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3 years ago

Find the inner product for (7, 2) * (0, -2) and state whether the vectors are perpendicular.

Mathematics

2 answers:

Kryger [21]3 years ago

5 0

Answer:

a) -4, no

Step-by-step explanation:

a•b = (x1 × x2) + (y1 × y2)

= (7 × 0) + (2 × -2)

= 0 - 4

= -4

Hence they are not Perpendicular

Andrews [41]3 years ago

3 0

Answer: A

Step-by-step explanation:

To find the inner product of two vectors (a,b) and (c,d) you would use the equation (a * c) + (b * d)

So for (7,2) and (0,-2) the inner product would be

(7 * 0) + (2 * -2)

= 4

The vectors are only perpendicular when the inner product is equal to 0. Since it is equal to -4 in this case, the vectors are not perpendicular.

A -4; no

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7. Factor the expression.<br> 42 - 64

Dmitriy789 [7]

Answer:

-22 = -2^1×11^1

Step-by-step explanation:

Factor the following integer:

-22

Hint: | Is 22 divisible by 2?

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

-22 = -2×11

Hint: | Now try to factor 11. Is 11 divisible by 2?

11 is not divisible by 2 since 11 is odd and 2 is even:

-22 = -2×11 (11 is not divisible by 2)

Hint: | Is 11 divisible by 3?

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

-22 = -2×11 (11 is not divisible by 2 or 3)

Hint: | Is 11 divisible by 5?

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

-22 = -2×11 (11 is not divisible by 2, 3 or 5)

Hint: | Is 11 divisible by 7?

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |

- | | 7 |

| | 4 | (remainder)

11 is not divisible by 7:

-22 = -2×11 (11 is not divisible by 2, 3, 5 or 7)

Hint: | Is 11 prime?

No primes less than 11 divide into it. Therefore 11 is prime:

-22 = -2×11

Hint: | Express -22 as a product of prime powers.

There is 1 copy of 2 and 1 copy of 11 in the product:

Answer: -22 = -2^1×11^1

3 0

3 years ago

What is the true solution to the equation below? In e^in x + in e^in x^2 = 2 in 8

mariarad [96]

To solve the given equation, w need to review some rules:
$(1) \ ln \ e = 1 \\ 
(2) \ ln \ b^{a} = a*ln \ b \\
(3) \ ln \ a + ln \ b = ln \ (ab) \\
(4) \ ln \ a - ln \ b = ln \ \frac{a}{b} \\$

The given equation is :
$ln \ e^{ln \ x} + ln \ e^{ln \ x^{2}} = 2 \ ln \ 8$
$ln \ x * ln \ e + ln \ x^{2} * ln \ e = 2 \ ln \ 8$ ⇒⇒⇒⇒ rule (2)
$ln \ x + ln \ x^{2} = ln \ 8^{2}$ ⇒⇒⇒⇒ rule (1) and rule (2)

$ln \ ( x* x^{2} ) = ln \ 64$ ⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides

$x^{3} = 64 = 4^{3}$
∴ x = 4

So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4

5 0

3 years ago

Read 2 more answers

For all values of x,

Nana76 [90]

Answer:

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

= 2 (g(x)) + 3

= 2( -x 2 + 1 ) + 3

= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)

Step-by-step explanation: