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3 years ago

C= 7/6 (k-17) Solve for k.

Mathematics

1 answer:

Fed [463]3 years ago

7 0

Answer:

The brainliest!

Step-by-step explanation:

c= 7/6k- 17(7/6)

6/7c = k - 17

k = 6/7c+17

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in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

3 years ago

5. Which of 1

Serjik [45]

Answer:

0 3 x 6=(3 X 2)+(3 X 4)

Step-by-step explanation:

Distribution property :

The distribution property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis.The distributive property states that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.

Distribution property A(B+C)= A.B+A.C

Given 3 x 6= 3 x (2+4)

by using distribution property A(B+C)= A.B+A.C

3 x 6= 3 x (2+4) = (3 x 2) +(3 x 4)

conclusion:- 3 x 6 = (3 x 2) +(3 x 4)

8 0

4 years ago

Match the pairs of variables with the type of relationship they show.

Luda [366]

"-the time people spend at work and the number of friends they have"
would be "causation"; because the more/less time someone spends at work is implied to be the *cause* of their number of friends.

"-the length of a person's hair and his or her math skills"
would be "no relationship" seeing as there's nothing that relates these two variables that could have an affect on the outcome of one or the other.

"-a student's test scores in math and physics" would be "correlation" because the two subjects are similar enough that any outcome in one could very well be similarly related to the outcome in the other.

7 0

3 years ago

Use the Euclidean algorithm to calculate gcd(259, 621) and gcd(108, 156).

zvonat [6]

Answer:

The gcd(259, 621) = 1 and gcd(108, 156) = 12

Step-by-step explanation:

The Euclidean algorithm solves the problem:

Given integers a, b, find d = gcd(a,b)

These are the steps of the Euclidean algorithm:

Let a = x, b = y.
Given x, y use the division algorithm to write $x=y\cdot q+r$ where q is quotient and r is the remainder
If r = 0, stop and output y; this is the gcd of a, b.
if r ≠ 0, replace (x, y) by (y,r). Go to step 2.

These are the steps for the division algorithm:

Subtract the divisor from the dividend repeatedly until we get a result that lies between 0 and the divisor
The resulting number is known as the remainder, and the number of times that the divisor is subtracted is called the quotient.

To find the greatest common divisor of 621 and 259 by the Euclidean algorithm you need to: