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3 years ago

Find an ordered pair to represent t in the equation t = u + v if u = (-1, 4) and v = (3, -2)

Mathematics

1 answer:

KonstantinChe [14]3 years ago

3 0

Given:

$u=(-1,4)$

$v=(3,-2)$

The equation is:

$t=u+v$

To find:

The ordered pair to represent t in the given equation.

Solution:

We have,

$t=u+v$

Substituting the given values, we get

$t=(-1,4)+(3,-2)$

$t=((-1)+3,4+(-2))$

$t=(-1+3,4-2)$

$t=(2,2)$

Therefore, the ordered pair to represent t in the given equation is (2,2).

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What Force would be needed to extend a spring with a spring constant k=7 N/m that extends<br>0.3m?

vladimir2022 [97]

Answer:

Force = - 2.1 Newton

Step-by-step explanation:

According to question ,

The value of Spring constant , K = 7 N/m Newton per meter

And the spring is extended up to 0.3 meter

The Force experience on the spring is calculated from the Hook's Law

<u>The principal state that , the force applied on spring to extend or compress the spring to some distance is proportion to that distance. </u>

Let the force be F

So, F = - K X

where K is spring constant and X is its displacement

Negative sign shows displacement of spring once it is stretched

And K is spring constant

So ,Force = ( - ) 7 × 0.3

I.e Force = - 2.1 Newton Answer

4 0

3 years ago

How many integers between 10000 and 99999, inclusive, are divisible by 3 or<br> 5 or 7?

Yuki888 [10]

Answer: Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.

Step-by-step explanation:

Since we have given that

Integers between 10000 and 99999 = 99999-10000+1=90000

n( divisible by 3) = $\dfrac{90000}{3}=30000$

n( divisible by 5) = $\dfrac{90000}{5}=18000$

n( divisible by 7) = $\dfrac{90000}{7}=12857.14$

n( divisible by 3 and 5) = n(3∩5)= $\dfrac{90000}{15}=6000$

n( divisible by 5 and 7) = n(5∩7) = $\dfrac{90000}{35}=2571.42$

n( divisible by 3 and 7) = n(3∩7) = $\dfrac{90000}{21}=4285.71$

n( divisible by 3,5 and 7) = n(3∩5∩7) = $\dfrac{90000}{105}=857.14$

As we know the formula,

n(3∪5∪7)=n(3)+n(5)+n(7)-n(3∩5)-n(5∩7)-n(3∩7)+n(3∩5∩7)

$=30000+18000+12857.14-6000-2571.42-4258.71+857.14\\\\=48884.15$

Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.

5 0

4 years ago

What are the like terms of 10a+4b+3a-15b

TiliK225 [7]

The like terms in 10a+4b+3a-15b consist of a and b. First, we have to combine like terms.
(10a+3a) + (4b-15b)
solve a and b
13a - 11b. Thus, the like terms in your original expression are 13a and -11b :)

3 0

4 years ago

Read 2 more answers

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

solniwko [45]

Complete Question

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267 Suppose you sit on a bench in a mall and observe people's habits as they sneeze

(a) What is the probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing?

Answer:

$P(X=6)=(0.162)$