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3 years ago

Evaluate the expression: v ⋅ w

Mathematics

2 answers:

Ierofanga [76]3 years ago

8 0

Answer:

Value of v.w equals:

-12

Step-by-step explanation:

If we are given two vectors a and b as:

a=<x1,x2,x3> and b=<y1,y2,y3>

Then, a.b equals:

a.b=x1y1+x2y2+x3y3

Here, v = <2, -8, -8>

and w = <-2, 6, -5>

v.w= 2×(-2)+(-8)×6+(-8)×(-5)

= -4-48+40

= -4-8

= -12

Hence, Value of v.w equals:

-12

dexar [7]3 years ago

4 0

V ⋅ w = <2, -8, -8> ⋅ <-2, 6, -5> = 2(-2) + -8(6) + -8(-5) = -4 + -48 + 40 = -12

v ⋅ w = -12

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The hypotenuse of a right triangle measures 58 cm and one of its legs measures 42 cm. What is the length of the missing leg? 10

Nutka1998 [239]

If the hypotenuse is 58cm, and one of the others legs is 42cm the answer would be 40cm

Explanation:

Here you have to use the formula

${a}^{2} + {b}^{2} = {c}^{2}$
Then you have to pose the formula in terms of one of the legs, so:

${a}^{2} = {c}^{2} - {b}^{2}$
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So when you change the letter for numbers you have that:

$a = \sqrt{ {58}^{2} - {42}^{2} }$

a=40

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DiKsa [7]

Working with fractions, you'll need to find the least common denominator (LCD). In this case, the LCD is 20.

Rewriting the four given numbers to the LCD, you would get:

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Now, you just organize it from least to greatest as:

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In other words, it is:

1/5 < 1/2 < 7/10 < 3/4.

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A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of sel

Delvig [45]

Answer:

a. The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

b. z=-1.6

c. SEM = 2.212

Step-by-step explanation:

The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

Sample mean

$M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35$

Sample variance and standard deviation

$s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\$

$s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255$