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ohaa [14]
3 years ago
14

Evaluate the dot product of (5,7) and (-8,2)

Mathematics
2 answers:
Viefleur [7K]3 years ago
6 0
You have to multiple and then add to get
(5)(-8)+(7)(2)=-26
seraphim [82]3 years ago
6 0

Answer:

A=Point (5,7) when represented in terms of vector = 5 i + 7 j

B=Point (-8,2) ,when represented in terms of vector = -8 i + 2 j

Dot Product of two vectors = A.B

Keep in mind

1.⇒i.i=1, j.j=1,i.j=j.i=0

2.Dot product of two vectors is Scalar Quantity.

So,→ A. B= (5 i + 7 j) . (-8 i +2 j)

       = 5 × -8 +7 × 2

         = -40 +14

        = -26

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The circumference of a circle is 100.48 inches. What is the circle's diameter? Use 3.14 for ​.
krok68 [10]

Answer:

<u>d = 32 inches</u>

Step-by-step explanation:

C = 2 × 3.14 × r

100.48 = 2 × 3.14 × r

Now divide 100.48 by 2 and 3.14 to get the radius:

r = 16 inches

The radius is half of the diameter, so...

<u>d = 32 inches</u>

7 0
2 years ago
A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 rebate off
Slav-nsk [51]

Answer:

a) P(x) = 550 - x/10

b) $175

c) $100

Step-by-step explanation:

Number of television sold per week = 1000

The selling price for each = $450

a) If $10 rebate offered to the buyer increases the sale by 100 per week, the price will decrease by

1/100*10 = 1/10 per unit

Let X be the number of television sold per week

The increase in number sold per week = x - 1000

P(x) = 450 - 1/10(x-1000)

P(x) = 450 - x/10 + 100

= 550 - x/10

The demand function is

P(x) = 550 - x/10

b) Let R(x) be the revenue

R(x) = xP(x)

= x[550 - x/10]

= 550x - x^2/10

Differentiate R(x) with respect to x

R'(x) = 550 - 2x/10

= 550 - x/5

R'(x) is the marginal revenue

The revenue is maximized when R'(x) = 0

550 - x/5 = 0

550 = x/5

x = 550*5

x = 2750

Recall that P(x) = 550 - x/10

Put x= 2750

P(2750) = 550 - 2750/10

= 550 - 275

= 275

The rebate to maximize the revenue will be 450 - 275 = $175

c) C(x) = 74000 + 150x

P(x) = R(x) - C(x)

P(x) = 550x - x^2/10 - (74000 + 150x)

= 550x - x^2/10 - 74000 - 150x

Collect like terms

P(x) = 550x - 150x - x^2/10 - 74000

= 400x - x^2/10 - 74000

Differentiate P(x) with respect to x

P'(x) = 400 - 2x/10

= 400 - x/5

P'(x) is the marginal profit.

The profit is maximum when P'(x) = 0

400 - x/5 = 0

400 = x/5

x = 400*5

x = 2000

Recall that P(x) = 550 - x/10

P(2000) = 550 - 2000/10

= 550 - 200

= 350

The rebate to maximize the revenue = 450 - 350

= $100

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3 years ago
Help me please answer neede asap
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A slice is made perpendicular to the base of a right rectangular prism as shown.
Gala2k [10]
The cross section is just a rectangle. So to work out the area, multiply the length of the base together by the height.
This is 22 x 12 = 264cm²
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Simplify each each expression. If not possible, write simplified.
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10. 16x-y+3
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