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4 years ago

Given u=(1,-1,3) and v=(-4,5,3) find ordered triple that represents 3u-2v

Mathematics

1 answer:

vodka [1.7K]4 years ago

8 0

Answer:

< 11, - 13, 3 >

Step-by-step explanation:

Multiply the components of u by 3 and the components of v by 2

3u - 2v

= 3 < 1, - 1, 3 > - 2 < - 4, 5, 3 >

= < 3, - 3, 9 > - < - 8, 10, 6 >

Subtract corresponding components

= < 3 + 8, - 3 - 10, 9 - 6 >

= < 11, - 13, 3 >

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Find the derivative of f(x) = -2x2 + 11x at x = 9.

zavuch27 [327]

$\bf f(x)=-2x^2+11x\qquad\qquad \lim\limits_{h\to 0}\ \cfrac{f(x+h)-f(x)}{h}\\\\
-----------------------------\\\\
\cfrac{[-2(\underline{x+h})^2+11(\underline{x+h})]\quad -\quad [-2x^2+11x]}{h}
\\\\\\
\cfrac{[-2(x^2+2xh+h^2)+11x+11h]\quad -\quad [-2x^2+11x]}{h}
\\\\\\
\cfrac{\underline{-2x^2}-4xh-2h^2\underline{+11x}+11h\quad \underline{+2x^2}\underline{-11x}}{h}$

$\bf \cfrac{-4xh-2h^2+11h}{h}\implies \cfrac{\underline{h}(-4x-2h+11)}{\underline{h}}
\\\\\\
\lim\limits_{h\to 0}\ -4x-2h+11\implies -4x-2(0)+11
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6 0

4 years ago

a ABC company stock dropped from 25 3/8 to 22 1/4 during a one month period of time so how much stock fall during this period of

OLEGan [10]

First, let's convert the mixed fraction into an improper fraction (trust me, mixed fraction are pretty much the worst things to deal with, especially with higher level math):
$25 \frac{3}{8} = \frac{203}{8}$
$22 \frac{1}{4} = \frac{89}{4}$

Then, to subtract, since you need a common denominator, I would multiply the second fraction by 2 to get:
$2 (\frac{89}{4} ) = \frac{178}{8}$

Now that we have a common denominator, we are ready to subtract:
$\frac{203}{8} - \frac{178}{8} = \frac{25}{8}$

Since that's the most simplified form, and you have been asked the question in a mixed fraction form, let's convert that to a mixed fraction. The remainder of the numerator divided by the denominator is 1, and the quotient is 3. The denominator stays the same. So, this is what results:
$3 \frac{1}{8}$

And that's your answer: $3 \frac{1}{8}$

Hope this all makes sense. If anything doesn't, feel free to tell me!

7 0

4 years ago

I need help thank you

IRISSAK [1]

Answer:

1) k = 3

2) 3, 4, 5

3) k + (k + 2) + (k + 4) = 4k

4) 6, 8, 10

Step-by-step explanation:

Jared used the equation;

k + (k + 1) + (k + 2) = 4k

Let's find k.

3k + 3 = 4k

4k - 3k = 3

k = 3

Thus,the integers will be;

3, (3 + 1) and (3 + 2)

This is; 3, 4, 5

He is looking for consecutive even integers but yet got 3 and 5 which are odd numbers. However, he should have used the format;

k, (k + 2), (k + 4) as the 3 consecutive even integers.

Thus, rewriting the main equation gives;

k + k + 2 + k + 4 = 4k

3k + 6 = 4k

4k - 3k = 6

k = 6

Thus,the integers are;

6, (6 + 2), (6 + 4)

This is; 6, 8, 10

6 0

3 years ago

Q8 Q2.) What are the lot's dimensions?

Triss [41]

Equation for perimeter is 2L +2W

perimeter of the lot is 390 ft

so we have 390 = 2L +2w

divide all terms by 2:

195 = L + W

rewrite this as L = 195-W ( eq.1)

cost of fence for the length = 36 per foot so we have 36L
cost of fence for width = 6 per foot so we have 6W

the fence was 1 length and 2 sides
so we have 36l + 6w +6w = total cost

total cost is 4980

so we have 4980 = 36L + 6w +6w

combine like terms:

4980 = 36L +12w

replace L with eq1 from above:

4980 = 36(195-w) +12w

distribute:

4980 = 7020 -36w +12w

combine like terms:

4980 = 7020-24w

subtract 7020 from both sides:

-2040 = -24w
divide both sides by -24:

-2040 / -24 = 85
width = 85 feet

using eq1 L = 195 - 85

Length = 110 feet

lond = 110 feet
short = 85 feet

7 0

3 years ago

Express the sum of 3x³ - 7x² +2 and -x³ +9x² - 5<br> as a trinomial

saw5 [17]

2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.

Given: To express the sum 3x³ - 7x² +2 and -x³ +9x² - 5 of as a trinomial.

What are algebraic equations?

Algebraic equations are a sequence or combination of characters containing variables, alphabets, numbers, symbols, etc. which are equated to some value.

What are polynomials?

Polynomials are algebraic expressions that consist of variables, coefficients, and operators. A polynomial is usually depicted as the sum of m terms for some unknown variable x, raised to the power of n with some constants.

For example: Let us consider p(x) to be a polynomial of degree n. The p(x) can be represented as

p(x) = Cₙ xⁿ + Cₙ₋₁xⁿ⁻¹ . . . . . . . + m terms . . . . . + K (where K is some constant and C's are coefficients of x)

What are trinomials?

Trinomials are algebraic expressions that consist of three non-zero terms or monomials.

For example: f(x) = x + y + z is a linear trinomial of 3 variables x, y, and z.

f(x) = x² + 4x + 1 is a quadratic trinomial of 1 variable x and so on.

Let's solve the problem:

Consider f(x) = 3x³ - 7x² +2 and g(x) = -x³ +9x² - 5

We have to express it as a sum of trinomials.

We can see both f(x) and g(x) are Cubic trinomials of one variable x and the lower degrees of x are the same.

So f(x) + g(x) will also given a cubic trinomial of one variable x

f(x) + g(x) = (3x³ - 7x² +2) + (-x³ +9x² - 5)

Grouping similar terms

f(x) + g(x) = (3x³ - x³) + (-7x² + 9x²) + (2 - 5)

f(x) + g(x) = 2x³ + 2x² - 3

Therefore, the required trinomial is 2x³ + 2x² - 3.

Hence 2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.

Know more about "trinomials" here: brainly.com/question/16347049

#SPJ9

6 0

2 years ago