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Semmy [17]
3 years ago
15

Given that P = (-7, 16) and Q = (-8, 7), find the component form and magnitude of vector QP .

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
7 0

Answer:

a)The component form is

\vec {QP}=\binom{ - 1}{ - 8}

b)The magnitude is √65

c) <2,14>

Step-by-step explanation:

Recall that:

\vec {QP}=\vec {OP}-\vec{OQ}

We substitute the position vectors to get:

\vec {QP}=\binom{ - 8}{7} -  \binom { - 7}{15}

We subtract the corresponding components to obtain:

\vec {QP}=\binom{ - 8 -  - 7}{7 - 15}

This gives:

\vec {QP}=\binom{ - 8  + 7}{7 - 15}

This simplifies to:

\vec {QP}=\binom{ - 1}{ - 8}

The magnitude of a vector in the component form:

\binom{x}{y}

is

\sqrt{ {x}^{2}  +  {y}^{2} }

This means:

|\vec {QP}|= \sqrt{ {( - 1)}^{2}  +  {( - 8)}^{2} }

This simplifies to:

|\vec {QP}| = \sqrt{ 1 +  64 }

|\vec {QP}| = \sqrt{ 65 }

c) We have the vectors u = <4, 8>, v = <-2, 6>.

We want to find:

u+v

This implies that:

u+v=<4,8>+<-2,6>

We add the corresponding components to get;

u+v=<4+-2,8+6>

This simplifies to:

u+v=<2,14>

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Answer:

15 is the total number of animals for which (p ∨ q) ∧ r true.

Step-by-step explanation:

From the diagram it is clear that

p contains {2, 5, 8, 9}

q contains {2, 4, 7, 5}

r contains {2, 4, 6, 9}

p ∨ q is the union of p and q which include all the animals which are in p, in q, or in both p and q.

Note: p ∨ q can not have duplicate animals

So,

p ∨ q = {2, 4, 5, 7, 8, 9}

(p ∨ q) ∧ r contains the animals which need to be common in both (p ∨ q) and r.

As

p ∨ q = {2, 4, 5, 7, 8, 9}

r = {2, 4, 6, 9}

So,

(p ∨ q) ∧ r = {2, 4, 9}

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2 + 4 + 9 = 15

Therefore, 15 is the total number of animals for which (p ∨ q) ∧ r true.

Keywords: union, and operation, or operation

Learn more about union, and operation, or operation from brainly.com/question/13637539

#learnwithBrainly

8 0
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Help me do this plz
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

The answer is 20812

The numeral system we use is a base ten numeral system. Base ten numeral numbers are: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The number has:

2 "tens thousands" = 2 * 10000 = 20000

0 "thousands" = 0

8 "hundreds " = 8 * 100 = 800

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