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Masja [62]
3 years ago
14

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. Ans

wer to the nearest integer.
Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

43

Step-by-step explanation:

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles

First we find out the width of the rectangle

Δx=b−a/n,  a= 0 and b= 3, n= 3

so Δx= 1

Divide the interval [0,3] into  3 sub intervals of width=1

[0,1]     [1,2]     [2,3]

Now we plug in end point and evaluate the function

We take left endpoints

f(x) = 16 - x^2

f(0) = 16 - 0^2=16

f(1) = 16 - 1^2= 15

f(2) = 16 - 2^2= 12

Now sum = Δx(f(0) + f(1)+f(2))

= 1 (16+15+12)= 43


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1 year ago
. Shanice is making a garden. The area of the garden is 24 ft2. Use the following shape and information to find the base (6−4) a
crimeas [40]

Answer:

The base and height  of the garden are 4.60 ft and 5.60 ft.

Step-by-step explanation:

The area of the garden is, <em>A</em> = 24 ft².

The base height of the garden are:

base (<em>b</em>) = 6x - 4

height (<em>h</em>) = x + 3

Compute the value of <em>x</em> as follows:

A=\frac{1}{2}\times b \times h\\\\24=\frac{1}{2}\times (6x-4) \times (x+3)\\\\48=6x^{2}+18x-4x-12\\\\6x^{2}+14x-60=0\\\\3x^{2}+7x-30=0\\

The last equation is a quadratic equation.

Compute the roots of the quadratic equation as follows:

x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\x = \frac{ -14 \pm \sqrt{14^2 - 4(3)(-30)}}{ 2(3) }\\x = \frac{ -14 \pm \sqrt{556}}{ 6 }\\x = \frac{ -14 }{ 6 } \pm \frac{2\sqrt{139}\, }{ 6 }\\x = -\frac{ 7}{  3 } \pm \frac{ \sqrt{139}\, }{  3 }\\x = 1.59661\\x\approx 1.60

The value of base and height are:

\text{base}=6x-4=(6\times 1.60)-4=5.60\ \text{ft}\\\\\text{height}=x+3=1.60+3=4.60\ \text{ft}

Thus, the base and height  of the garden are 4.60 ft and 5.60 ft.

3 0
3 years ago
The dinner bill came to $24.29 before tax and tip. If the taxes were 6% and they decided to leave an 18% tip, what was the total
olga_2 [115]

Answer:

$30.64 +6% tax and 18% tip

Step-by-step explanation:

Hope it helps

3 0
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Malika earn $40.25 for three and a half hours of overtime work on Saturday determine Malika's overtime pay rate
Roman55 [17]
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8 0
3 years ago
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the
Delvig [45]

Answer:

Width of the archway at its base: 11 units, height of the archway at its highest point: 30.25 units.

Step-by-step explanation:

The graph that represents the equation y = -x^{2} + 5\cdot x + 24 is now sketched with the help of a graphing tool and whose representation is included in a file attached below. The point associated with x-intercepts are (-3, 0) and (8, 0) and the point associated with the highest point is (2.5, 30.25). The width of the archway at its base (\Delta x) and the height of the archway at its highest point (\Delta y) are, respectively:

\Delta x = 8 - (-3)

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\Delta y = 30.25

Width of the archway at its base: 11 units, height of the archway at its highest point: 30.25 units.

7 0
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