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4 years ago

The function A(b) relates the area of a trapezoid with a given height of 10 and

Mathematics

1 answer:

Natali5045456 [20]4 years ago

6 0

The function of the trapezoid area is:

A(x)=(B+b)*h/2

Where B and b are the bases and h is the height.

With the given data: h=10 B and b =7 and x (it may vary which one is bigger)

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So that function becomes:

A(x)=(7+x)*10/2

A(x)=(7+x)*5

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So if you want the inverse function, you have to operate to find x:

A(x)/5=7+x

A(x)/5-7=x

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So the new function is:

x(A)=A/5-7

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Find the x-coordinates where f ' (x)=0 for f(x)=2x+sin(4x) in the interval [0, pi]

MAVERICK [17]

Answer:

The x-coordinate is \dfrac{\pi}{6}[/tex].

Step-by-step explanation:

We are given a function f(x) as:

$f(x)=2x+\sin (4x)$

Now on differentiating both side with respect to x we get that:

$f'(x)=2+4 \cos (4x)$

When $f'(x)=0$

this means that $2+4\cos (4x)=0\\\\4\cos (4x)=-2\\\\\cos(4x)=\dfrac{-1}{2}$

Hence, cosine function takes the negative value in second and third quadrant but we have to only find the value in the interval $[0,\pi]$ .

also we know that $\cos (\dfrac{2\pi}{3})=\dfrac{-1}{2}$ ----(1) (which lie in the second quadrant)

so on comparing our equation with equation (1) we obtain:

$4x=\dfrac{2\pi}{3}\\\\x=\dfrac{\pi}{6}$

Hence, the x-coordinates where $f'(x)=0$ for $f(x)=2x+\sin(4x)$ is $\dfrac{\pi}{6}$ .

5 0

4 years ago

A manager needs to order company shirts for each employee. She was quoted the following rates. If she orders 75 shirts and passe

docker41 [41]

The answer is B.$7.47.

Let's first calculate how much in total 75 shirts cost:
- first 19 (less than 20) cost $10: 19 * $10 = $190
- the next 30 cost $8: 30 * $8 = $240
- the rest (26 = 75 - 19 - 30) cost $5: 26 * $5 = $130

So, in total 75 shirts cost $560:
19 * $10 + 30 * $8 + 21 * $5 = $190 + $240 + $130 = $560

Since 75 shirts are ordered, there must be 75 employees, so each employee must pay $7.47:
$565 ÷ 75 = $7.47

7 0

3 years ago

Read 2 more answers

Two vertices of a right triangle have coordinates (5, 12) and (11, 12) . The segment that connects these points is a leg of the

padilas [110]

You need a right triangle correct. If you used a graph and put the points (5,12) & (11,12) it would make sense to have the next point --this(11,4)

5 0

3 years ago

Read 2 more answers

ASAP

mojhsa [17]

Answer:

cost = 8p + 5

Step-by-step explanation:

$8*[number of pizzas] + $5 delivery fee

$8p + $5

8p + 5

cost = 8p + 5

3 0

3 years ago

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On a particular map, 1 inch represents an actual distance of 2.5 miles. the actual area of a lake is 12 square miles. find the a

Anton [14]

We have that
scale factor=1 in/2.5 miles
<span>the actual area of a lake is 12 square miles

</span>we know that
[area on the map]=[scale factor]²*[area actual]
[area on the map]=[1/2.5]²*[12]-----> 1.92 in²

the answer is
1.92 in²

5 0

4 years ago