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2 years ago

Why do systems of nonlinear equations sometimes have more than one solution

Mathematics

1 answer:

Nitella [24]2 years ago

3 0

Answer:

System has equal number of unknowns and equations.

Manipulation easily yielded expressions for 4 of the 7 unknowns.

However it seems that the remaining 3 unknowns x,y,z are not fixed by the equations. Different combinations (x0,y0,z0) seem possible without violating the system equations.

Is this possible, or did I most probably make a mistake in counting degrees of freedom?

Step-by-step explanation:

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A man invests a total of $9,493in two savings accounts. One account yields 9% simple interest and the other 10% simple interest.

Tju [1.3M]

$ 1850 was invested in 9% account

Solution:

Given that

Total amount invested by man in two saving accounts = $9493

Simple interest on one account =9%

Simple interest on second account = 10%

Total interest earned = $930.80

Need to determine amount invested in 9 % account.

Let assume amount invested in account where Simple Interest is 9% = x

And assume amount invested in account where Simple Interest is 10% = y

As total amount invested in two accounts is $9493

=> x + y = 9493

=> y = 9493 - x ------(1)

$\text { Simple Interest }=\frac{\text { Amount Invested } \times \text {rate of interest } \times \text {time}}{100}$

$\begin{array}{l}{\text { Simple interest when rate of interest is } 9 \%=\frac{x \times 9 \times 1}{100}=\frac{9 x}{100}} \\\\ {\text { Simple interest when rate of interest is } 10 \%=\frac{y \times 10 \times 1}{100}=\frac{10 y}{100}}\end{array}$

As total interest earned = $930.80

$\begin{array}{l}{\Rightarrow \frac{9 x}{100}+\frac{10 y}{100}=930.80} \\\\ {\Rightarrow 9 x+10 y=930.80 \times 100} \\\\ {\Rightarrow 9 x+10 y=93080}\end{array}$

On substituting value of y from equation(1) in above equation , we get

9x + 10 (9493 – x) = 93080

=> 9x + 94930 – 10x = 93080

=> -x = 93080 – 94930

=> -x = -1850

=> x = 1850

Amount invested in account where Simple Interest is 9% = x = $1850

Hence $1850 was invested in 9% account.

5 0

3 years ago

If 3x plus 2 equals 90 then what is the value of x

Firdavs [7]

Hello!

$3x+2=90$

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to subtract by 2 from both sides of the equation.

$3x+2-2=90-2$

Simplify

$3x=88$

Then you divide by 3 from both sides of the equation.

$\frac{3x}{3}=\frac{88}{3}$

Simplify it should be the correct answer.

$x=\frac{88}{3}$

Answer⇒⇒⇒⇒⇒x=88/3

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

4 0

3 years ago

An investigator wants to estimate caffeine consumption in high school students. how many students would be required to estimate

astraxan [27]

We can solve this problem by referring to the standard probability distribution tables for z.

We are required to find for the number of samples given the proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value of z equivalent to:

z = 1.96

Since the problem states that it should be within the true proportion then p = 0.5

Now we can find for the sample size using the formula:

n = (z^2) p q /E^2

where,

p = 0.5

q = 1 – p = 0.5

E = estimate of 5% = 0.05

Substituting:

n = (1.96^2) 0.5 * 0.5 / 0.05^2

n = 384.16

Around 385students are required.

6 0

3 years ago

Please answer this question, I am timed. Thank you! :)

frutty [35]

The perimeter of the rectangle is 16

4 0

3 years ago

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Calculate the area of a regular octagon if the radius is 10 cm long.

charle [14.2K]

Answer:

Area is A≈282.8 cm

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers