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Lyrx [107]
3 years ago
6

Active

Mathematics
1 answer:
Ber [7]3 years ago
7 0

Answer:

The expressions for the payment made to Mary are,

(Monday) 90 = 15m + b

(Tuesday) 62 = 8m + b

where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.

The equation that represents Mary's earning is

y = 4x + 30

For 20 students,

y = 4(20) + 30 = 110

For Lisa's earnings,

y = 8x + 15

Substituting 20,

y =8(20) + 15 = 175

Thus, Lisa would earn more than Mary by $65.

(Btw this is not my work, I got it from someone else on brainly and wanted to help lol)

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The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum? ​
VLD [36.1K]

Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that

<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>

<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>

where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.

Then the sum is

<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>

and its magnitude is

||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)

… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))

… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))

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… = √(20 + 16 cos(90°))

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5 0
3 years ago
Read 2 more answers
If f(x)=5x^2 and g(x)=x-2 what is (fog)(-3)
olga2289 [7]

Answer:

(fog)(-3) = 125

Step-by-step explanation:

So, we need to first evaluate g(-3) and then plug the value of g(-3) into f(x) to find (fog)(-3). So, let's do that:

g(-3) = -3-2 = -5

f(g(-3)) = f(-5) = 5(-5)^2 = 5(25) = 125

Thus, (fog)(-3) = 125.

7 0
3 years ago
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