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3 years ago

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Describe a vectors v = [x y] that are orthogonal to u = [a b]. If u is not the zero vector, then v is a multiple of [a b]. If u

is not the zero vector, then v is a multiple of [a -b]. If u is not the zero vector, then v is a multiple of [a -b]. If u is not the zero vector, then v is a multiple of [a -b]. If u is not the zero vector, then v is a multiple of [a + b a - b].

1 answer:

hoa [83]3 years ago

6 0

Answer:

Step-by-step explanation:

Sbdbshee

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In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year l

faust18 [17]

Complete Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A -1.645

B -2.066

C -2.000

D-1.960

Answer:

The correct option is C

Step-by-step explanation:

From the question we are told that

The population mean is $p = 0.50$

The sample size is $n = 64$

The number that met the standard is $k = 24$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{24}{64}$

$\r p =0.375$

Generally the standard error is mathematically evaluated as

$SE = \sqrt{ \frac{p(1- p )}{n} }$

=> $SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }$

=> $SE = 0.06525$

The test statistics is evaluated as

$t = \frac{ \r p - p }{SE}$

$t = \frac{ 0.375 - 0.5 }{0.0625}$

$t = -2$

8 0

3 years ago

When you do this please show the work

mart [117]

Answer:

2) $\displaystyle -9a^3b^5$

1) $\displaystyle \frac{x^8}{3}$

Step-by-step explanation:

2) $\displaystyle \frac{(27a^3b^3)(-2ab^4)}{6ab^2} \Rightarrow \frac{(3ab)^3(-2ab^4)}{6ab^2} \\ \\ \boxed{-9a^3b^5} \rightarrow \frac{-54a^4b^7}{6ab^2}$

1) $\displaystyle \frac{16x^{10}y^2}{48x^2y^2} \Rightarrow \frac{(-4x^5y)^2}{48x^2y^2} \\ \\ \boxed{\frac{x^8}{3}}$

The Quotient-to-Power Rule states that whenever you are dividng like-terms, you <em>keep</em> the coefficients and deduct the exponents.

I am joyous to assist you at any time.

7 0

2 years ago

I) Find the first 4 terms in the expansion of

Katyanochek1 [597]

Answer:

(i) $64+192 x^2+240 x^4+160x^6$

(ii) 1072

Step-by-step explanation:

<u>Part (i)</u>

Using Binomial series formula:

$(2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3$

$=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6$

$=64+192 x^2+240 x^4+160x^6$

<u>Part (ii)</u>

<u /> $(1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})$

$=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}$

$(2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)$

$=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...$

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

6 0

2 years ago

Solve the inequality and enter your solution as an inequality in the box below,

Degger [83]

Answer:

x<3

Step-by-step explanation:

7 0

2 years ago

Help please hurry!!!!!!!!!!!!!!!!!!!!!!!!! What is a correct name for the angle shown?

Pavlova-9 [17]

Answer:

Angle RTS

Step-by-step explanation

Say it out loud it goes, RS, ST.

If you put RS and ST together the angle RTS

3 0

3 years ago