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3241004551 [841]
3 years ago
14

(1 point) Find two unit vectors orthogonal to a=⟨4,5,0⟩a=⟨4,5,0⟩ and b=⟨0,1,−3⟩b=⟨0,1,−3⟩ Enter your answer so that the first no

n-zero coordinate of the first vector is positive. First Vector: ⟨⟨ , , ⟩⟩ Second Vector: ⟨⟨ , , ⟩
Mathematics
1 answer:
Anni [7]3 years ago
5 0

Answer:

 First vector

V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}

Second vector

V=- \dfrac{-15i+12j+4k}{\sqrt{385}}

Step-by-step explanation:

Given that

Vector a ,  a= 4 i + 5 j + 0 k

Vector b , b= 0 i + 1 j  - 3 k

The orthogonal vector V is given as

V = a x b

V is the cross product of the above two vector which is orthogonal to the vectors a and b.

V=\begin{vmatrix}i & j & k\\ 4 & 5 & 0\\  0& 1 &-3 \end{vmatrix}\\V=i(-15-0)-j(-12-0)+k(4-0)\\V=-15i+12j+4k

The unit vectors

V=\pm \dfrac{-15i+12j+4k}{\sqrt{15^2+12^2+4^2}}\\\\V=+\dfrac{-15i+12j+4k}{\sqrt{385}}\\V=-\dfrac{-15i+12j+4k}{\sqrt{385}}

First vector

V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}

Second vector

V=- \dfrac{-15i+12j+4k}{\sqrt{385}}

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A bank sampled its customers to determine the proportion of customers who use their debit card at least once each month. A sampl
Zinaida [17]

Answer:

(0.084,0.396)

Step-by-step explanation:

The 99% confidence interval for the proportion of customers who use debit card monthly can be constructed as

p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }

p=\frac{x}{n}

p=\frac{12}{50}

p=0.24

q=1-p=1-0.24=0.76

\frac{\alpha }{2} =\frac{\0.01 }{2}=0.005

p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }

0.24-z_{0.005} \sqrt{\frac{0.24*0.76}{50} }

0.24-2.58(0.0604)

0.24-0.155832

By rounding to three decimal places we get,

0.084

The 99% confidence interval for the proportion of customers who use debit card monthly is (0.084,0.396).

3 0
3 years ago
Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π
lorasvet [3.4K]

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

g(x) = \cos x

Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

4 0
2 years ago
The science fair judges will be science teachers. Each judge will only have time to view 5 science fair projects. There are 133
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There will need to 27 science teachers
5 0
3 years ago
PLEASE HELP IM OFFERING 15PTS AND BRAINLIEST ANSWER. PLEASE SHOW YOUR WORK
Murljashka [212]
I need to se the blanket to answer
8 0
3 years ago
Help me pls pls i am struggling i will give u brainliest ​
s2008m [1.1K]

<em>Answer:</em>

<em>Hello There. The answer is 268</em>

Explanation

He spend £140 for 60 jumper

He sells 40%of jumper at £8 for each.

40%of 60

= 40/100 × 60

= 24 jumper

=sells at £8

= 24 ×8 =£192

After ,he sell buy 1 get one half price offer.

Ryan have 60% jumper of 60

= 36/2×8 +36/2×4

=144 + 72

= £216

Total earning= £192 + £216

=£408

So, profit = 408 - 140 = £268

Hope It Helps!

<h3>ItsNobody</h3>
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3 years ago
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