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3 years ago

Find b and c so that (5,b,c) is orthogonal to both (1,2,3) and (1,-2,1)

Mathematics

2 answers:

Ipatiy [6.2K]3 years ago

6 0

{5+2b+3c=0
5−2b+c=0
adding both equations u get10+4c=0⇒c=−10/4=−5/2
then5−2b+(−5/2)=0⇒b=(5/2−5)/(−2)=5/2−5/4=5/4

MariettaO [177]3 years ago

4 0

Answer: The answer is 3.75 and -2.5.

Step-by-step explanation: We are given to find the values of b and c if the vector (5, b, c) is orthogonal to (1, 2, 3) and (1, -2, 1).

We know that if two vectors are orthogonal, then their dot product is equal to zero. So, we have

$(5, b, c).(1,2,3)=0\\\\\Rightarrow 5+2b+3c=0\\\\\Rightarrow 2b+3c=-5,~~~~~~~~~~~~~~~~~~~~(A)$

and

$(5,b,c).(1,-2,1)=0\\\\\Rightarrow 5-2b+c=0\\\\\Rightarrow -2b+c=-5.~~~~~~~~~~~~~~~~~~~~~(B)$

Adding equations (A) and (B), we have

$3c+c=-5-5\\\\\Rightarrow 4c=-10\\\\\Rightarrow c=-2.5,$

and from (B), we have

$-2b+2.5=-5\\\\\Rightarrow -2b=-7.5\\\\\Rightarrow b=3.75.$

Thus, the value of b is 3.75 and the value of c is -2.5.

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mel-nik [20]

Answer:

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Step-by-step explanation:

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2 years ago

Roxanne graphed this system of equations to find the solution.

Mice21 [21]

Answer:

Option C is correct.

She is not correct as she use the wrong y intercepts when graphing the equations.

Step-by-step explanation:

Given the system of equations:

$y = \frac{2}{3}x-5$ .....[1]

$y = -2x+3$ . .....[2]

equate these two equations we get;

$\frac{2}{3}x-5=-2x+3$

Add 5 to both sides we get;

$\frac{2}{3}x = -2x+8$

Add 2x to both sides we have;

$\frac{8}{3}x = 8$

Multiply both sides by 3 we get;

8x = 24

Divide both sides by 8 we get;

x = 3

Substitute the value of x in [2] we have;

y = -2(3)+3 = -6+3

Simplify:

y = -3

Therefore, the correct solution for this given system of equation is (3, -3)

You can see the graph of these equations below.

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3 years ago

Read 2 more answers

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

This Zscore is how many standard deviations the value of the measure X is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

$Z = \frac{X - \mu}{\sigma}$

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$