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3 years ago

Pls help! will give thx and 5star and whatever just plss help

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

3 0

Answer:

18. Scalene

19. Quadrilateral

20. option i)

Step-by-step explanation:

18. A triangle whose all the three sides are different is called a scalene Triangle . Where are whose two sides are equal is called an isosceles triangle and whose all the sides are equal is called an equilateral triangle. Here all the sides are of different measurement hence it is a scalene triangle.

19. A polygon containing

3 sides is a triangle

4 sides is Quadrilateral

5 Sides is a Pentagon

6 sides is a Hexagon

8 Sides is Octagon

Our polygon contains four sides, it is hence a quadrilateral

20.

Option i)

In two congruent figures , the corresponding sides and angles are equal.

corresponding side of s is side measuring 14 ft and that of t is the side measuring 12 ft

Hence s = 14 and t = 12

corresponding angles of u is angle measuring 90° and that of r is the angle measuring 90°

Hence ∠u = 90° and ∠r=90°

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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.

Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8$

$r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

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

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

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3 years ago

NO LINKS PLEASE I ACTUALLY NEED HELP THEY'RE 2 PARTS

eimsori [14]

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3 years ago

Tory deposited 3100 and to a savings account that pays simple annual interest rate of 3.38% how much interest will she earn afte

sergiy2304 [10]

Answer:

$157.17

Step-by-step explanation:

Interest is the amount of return that someone receive on the amount invested in a bank or in a business. The annual interest rate is defined on the invested amount. The amount invested is called the principal and.

By applying the interest rate on the principal amount, we can calculate the annual interest earning.

Principal = $3,100

Rate of simple interest = 3.38% per year

Now, define the total time period.

Time period = 18 months = 18 / 12 = 1.5 years

Now calculate the Total interest earning.

Interest Earned = $3,100 x 3.38% x 1.5 = $157.17

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gizmo_the_mogwai [7]

Answer:

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Step-by-step explanation:

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