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3 years ago

Find a b if a = 3i + 8j and b = -0.5i -4j.

Mathematics

2 answers:

Gekata [30.6K]3 years ago

3 0

Answer:

-33.5

Step-by-step explanation:

So this is a dot products vector problem, so the i and j represent x and y or horizontal and vertical components. So you multiple 3i and -0.5i and then separately multiply 8j and -4j. You get -1.5 and -32. Now all you have to do is add them and you get -33.5.

Basically in short:

1. Multiply the “i’s”.

2. Multiply the “j’s”.

3. Add the two products together.

HOPE THIS HELPS !! :-)

IceJOKER [234]3 years ago

3 0

Answer:

letter is A on edg

Step-by-step explanation:

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Question 8(Multiple Choice Worth 1 points)

Marianna [84]

Q8: a. 270

Q9: b. 78.5%

Q10: c. 36

Q11: d. 1/5

Q12: a. 0.4

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4 years ago

Write the equation of a line perpendicular to y = -5x + 1 that goes through (10. 4).

alexandr1967 [171]

Answer:

y = 1/5x + 2

Step-by-step explanation:

y = 1/5x + b

4 = 1/5(10) + b

4 = 2 + b

2 = b

4 0

3 years ago

Please help me with these calculus bc questions

zhannawk [14.2K]

4. Compute the derivative.

$y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1$

Find when the gradient is 7.

$4x - 1 = 7 \implies 4x = 8 \implies x = 2$

Evaluate $y$ at this point.

$y = 2\cdot2^2-2-1 = 5$

The point we want is then (2, 5).

5. The curve crosses the $x$ -axis when $y=0$ . We have

$y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4$

Compute the derivative.

$y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}$

At the point we want, the gradient is

$\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}$

6. The curve crosses the $y$ -axis when $x=0$ . Compute the derivative.

$\dfrac{dy}{dx} = 3x^2 - 4x + 5$

When $x=0$ , the gradient is

$\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}$

7. Set $y=5$ and solve for $x$ . The curve and line meet when

$5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92$

Compute the derivative (for the curve) and evaluate it at these $x$ values.

$\dfrac{dy}{dx} = 4x + 7$

$\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}$

$\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}$

8. Compute the derivative.

$y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b$

The gradient is 8 when $x=2$ , so

$2a\cdot2 + b = 8 \implies 4a + b = 8$

and the gradient is -10 when $x=-1$ , so

$2a\cdot(-1) + b = -10 \implies -2a + b = -10$

Solve for $a$ and $b$ . Eliminating $b$ , we have

$(4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}$

so that

$4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}$ .

5 0

2 years ago

(x + y = 17<br> (y = x+7<br> Solve using substitution

Cloud [144]

X+y=17
Y=x+7
X+x+7=17
2x+7=17
-7. -7
2x. =10
—- —
2. 2
X. = 5

Check:
Y=5+7
Y=12

Answer
X=5
Y=12

7 0

4 years ago

What are the solutions of-4(x-4) < -8

Andrew [12]

Answer:

-4x+16 < -8

Step-by-step explanation:

x*-4=-4x

4*-4=-16

-16

4 0

2 years ago