Ask question

Ask question

All categories

4 years ago

5

Hooke's Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the

distance is 15 cm when the weight is 2 kg, what is the distance when the weight is 7 kg?

1 answer:

algol [13]4 years ago

8 0

The distance is 52.5 cm when weight is 7kg

Step-by-step explanation:

Distance is 15 cm when weight is 2 kg

We need to find the distance d when weight is 7 kg

Since distance and weight varies directly so,

$\frac{15}{2}=\frac{d}{7}$

Solving the above expression:

$\frac{15}{2}=\frac{d}{7}\\Cross\,\,multiply\\15*7=d*2\\105=d*2\\d=\frac{105}{2}\\d=52.5$

So, The distance is 52.5 cm when weight is 7kg

Keywords: Direct relation between two quantities

Learn more about Direct relation between two quantities at:

#learnwithBrainly

You might be interested in

Simplify the expression.<br> -5+i /2i

Andrei [34K]

Answer:

$\frac{1+5i}{2}$

Step-by-step explanation:

We know i×i=i^2 which has value of -1.

We will multiply numerator and denominator by i so the denominator will no longer contain imaginary part(s).

Also multiplying by i/i does not change the value of the fraction because i/i=1.

Numerator × i gives (-5+i)i=-5i+i^2=-5i-1

=-1-5i.

Denominator × i gives (2i)i=2i^2=-2.

So the simplified version of this fraction given is:

$\frac{-1-5i}{-2}=\frac{1+5i}{2}$

The last simplification come from me multiplying fraction by -1/-1.

6 0

4 years ago

What is the volume of the given prism? round the answer to the nearest tenth of a centimeter. 9.4 cm 5.4 cm 11.7 cm?

Setler79 [48]

The volume of a cuboid is the product of its dimensions.
(9.4 cm)·(5.4 cm)·(11.7 cm) = 593.892 cm³ ≈ 593.9 cm³

6 0

3 years ago

Read 2 more answers

P(k)=a^k=2 3 4 find value of a that makes this is a valid probability distribution

Vesna [10]

Sounds like you're asked to find $a$ such that

$\displaystyle\sum_{k=2}^4\mathbb P(k)=\mathbb P(2)+\mathbb P(3)+\mathbb P(4)=1$

In other words, find $a$ that satisfies

$a^2+a^3+a^4=1$

We can factorize this as

$a^4+a^3+a^2-1=a^3(a+1)+(a-1)(a+1)=(a+1)(a^3+a-1)=0$

In order that $\mathbb P(k)$ describes a probability distribution, require that $\mathbb P(k)\ge0$ for all $k$ , which means we can ignore the possibility of $a=-1$ .

Let $a=y+\dfrac xy$ .

$a^3+a-1=\left(y+\dfrac xy\right)^3+\left(y+\dfrac xy\right)-1=0$
$\left(y^3+3xy+\dfrac{3x^2}y+\dfrac{x^3}{y^3}\right)+\left(y+\dfrac xy\right)-1=0$

Multiply both sides by $y^3$ .

$y^6+3xy^4+3x^2y^2+x^3+y^4+xy^2-y^3=0$

We want to find $x\neq0$ that removes the quartic and quadratic terms from the equation, i.e.

$\begin{cases}3x+1=0\\3x^2+x=0\end{cases}\implies x=-\dfrac13$

so the cubic above transforms to

$y^6-y^3-\dfrac1{27}=0$

Substitute $y^3=z$ and we get

$z^2-z-\dfrac1{27}=0\implies z=\dfrac{9+\sqrt{93}}{18}$
$\implies y=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}$
$\implies a=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}-\dfrac13\sqrt[3]{\dfrac{18}{9+\sqrt{93}}}$

6 0

4 years ago

Which fractions are equivalent to 3/4? check all tha apply.

Alik [6]

Answer:

6/8, 9/12, and 15/20

Step-by-step explanation:

just do 3 divided by 4 (3/4) and it equals 0.75 then do each and everyone like 6 divided by 8 (6/8) so it equals 0.75

7 0

3 years ago

What polynomial has roots of −4, 1, and 6?

dlinn [17]

(X + 4)(x - 1)(x -6) = (x^2 - x + 4x -4)(x - 6)
(x^2 + 3x -4)(x - 6) = x^3 -6x^2 + 3x^2 - 18x - 4x + 24 = x^3 - 3x^2 - 22x + 24
It is the first one

8 0

4 years ago

Read 2 more answers