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Leya [2.2K]
3 years ago
9

Standard form for64x10 forth power

Mathematics
2 answers:
nikitadnepr [17]3 years ago
6 0
Standard form for 64×10=640
laila [671]3 years ago
5 0
Standard form essentially means to not have any symbols such as "x","÷", or "power".

The equation would be written as:

(64 x 10) ^4
Then
(640) ^ 4

Which equals: <span>167772160000</span>

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Suppose someone tells you that she has a triangle with sides having lengths 2.2, 4.5, and 6.7. Is this a right triangle?
laila [671]
You can apply the Pythagorean theorem:
a^2 + b^2 = c^2
c is the longest side of the triangle
2.2^2 + 4.2^2 = 6.7^2
4.84 + 17.64 = 44.89
22.48 =/= 44.89
That is not a right triangle
6 0
2 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.

3 0
3 years ago
fond two consecutive odd integers whose sum is 36 which of the following equations could be used to solve the problem
Travka [436]

Answer:

17 is the answer.

Step-by-step explanation:

4 0
3 years ago
How many solutions douse -5x-8=+8
larisa [96]

Answer: One solution

Step-by-step explanation:

Given

-5x-8=8

Add 8 on both sides

-5x-8+8=8+8

-5x=16

Divide -5 on both sides

-5x/-5=16/-5

x=-3.2

Therefore, it has one solution

Hope this helps!! :)

Please let me know if you have any questions

8 0
2 years ago
What is 3 3/8 + 32 1/2
EleoNora [17]

3+32= 35

3/8 + 4/8(1/2) = 7/8

Answer is 35 7/8

5 0
3 years ago
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