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3 years ago

Consider the figure shown below. Find the value of BL

Mathematics

1 answer:

Gnesinka [82]3 years ago

7 0

Answer:

BL = 2

Step-by-step explanation:

Given:

AL = 3

AC = 10

BC = 9

AL = AM = 3 (tangents drawn form am external point)

CM = AC - AM

CM = 10 - 3

CM = 7

CM = CN = 7 (tangents drawn form am external point)

BN = BC - CN

BN = 9 - 7

BN = 2

BN = BL = 2 (tangents drawn form am external point).

BL = 2

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HELP !!!! can someone help me please how can i use the vertex formula to find this equation for this graph ?

DedPeter [7]

Based on that table of values, we know the highest point(vertex) is at 0.9, 5.9

we can also use just one another point... say 1.4, 4.6

$\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
y=a(x-{{ h}})^2+{{ k}}
\end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\$

$\bf \begin{cases}
h=0.9\\
k=5.9
\end{cases}\implies y=a(x-0.9)^2+5.9
\\\\\\
\begin{cases}
\textit{another point}\\
x=1.4\\
y=4.6
\end{cases}\implies 4.6=a(1.4-0.9)^2+5.9
\\\\\\
4.6=a(0.5)^2+5.9\implies 4.6-5.9=a(0.5)^2\implies -1.3=a(0.5)^2
\\\\\\
\cfrac{-1.3}{0.5^2}=a\implies -5.2=a
\\\\\\
thus\qquad \qquad \boxed{y=-5.2(x-0.9)^2+5.9}$

5 0

3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 7x6, y

IgorC [24]

Answer:

The volume is $\frac{490\pi}{39}$ cubic units.

Step-by-step explanation:

The given curve is

$y=7x^6$

The given line is

$y=7x$

Equate both the functions to find the intersection point of both line and curve.

$7x^6=7x$

$7x^6-7x=0$

$7x(x^5-1)=0$

$7x=0\rightarrow x=0$

$x^5-1=0\rightarrow x=1$

According to washer method:

$V=\pi \int_{a}^{b}[f(x)^2-g(x)^2]dx$

Using washer method, where a=0 and b=1, we get

$V=\pi \int_{0}^{1}[(7x)^2-(7x^6)^2]dx$

$V=\pi \int_{0}^{1}[49x^2-49x^{12}]dx$

$V=49\pi \int_{0}^{1}[x^2-x^{12}]dx$

$V=49\pi [\frac{x^3}{3}-\frac{x^{13}}{13}]_0^1$

$V=49\pi [\frac{1^3}{3}-\frac{1^{13}}{13}-(0-0)]$

$V=49\pi [\frac{1}{3}-\frac{1}{13}]$

$V=49\pi (\frac{13-3}{39})$

$V=49\pi (\frac{10}{39})$

$V=\frac{490\pi}{39}$

Therefore the volume is $\frac{490\pi}{39}$ cubic units.

5 0

3 years ago

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In-s [12.5K]

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8 0

3 years ago

Solve for y.<br> In(2y – 1) =

Mrrafil [7]

Answer:

~ 2y-1

Explanation:

~ There’s no like terms for us to collect

~ So we just leave it as it is, we only have to get rid of the bracket and that’s the answer

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4 years ago

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EleoNora [17]

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3 years ago