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3 years ago

Find a ⋅ b. a = <2, 4>, b = <2, 5>

2 answers:

3 0

We have that
<span>a = <2, 4>-------> 2i+4j
b = <2, 5>------> 2i+5j

a.b-------> 2*2+4*5--------> 24

the answer is 24</span>

dolphi86 [110]3 years ago

3 0

Answer: The value of a.b = 24.

Step-by-step explanation:

Since we have given that

$\vec{a}=2\hat{i}+4\hat{j}\\\\and\\\\\vec{b}=(2\hat{i}+5\hat{j})$

We need to find the dot product of a.b:

As we know that

$\hat{i}.\hat{i}=1\\\\and\\\\\hat{j}.\hat{j}=1$

So, it becomes,

$\vec{a}.\vec{b}=(2\hat{i}+4\hat{j}).(2\hat{i}+5\hat{j})\\\\\vec{a}.\vec{b}=2\times 2+4\times 5\\\\\vec{a}.\vec{b}=4+20\\\\\vec{a}.\vec{b}=24$

Hence, the value of a.b = 24.

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What is the definition of "constant of proportionality"? Define or show an expression to prove your answer

Feliz [49]

Answer:

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

(G o o g l e)

Step-by-step explanation:

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7 0

3 years ago

I’ve tried so many things but I can’t find the Answer

Virty [35]

Answer:

$let \: that \: be \: \: x \\ 20\% \: of \: x \: is \: 6 \\ \frac{20}{100} \times x = 6 \\ 20x = 600 \\ x = 30$

3 0

3 years ago

Read 2 more answers

At a baseball game henry bought 5 hot dogs and three bags of chips for $14.82. Scoot bought 7 hotdogs and 6 nags of chip for $22

laiz [17]

2.25

per hot dog

1.19

per bag o' chips

Explanation:

5x +3y = 14.82

7 x+6y = 22.89

− 10x−6y = −29.64

7 x+6y = 22.89

−3x = −6.75

x=2.25

5⋅2.25+3y = 14.82

3y = 14.82 − 11.25

y = 3.57 /3 = 1.19

8 0

3 years ago

Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is the angle?

tatyana61 [14]

Answer:

Angle = Ф = $cos^{-1}$ (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

Step-by-step explanation:

Given vector r(t) = $e^{t}cost i + e^{t}sint j$

As we know that,

velocity vector = v = $\frac{dr}{dt}$

Implies that

velocity vector = $(e^{t} cost - e^{t} sint)i + (e^{t} sint - e^{t}cost )j$

As acceleration is velocity over time so:

acceleration vector = a = $\frac{dv}{dt}$

Implies that

vector a =

$(e^{t}cost - e^{t}sint - e^{t}sint - e^{t}cost )i + ( e^{t}sint + e^{t}cost + e^{t}cost - e^{t}sint )j$

vector a = $(-2e^{t}sint) i + ( 2e^{t}cost)j$

Now scalar product of position vector r and acceleration vector a:

r. a = $. \\$

r.a = $-2e^{2t}sintcost + 2e^{2t}sintcost$

r.a = 0

Now, for angle between position vector r and acceleration vector a is given by:

cosФ = $\frac{r.a}{|r|.|a|}$ = $\frac{0}{|r|.|a|} = 0$

Ф = $cos^{-1}$ (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

4 0

3 years ago

Rite cut riding lawnmower obeys the demand equation p=-1/20x+1060. The cost of producing x lawnmowers is given by the function c

slega [8]

A.) Revenue = price * quantity = px = -1/20x^2 + 1060x
R(x) = -1/20x^2 + 1060x.

b.) Profit = Revenue - Cost = R(x) - C(x) = -1/20x^2 + 1060x - 120x - 5000
P(x) = -1/20x^2 + 940x - 5000

c.) For maximum profit, dP/dx = 0
-1/10x + 940 = 0
1/10x = 940
x = 940 * 10 = 9,400
x = 9,400
Maximum profit = P(9400) = -1/20(9400)^2 + 940(9400) - 5000 = $4,413,000

d.) The price to be charged for maximum profit = -1/20(9400) + 1060 = $590

4 0

3 years ago