<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bx%2B7%7D%20%2B%5Cfrac%7B4%7D%7Bx-8%7D" id="TexFormula1" title="\frac{3}{x+7}

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amm1812

2 years ago

+\frac{4}{x-8}" alt="\frac{3}{x+7} +\frac{4}{x-8}" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

sattari [20]2 years ago

6 0

{7x+4}/{x^2-x-56}

using common denominators

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What is the volume of the prism

Scilla [17]

Hey there :)

We know the volume formula of triangular prism
Volume = base x height of prism
= $\frac{1}{2} (base)(height)(height of prism)$

We are given:
The base = 8 in
The height = 15 in
You do not need the 17 in ( it is there to trick you )
The height of the prism = 10 in

Apply the formula,
V = $\frac{1}{2} (8)(15)(10)$
= 600 in³

Your final answer will be the last option

6 0

3 years ago

Pls help trig question!!

s2008m [1.1K]

$4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\$

$\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68$