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3 years ago

A=1/2(B+b)h ; solve for b.

Mathematics

1 answer:

Tju [1.3M]3 years ago

5 0

Answer:

$b = \frac{2A -Bh}{h}$

Step-by-step explanation:

The given relation is :

$A = \frac{1}{2} (B + b)h$

We want to solve for b

We multiply both sides by 2 to get

$2A = (B + b)h$

Divide through by h

$\frac{2A}{h} =B + b$

Subtract B from both sides

$\frac{2A}{h} - B = b$

We now simplify the left hand side to get

$\frac{2A -Bh}{h}=b$

$b = \frac{2A -Bh}{h}$

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Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?

QveST [7]

<span>I note that this problem starts out with "Which is a factor of ... " This implies that you were given several answer choices. If that's the case, it's unfortunate that you haven't shared them.

I thought I'd try finding roots of this function using synthetic division. See below:

f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation. Thanks.

Possible zeros of this poly are factors of 35: plus or minus 1, plus or minus 5, plus or minus 7. Use synthetic division; determine whether or not there is a non-zero remainder in each case. If none of these work, form rational divisors from 35 and 6 and try them: 5/6, 7/6, 1/6, etc.

Provided that you have copied down the function
</span>f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35 properly, this approach will eventually turn up 1 or 2 zeros of this poly. Obviously it'd be much easier if you'd check out the possible answers given you with this problem.

By graphing this function, I found that the graph crosses the x-axis at 7/2. There is another root.

Using synth. div. to check whether or not 7/2 is a root:

___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.

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Find an equation of the line satisfying the given conditions Through (6,4); perpendicular to 3X + 5Y =38

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To answer this, we will need to know:

• The slope of the equation we are trying to get
• The point it passes through using the

First, we will need to find the slope of this equation. To find this, we must simplify the equation $3x+5y=38$ into $y=mx+b$ form. Lets do it!

$3x+5y=38$
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The slope of a line perpendicular would have to multiply with the equation we just changed to equal -1. In other words, it would have to equal the negative reciprocal.

The negative reciprocal of the line given is $\frac{5}{3}$ .

Now that we know the slope, we have to find out the rest of the equation using the slope formula, which is:

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Substituting values, we find that:

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By simplifying this equation to slope-intercept form (By cross-multiplying then simplifying), we then get that:

$y= \frac{5}{3}x-6$ , which is our final answer.

Thank you, and I wish you luck.

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