Question

4+168×10³×d1+36×10³×d2=-12 -10+36×10³×d1+72×10³×d2=0

264

likes
1319 views

Answer to a math question 4+168×10³×d1+36×10³×d2=-12 -10+36×10³×d1+72×10³×d2=0

Expert avatar
Madelyn
4.7
83 Answers
To solve the system of equations:

\begin{align*}4+168\times 10^3\times d_1+36\times 10^3\times d_2 & = -12 \quad (1) \-10+36\times 10^3\times d_1+72\times 10^3\times d_2 & = 0 \quad (2)\end{align*}

We can use the method of substitution to eliminate one variable and solve for the other.

Let's solve equation (2) for d_1:

-10 + 36\times 10^3 \times d_1 + 72\times 10^3\times d_2 = 0

Rearranging the equation, we have:

36\times 10^3 \times d_1 = 10 + 72\times 10^3\times d_2

Dividing both sides by 36\times 10^3, we get:

d_1 = \frac{10 + 72\times 10^3\times d_2}{36\times 10^3} \quad (3)

Substituting equation (3) into equation (1), we have:

4 + 168\times 10^3\times \left(\frac{10 + 72\times 10^3\times d_2}{36\times 10^3}\right) + 36\times 10^3\times d_2 = -12

Simplifying the equation, we get:

4 + \frac{168}{36}\times (10 + 72\times 10^3\times d_2) + 36\times 10^3\times d_2 = -12

Simplifying further, we have:

4 + \frac{4}{3}\times (10 + 72\times 10^3\times d_2) + 36\times 10^3\times d_2 = -12

Expanding and simplifying, we get:

4 + \frac{40}{3} + \frac{288}{3}\times 10^3\times d_2 + 36\times 10^3\times d_2 = -12

Combining like terms, we have:

\frac{128}{3}\times 10^3\times d_2 + 36\times 10^3\times d_2 = -12 - \frac{40}{3}

Simplifying further, we get:

\frac{164}{3}\times 10^3\times d_2 = -\frac{76}{3}

Dividing both sides by \frac{164}{3}\times 10^3, we have:

d_2 = -\frac{76}{3} \div \frac{164}{3}\times 10^3

Simplifying the division, we get:

d_2 = -\frac{76}{164}\times 10^3

Simplifying the fraction, we have:

d_2 = -\frac{19}{41}\times 10^3

Finally, we can substitute the value of d_2 into equation (3) to solve for d_1:

d_1 = \frac{10 + 72\times 10^3\times \left(-\frac{19}{41}\times 10^3\right)}{36\times 10^3}

Simplifying the equation, we get:

d_1 = \frac{10 - \frac{72\times 19}{41}}{36}

Simplifying the fraction, we have:

d_1 = \frac{10 - \frac{1368}{41}}{36}

Calculating the numerator and denominator separately, we have:

d_1 = \frac{410 - 1368}{36} = \frac{-958}{36} = -\frac{479}{18} \quad (4)

Therefore, the solution to the system of equations is d_1 = -\frac{479}{18} and d_2 = -\frac{19}{41}\times 10^3.

\textbf{Answer:} d_1 = -\frac{479}{18}, d_2 = -\frac{19}{41}\times 10^3

Frequently asked questions (FAQs)
Question: How many types of triangles can be formed given the lengths of sides a = 8, b = 15, and c = 17?
+
What is the radian measure of an angle with a central angle of 270 degrees?
+
What is the value of 2 raised to the power of 5, plus the cube root of 125?
+
New questions in Mathematics
Add. 7/w²+18w+81 + 1/w²-81
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?
Write 32/25 as a percent
A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had
Use the elimination to find the solution to each linear system. X+y=43 2x-y=20
what is the annual rate on ​$525 at 0.046​% per day for 3 months?
"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.
(2b) to the 1/4th power. Write the expression in radical form.
v Is the following statement a biconditional? If Shannon is watching a Tigers game, then it is on television.
Solve : 15/16 divide 12/8 =x/y
show step by step simplification: (¬𝑑∨((¬b∧c)∨(b∧¬c)))∧((𝑎 ∧ 𝑏) ∨ (¬𝑎 ∧ ¬𝑏))∧(¬𝑐∨((¬𝑑∧𝑎)∨(𝑑∧¬𝑎)))
How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
9 x² + 2x + 1 = 0
The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom
The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the x−axis is
The following incoming payments show up at a tax inspection: 25 000€ on 19.01.2008, 140 000€ on 27.03.2008 and 19 000€ on a date that which is illegible, and 60 000€ on 15.06.2008. On which date did the payment of the 19 000€ appear, if on 30.06.2008 the money on the account (incl. interest at 4%) is 246 088.89€? Use simple interest and 30E/360 DCC. Solution: 45 days, 15.05.08
The slope of the tangent line to the curve f(x)=4tan x at the point (π/4,4)