Find the equation of the line through (2, 3, 0) perpendicular to the vectors a = (1, 2, 3) and b = (3, 4, 5).

Answers

Answer 1

Answer: The cross product a×b is a vector perpendicular to both. That cross product is
(1, 2, 3)×(3, 4, 5) = (-2, 4, -2)

This can have common factors removed and be sign-adjusted to (1, -2, 1), so the equation of the line can be written in parametric form as ...
(x, y, z) = (2, 3, 0) + t·(1, -2, 1)

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When working with vectors and matrices, a suitable calculator can be very helpful. There are several phone and tablet apps and web sites that can do these calculations for you.

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Find the solution set of the inequality: -3x + 8 < 15−3x+8<15minus, 3, x, plus, 8, is less than, 15 x

Answers

Answer:

The solution to the inequality is;

x > -7/3

Step-by-step explanation:

We want to find the solution to the inequality;

-3x + 8 < 15

We can have this as;

-3x < 15-8

-3x < 7

x > -7/3

Answer:

x>-7/3

Step-by-step explanation:

Melissa bought a cake that cost $75. The sales-tax rate is 10 percent. What is the total amount she paid for the cake?

Answers

Answer:

the total amount she paid for the cake, $82.5

Step-by-step explanation:

As per the statement:

Melissa bought a cake that cost $75.

⇒Cost of cake = $75

It is also given that:

The sales-tax rate is 10 percent.

then

Sale tax she gave on cake = $(10)/(100) * 75 = \$7.5$

We have to find the total amount she paid for the cake.

$\text{Total amount she paid for the cake} = \text{Cost of the cake}+\text{Sale tax}$

Substitute the given values we have;

$\text{Total amount she paid for the cake} = 75+7.5 = \$ 82.5$

therefore, the total amount she paid for the cake, $82.5

Statements:

1# Melissa bought a cake of cost $75.
2# The tax that has to be paid for the product is 10% of the cost of the product, itself.

=================================

Total amount of money = $$75 +( (10)/(100)*75 )$

= $75 + $7.5
= $82.5

Find the inverse of the one to one function. f(x)=2x+5/7

Answers

$f(x)=(2x+5)/(7)\n\n y=(2x+5)/(7)\n 7y=2x+5\n 2x=7y-5\n x=(7y-5)/(2)\n \boxed{f^(-1)(x)=(7x-5)/(2)}$

$e^(2x) = ln 5$ (solve with explanation)

Answers

$e ^(2x) = ln5$

Solve for the real domain

$e ^(2x) = ln(5)$

if $f(x) =g(x),$ then $ln(f(x))= ln(g(x))$

$ln(e ^(2x) ) = ln(ln(5))$

Solve : $ln(e ^(2x) ) = ln(ln(5))$

use the logarithmic definition :

$ln(e^(f(x)) ) = f(x)$

$ln(e^(2x) ) = 2x$

$2x=ln(ln(5))$

Divide both sides by 2 :

$(2x)/(2) = (ln(ln(5)))/(2)$

$x= (ln(ln(5)))/(2)$

hope this helps!

Pls help me ??

$help$

Answers

Answer:

a=110

b=70

c=110

d=70

e=110

f=70

g=110

Can there be more than one point of intersection between the graphs of two linear equations? Explain

Answers

the only way that 2 lines can intersect more than 1 time is if they are the same line, then they intersect infinitely
if they are differnet lines, then they can only intersect 1 time at max

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