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Ymorist [56]
3 years ago
14

Find the dot product of two vectors if their lengths are 4 and 1/2 and the angle between them is π/4.

Mathematics
1 answer:
Luba_88 [7]3 years ago
4 0
The dot product is a technique that solves the resultant vector through the use of matrices. Since we have no coordinates, we can't use matrices. However, we can still solve the resultant vector (red line) through cosine law. The solution is as follows:

R² = 4² + (1/2)² - 2(4)(1/2)(cos π/4)
R = √13.42
R = 3.66

The resultant vector has a magnitude of 3.66.

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Which solution finds the value of x in the triangle below? HELP!
Vinvika [58]
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sec 60 degrees = 8/x

Next, in a 30 60 90 triangle, you know that the side lengths are 1, 1/2 and sqrt(3)/2. So the secant of 60 degrees is 1 divided by 1/2 which is 2. 

So the answer is the first question: x = 4
3 0
3 years ago
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Which equations represent the asymptotes of the hyperbola (x-1)^2/36-(y-2)^2/64=1 ?
allochka39001 [22]

Answer:

4x+3y=10 and  4x-3y=-2

Step-by-step explanation:

The asymptote equation of a translate hyperbola with equation \frac{(x-h)^2}{b^2}-\frac{(y-k)^2}{a^2}=1 is y=\pm\frac{b}{a}(x-h)+k

The given hyperbola has equation: \frac{(x-1)^2}{36}-\frac{(y-2)^2}{64}=1

Or \frac{(x-1)^2}{6^2}-\frac{(y-2)^2}{8^2}=1

Comparing to \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

We have  a=6 and b=8, h=1 and k=2.

We substitute this values to get:

y=\pm\frac{6}{8}(x-1)+2

y=\pm\frac{4}{3}(x-1)+2

3y=\pm4(x-1)+6

We split the plus or minus sign to get:

3y=4x-4+6

3y=4x+2

3y-4x=2

Or

3y=-4(x-1)+6

3y=-4x+4+6

3y+4x=10

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4 years ago
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cestrela7 [59]

Answer:

28 hours

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3 0
3 years ago
Anja represents the inequality 4-g/8 < - 15 with the phrase “the quotient of the difference of 4 and a number and 8 is at lea
scoundrel [369]

Answer:

Anja’s phrase should have ended with “less than –15”, not “at least –15”.

Step-by-step explanation:

Given the statement:

Anja represents the inequality \frac{4-g}{8}< -15

with the phrase “the quotient of the difference of 4 and a number and 8 is at least –15.”

Let the number be g.

“the quotient of the difference of 4 and a number and 8" translated to \frac{4-g}{8}

"at least" means \leq

then;

“the quotient of the difference of 4 and a number and 8 is at least –15.” translated to \frac{4-g}{8}\leq -15

Therefore, Anja’s phrase should have ended with “less than –15”, not “at least –15”.

4 0
3 years ago
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What is 12.7, 12 3/5 and 12 3/4 form greatest to least
Brrunno [24]
12.7 , 12 3/4, 12 3/5

Hope this helps!
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4 years ago
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