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2 years ago

Explain the attributes that make a rhombus different from a rectangle

Mathematics

1 answer:

Rudik [331]2 years ago

7 0

Answer:

Angles and sides are the main differences! In a rectangle, all angles will be 90 degrees. In a rhombus, opposite angles will always be congruent. And, all sides in a rhombus are congruent, while in a rectangle, opposite sides are congruent

Step-by-step explanation:

here

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Find the sum of the first 325325 positive even whole numbers.

iris [78.8K]

Multiply 325326×(325325/2)=52,918,503,138 How it works:
know that 325325+1 is 325326, then 325324+2 is the same number, therefore you will get this number as many times as half of biggest number since you sum every last biggest number-1 with every last smallest number+1. so just multiply and you will get

6 0

2 years ago

Find T5(x) : Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0 . (You need to enter function.) T5(x)= Find all va

Burka [1]

Answer:

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

The polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

Step-by-step explanation:

According to Taylor's theorem

$\bf f(x)=f(0)+f'(0)x+f''(0)\displaystyle\frac{x^2}{2}+f^{(3)}(0)\displaystyle\frac{x^3}{3!}+f^{(4)}(0)\displaystyle\frac{x^4}{4!}+f^{(5)}(0)\displaystyle\frac{x^5}{5!}+R_6(x)$

with

$\bf R_6(x)=f^{(6)}(c)\displaystyle\frac{x^6}{6!}$

for some c in the interval (-x, x)

In the particular case f

f(x)=cos(x)

we have

$\bf f'(x)=-sin(x)\\f''(x)=-cos(x)\\f^{(3)}(x)=sin(x)\\f^{(4)}(x)=cos(x)\\f^{(5)}(x)=-sin(x)\\f^{(6)}(x)=-cos(x)$

therefore

$\bf f'(x)=-sin(0)=0\\f''(0)=-cos(0)=-1\\f^{(3)}(0)=sin(0)=0\\f^{(4)}(0)=cos(0)=1\\f^{(5)}(0)=-sin(0)=0$

and the polynomial approximation of T5(x) of cos(x) would be

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that

$\bf R_6(x)=-cos(c)\displaystyle\frac{x^6}{6!}$

for some c in (-x,x). So

$\bf |R_6(x)|\leq|\displaystyle\frac{x^6}{6!}|=\displaystyle\frac{|x|^6}{6!}$

and we must find the values of x for which

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652$

Working this inequality out, we find

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652\Rightarrow |x|^6\leq1.90944\Rightarrow\\\\\Rightarrow |x|\leq\sqrt[6]{1.90944}\Rightarrow |x|\leq1.113826815$

Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

8 0

2 years ago

What is the missing value: <img src="https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B1%7D" id="TexFormula1" title="\frac{16}{1

mamaluj [8]

The answer is 40 bc you cross multiply

7 0

2 years ago

Read 2 more answers

What is 4 and square root of 72

Katarina [22]

Answer:

square root of 72 is approximately 8.49

i hope that right!

Step-by-step explanation:

8 0

2 years ago

Which choices are equivalent to the exponential expression below? check all that apply. (2/3)^3

rosijanka [135]

Answer:

B. (2/3) x (2/3) x (2/3)

C. 8/27

D. 2^3 /3^3

Step-by-step explanation:

You need to know the following property

$\LARGE \left(\frac{a}{b} \right)^c = \frac{a^c}{b^c}$

Exponent also means you're multiplying the same number for an 'n' number of times.

For example, 2^3 = 2 * 2 * 2

we multiply it by itself 3 times since 3 is the exponent.

x^y

x is the base, y is the exponent

we read it as x to the power of y

If the exponent is 2, we say it as x squared

If the exponent is 3, we say it as x cubed

4 0

2 years ago