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Svetradugi [14.3K]
2 years ago
7

Here is a sketch of a curve.

Mathematics
1 answer:
Ugo [173]2 years ago
5 0

Answer:

The turning point of the graph is at (3,-16)

Step-by-step explanation:

The general equation of curve is given as:

y = x² + ax + b

The two point for which the equation satisfies is (0,-7) and (7,0).

Substitute (0,-7) in the general equation:

y = x² + ax + b

-7 = 0² + a(0) + b

b = -7

Substitute (7,0) in the general equation:

y = x² + ax + b

0 = 7² + 7a + b

Where b = -7

0 = 49 + 7a - 7

0 = 42 + 7a

a = -6

The equation of the curve is:

a = -6 and b = -7

y = x² + ax + b

y = x² - 6x - 7

Graph of the equation is attached below.

We can see that the the turning point of the graph is at (3,-16)

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ILL MARK BRAINLIESTTTTT
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Answer:

0.075 inches per year

Step-by-step explanation:

The average rate of change is measured as

( difference in diameter ) ÷ ( difference in years )

= ( 251 - 248 ) ÷ ( 2005 - 1965 )

= 3 inches ÷ 40 years

= 0.075 inches per year

7 0
2 years ago
PLZ HELP ASAP WILL MARK BRAINLIEST !!!!!Either Table C or Table D shows a proportional relationship.
NNADVOKAT [17]

Answer:

Table C

Step-by-step explanation:

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7 0
2 years ago
Read 2 more answers
Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y
DiKsa [7]

The area of the surface is given exactly by the integral,

\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx

We have

y(x)=\dfrac15x^5\implies y'(x)=x^4

so the area is

\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the i-th subinterval are, respectively,

\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2

r_i=\dfrac{5-0}{10}i=\dfrac i2

with midpoint

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

with 1\le i\le10.

Over each subinterval, we interpolate f(x)=\sqrt{1+x^8} with the quadratic polynomial,

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

Then

\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that the latter integral reduces significantly to

\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)

which is about 651.918, so that the area is approximately 651.918\pi\approx\boxed{2048}.

Compare this to actual value of the integral, which is closer to 1967.

4 0
3 years ago
Please help me figure this out it’s due on 15 minutes
Olin [163]

Answer:

Step-by-step explanation:

1. area of square=10²=100 cm²

area of circle=πr²=π×2.5²=6.25π cm²

reqd. area=100-6.25π ≈80.375 cm²

2.

area of circle=π×2.5²=6.25π≈6.25×3.14≈19.625 cm²

area of rectangle=4×3=12 cm²

reqd. area=19.625-12≈7.625 cm²

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area of square=12²=144 cm²

reqd. area=144-56.52≈87.48 cm²

4.

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area of bigger circle=π×8²=64π cm²

area of two circles=16π+64π=80π cm²

diameter of bigger circle=4+4+8+8=24 cm

diameter of biggest circle=π×12²=144π

area of shaded region=144π-80π=64π≈200.96 cm²

5 0
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36; 351; 66; 1,017; 113,331; 1,968; 537; 417; 3,813

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