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3 years ago

Which combination of shapes can be used to create the 3-D figure?

Mathematics

2 answers:

Leto [7]3 years ago

6 0

Answer: Two regular octagons and eight congruent rectangles

Step-by-step explanation:

An octagon has 8 sides and the shapes on the bottom of the shape are 8 rectangles.

Makovka662 [10]3 years ago

4 0

Answer:

2 regular nonagons and 9 rectangles

Step-by-step explanation:

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The coordinates of a point on a coordinate grid are (?1, 5). The point is reflected across the x-axis to obtain a new point. The

4vir4ik [10]

D. (?1, ?5) because it is only reflected across the x-axis, so it only effects the Y coordinates.

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3 years ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Otrada [13]

I guess the "5" is supposed to represent the integral sign?

$I=\displaystyle\int_1^4\ln t\,\mathrm dt$

With $n=10$ subintervals, we split up the domain of integration as

[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]

For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to

$\ell_i=1+\dfrac{3(i-1)}{10}$

and right endpoints are given by

$r_i=1+\dfrac{3i}{10}$

where $1\le i\le10$ .

a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, $\dfrac{4-1}{10}=\dfrac3{10}$ , and "bases" equal to the values of $\ln t$ at both endpoints of each subinterval. The area of the trapezoid over the $i$ -th subinterval is

$\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)$

Then the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}$

b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of $\ln t$ at the average of the subinterval's endpoints, $\dfrac{\ell_i+r_i}2$ . The area of the rectangle over the $i$ -th subinterval is then

$\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}$

so the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}$

c. For Simpson's rule, we find a quadratic interpolation of $\ln t$ over each subinterval given by

$P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

where $m_i$ is the midpoint of the $i$ -th subinterval,

$m_i=\dfrac{\ell_i+r_i}2$

Then the integral $I$ is equal to the sum of the integrals of each interpolation over the corresponding $i$ -th subinterval.

$I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt$

It's easy to show that

$\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)$

so that the value of the overall integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}$

4 0

3 years ago

6. Use the Rational Root (Zero) Theorem to list all the possible real roots (zeros).

maks197457 [2]

The left side
−
52
-
52
does not equal to the right side
0
0
, which means that the given statement is false.
False

8 0

3 years ago

What are the characteristics of the function f(x)=2(x-4)^5? Check all that apply

GaryK [48]

Answer:

Option B , C , E are characteristics of the function .

Step-by-step explanation:

Given : function f(x)=2(x-4)^5.

To find : What are the characteristics of the function .

Solution : We have given that f(x)=2 $(x-4)^{5}$ .

By the End Point behavior : if the degree is even and leading coefficient is odd of polynomial of function then left end of graph goes down and right goes up.

Since , Option E is correct.

It has degree 5 therefore, function has 5 zeros and atmost 4 maximua or minimum.

Option C is also correct.

By transformation rule it is vertical stretch and shift to right (B )

Therefore, Option B , C , E are characteristics of the function .

3 0

3 years ago

A plane intersects one nappe of a double-napped cone such that the plane is not perpendicular to the axis and is not parallel to

meriva

Ellipse is the correct answer

6 0

3 years ago

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