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2 years ago

What is the difference between the number of solutions for a two-step equation and for a two-step inequality

Mathematics

1 answer:

Sophie [7]2 years ago

7 0

Answer:

A two-step equation is something like:

A*X + B = C

In this case, like in a linear equation, we have only one solution that can be found as:

A*X = C - B

X = (C - B)/A

In the case of a two-step inequality, we have something like:

A*X + B > C

Solving this we get;

A*X > C - B

X > (C - B)/A

In this case, any value of X that is larger than (C - B)/A is a solution, so in this case, we have infinite solutions.

That is the difference between the number of solutions for each case, in a two-step equation we have only one, while in the case of the inequality we have infinite.

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Cellular phone service that charges per-minute will charge $5 for 50 minutes. How much would 1599 minutes cost?

Vlad1618 [11]

Answer:

$159.9

Step-by-step explanation:

5/50=.10 cents

.10•1599=159.9

Answer $159.90

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2 years ago

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

svetlana [45]

Answer:

The equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

Given

The equation of ellipsoid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation of tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ ( Given)

The equation of hyperboloid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The equation of tangent plane at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The equation of tangent plane to the hyperboloid

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The equation of tangent plane

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

3 years ago

Kevin worked 62 hours last week if Kevin makes $18 per hour for regular pay what was his gross pay for the week including overti

Travka [436]

1314 is the answer, hope it helped

5 0

3 years ago

Solve the problem.

liq [111]

This question is asking for the circumference of the basket, in which we can use the formula $\pi d$ , where, according to this question, $\pi$ is 3.14 and $d$ is 11 inches.

When we multiply them together, we get 34.54 inches as our total answer.

6 0

3 years ago

If $1,000 is loaned for 5 months at 6 % annual rate, how much interest is earned?

In-s [12.5K]

Answer:

Interest earned is $25.2

Step-by-step explanation:

The formula to find simple interest is:

I = P₀rt

Where

I = interest rate

P₀ = Principal amount

r = interest rate

t= time

5 months = 5/12 years = 0.42 years

I = 1000* 6/100*0.42

I = 1000*0.06*0.42

I = 60*0.42

I = 25.2

Interest earned is $25.2

5 0

2 years ago