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Vikentia [17]
3 years ago
9

If 9p=5q which is the correct ratio of p:q

Mathematics
2 answers:
tatyana61 [14]3 years ago
4 0

Answer: LHS = RHS

Step-by-step explanation:

Heya!!

Here, we need to compare the LHS and RHS

So, here is the solution -

(9p-5q)²+ 180 pq = (9p+5q)

LHS

= (9p-5q)²+ 180 pq

= 81 p² + 25 q² + 90 pq + 180 pq

= (9p - 5q) ²

RHS = (9p - 5q) ²

Hence, proved => LHS = RHS

Hope it helps!

zimovet [89]3 years ago
3 0

Answer:

5 : 9

Step-by-step explanation:

9p = 5q ( divide both sides by q )

9 × \frac{p}{q} = 5 ( divide both sides by 9 )

\frac{p}{q} = \frac{5}{9} , that is p : q = 5 : 9

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Solving Exponential Equations (lacking a common base)<br> 31^d=38
Bond [772]

Answer:

d = log 38/log31

d = 1.06

Step-by-step explanation:

31 ^ d = 38

Take log of both sides since the exponential equation have different base (always)

d log 31 = log 38

d = log 38 / log 31

d = 1.58 / 1.491

d = 1.06.

We can actually check to see if this is correct.

Substituting d = 1.06

31^ 1.06 = 38.092

(You see, that's approximately correct)

Keep learning, maths is fun!

8 0
3 years ago
Hunter bought a package of 36 pencils for $4.50. Solve an equation to determine the cost of each pencil in the package. (round t
zalisa [80]

Answer:

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7 0
3 years ago
Triangle ABC has an Area of 4 3/8 square feet. If the length of AC IS 1 2/3 feet, what is the length of BC?
Kaylis [27]

Answer:

length of BC = 5 1/4 feet

Step-by-step explanation:

Area of a triangle = 1/2×base×height

Area = 4 3/8 square feet

Base = AC= 1 2/3 feet

Height = BC = ?

Area of a triangle = 1/2×base×height

4 3/8 = 1/2 × 1 2/3 × height

35/8 = 1/2 × 5/3 × height

35/8 = 5/6 × height

Height = 35/8 ÷ 5/6

= 35/8 × 6/5

= (35 × 6) / (8 × 5)

= 210 / 40

= 5 1/4 feet

Height = BC = 5 1/4 feet

length of BC = 5 1/4 feet

8 0
3 years ago
In triangle ABC, D is the midpoint of side AC and E is the midpoint of side BC.
cestrela7 [59]

Answer:

14

Step-by-step explanation:

Since all sides are half of greater triangle.Then 7 × 2 = 14 is length of greater hypotenuse.

Suppose two triangles with similar conditions

1^2+1^2=2

Hypotenuse=2^1/2

We assume another triangle which is exactly double of previous triangle I.e

2^2+2^2=8

Hypotenuse=2×2^1/2

Which is exactly twice of previous triangle.

Hence proved hyootenuse is double of smaller triangle I.e 14

8 0
3 years ago
5. Find the general solution to y'''-y''+4y'-4y = 0
CaHeK987 [17]

For any equation,

a_ny^(n)+\dots+a_1y'+a_0y=0

assume solution of a form, e^{yt}

Which leads to,

(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0

Simplify to,

e^{yt}(y^3-y^2+4y-4)=0

Then find solutions,

\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}

For non repeated real root y, we have a form of,

y_1=c_1e^t

Following up,

For two non repeated complex roots y_2\neq y_3 where,

y_2=a+bi

and,

y_3=a-bi

the general solution has a form of,

y=e^{at}(c_2\cos(bt)+c_3\sin(bt))

Or in this case,

y=e^0(c_2\cos(2t)+c_3\sin(2t))

Now we just refine and get,

\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}

Hope this helps.

r3t40

5 0
3 years ago
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