option C or the third option for your quiz.

4 0

2 years ago

A new Community Center is being built in Oak Valley. The perimeter of the rectangular playing field is 382 yards. The length of

vesna_86 [32]

Answer:

The width is 50 yards and the length is 141 yards.

Step-by-step explanation:

Let's call: L the length of the field and W the width of the field.

From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:

2L + 2W = 382

Because the perimeter of a rectangle is the sum of two times the length with two times the width.

Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:

L = 3W - 9

So, replacing this last equation on the first one and solving for W, we get:

2L + 2W = 382

2(3W - 9) + 2W = 382

6W -18 +2W = 382

8W - 18 = 382

8W = 382 + 18

8W = 400

W = 400/8

W = 50

Replacing W by 50 on the following equation, we get:

L = 3W - 9

L = 3(50) - 9

L = 141

So, the width of the rectangular field is 50 yards and the length is 141 yards.

3 0

2 years ago

Help plz my teacher won't help

lesantik [10]

Answer:

y = -3x + 9

Step-by-step explanation:

y = mx + b where m is the slope and b is the y intercept

The hypotenuse is on the same line as BC but twice as long. So extend that line up and it will cross the y axis at (0,9). 9 will be your y intercept.

To find the slope start at C and count up 9 and to the left 3 to get to B.

So the slope is rise/run or 9/(-3) = -3.

Final equation would be y = -3x + 9

6 0

3 years ago

Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)

Amanda [17]

Answer:

$f_x(x,y,z)=4\sin (y-z)$

$f_x(x,y,z)=4x\cos (y-z)$

$f_z(x,y,z)=-4x\cos (y-z)$

Step-by-step explanation:

The given function is

$f(x,y,z)=4x\sin (y-z)$

We need to find first partial derivatives of the function.

Differentiate partially w.r.t. x and y, z are constants.

$f_x(x,y,z)=4(1)\sin (y-z)$

$f_x(x,y,z)=4\sin (y-z)$

Differentiate partially w.r.t. y and x, z are constants.

$f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)$

$f_y(x,y,z)=4x\cos (y-z)$

Differentiate partially w.r.t. z and x, y are constants.

$f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)$

$f_z(x,y,z)=4x\cos (y-z)(-1)$

$f_z(x,y,z)=-4x\cos (y-z)$

Therefore, the first partial derivatives of the function are $f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)$ .

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3 years ago

In cell e7, create a formula that calculates the salary for sarah, one of the servers at the good breeze hotel. her salary is ca

Cloud [144]

Answer:

The formula: e7 = (b7*d7)+(c7*d7*1.5)

Step-by-step explanation:

Given:

Hours worked = b7

Hourly rate = d7

Overtime hours = c7

Salary calculation = e7

Salary = Hours worked*hourly rate + (overtime*hourly rate)*1.5

Formula

e7 = (b7*d7)+(c7*d7*1.5)

The formula e7 = (b7*d7)+(c7*d7*1.5)

Hope this will helpful to you.

Thank you.

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3 years ago