If y varies directly as x and y is 180 when x is n and y is n when x is 5, what is the value of n?

2 answers:

4 0

"something" varies directly to "something else" means
"something" = "some value" * "something else"
y = "some value" * x
y = (a) x
y = (n)x
y=180, x=n⟹180=(a)n
y=n,x=5⟹n=(a)5
Thus 180=(a)n⟹180/n=a
Therefore,
n=(a)5⟹n=(180/n)5

The correct value of 'n' is 30.

11Alexandr11 [23.1K]2 years ago

4 0

Answer:

The value of n for this relation is 30

Step-by-step explanation:

If y varies directly as x, this means that the relation between y and x can be stated as a linear relation of the kind:

y=mx

In the equation, m must be a number, to know exact relation. The two situations that are given can be stated as:

180=m.n

n=m.5

Note that are two unknowns quantities in the equation, m and n. In this particular problem, we must find n. To doing this, we will solve the equation for m:

180=m.n → m =180/n

n=m.5 → m = n/5

As m in both equations must be equal:

m = m

180/n = n/5

180*5 = n*n

900=n^2 → n = 30

You might be interested in

Can anyone help me with this page i can’t find the answers

Dvinal [7]

1) f(x)=2x

when x=3 then f(x) =3×2=6

when x=4 then f(x)=4×2=8

2)At y=35(no. of mangoes),x corresponds to y=60(amount)

so$60, amount he need to spend!

3) f(x)= x+2

for x=1, f(x)=1+2=3

for x=2,f(x)=2+2=4

✌️:)

8 0

2 years ago

Write an expression for the nth term of the geometric sequence. Then find the indicated term. a1 = 3, r = 3 , n = 10

MissTica

Answer:

$A_{n} =3(3)^n^-^1$

$A_{10} = 59,049$

6 0

3 years ago

Six identical squares are cut from the corners and edges of an 80 cm by 50 cm cardboard rectangle. the remaining piece is folded

Anna11 [10]

Check the picture.

let the length of a side of each of the squares removed be x.

The box formed will have dimensions: 80-2x, 50-2x, x(the height)

So the volume can be expressed as a function of x as follows:

f(x)=(80-2x)(50-2x)x= $[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x$

so $f(x)=4 x^{3}-260x^{2}+4000x$

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

$f'(x)=12x^{2}-520 x +4000=0$

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions

x=10 and x=33.333

plug in f(x) these values to see which greater:

$f(10)=(80-20)(50-20)10=60*30*10=18000$ cm cubed

$f(33.333)=(80-66.666)(50-66.666)33.333=$ which is negative because (50-66.666)<0

Answer: 18000 cm cubed