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3 years ago

15

Find the missing lengths. Leave your answers as radicals in simplest form.

1 answer:

Aleksandr-060686 [28]3 years ago

4 0

Answer:

y = 5√2/2

x = 5

Step-by-step explanation:

First find y using the tan method: opposite/adjacent

tan(45) = 5√2/2 ÷ y

y = 5√2/2 ÷ tan(45)

y = 5√2/2

Then find x using the pythagoris theorem: c^2 = a^2 + b^2

x = √ (5√2/2)^2 + (5√2/2)^2

x = 5

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In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm

jeyben [28]

Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

$AB = 17$

$PAMC = 32$

$PBMC = 25$

From the attachment, we have:

$y + z = AB$

Since, M is the Midpoint

$y = z = \½AB$

Substitute 17 for AB

$y = z = \½ * 17$

$y = z = 8.5$

Also, from the attachment

$v + x + z = PAMC$

$v + x + y = 32$

Substitute 8.5 for y

$v + x + 8.5 = 32$

$v + x = 32 - 8.5$

$v + x = 23.5$ --------- (1)

Also, from the attachment

$v + w + z = 25$

Substitute 8.5 for z

$v + w + 8.5 = 25$

$v + w = 25 - 8.5$

$v + w = 17.5$ ----------- (2)

Subtract (2) from (1)

$v - v + x - w = 23.5 - 17.5$

$x - w = 6$

Make x the subject

$x = 6 + w$

Apply Pythagoras Theorem:

We have that:

$AB^2 = AC^2 + BC^2$

The above can be replaced with

$17^2 = x^2 + w^2$ (see attachment)

$289 = x^2 + w^2$

Substitute 6 + w for x

$289 = (6 + w)^2 + w^2$

$289 = 36 + 12w + w^2 + w^2$

$289 - 36 = 12w + 2w^2$

$253 = 12w + 2w^2$

Reorder

$2w^2 + 12w - 253 = 0$

Solve using quadratic equation:

$w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 2$

$b = 12$

$c = -253$

$w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}$

$w = \frac{-12 \± \sqrt{144 + 2024}}{4}$

$w = \frac{-12 \± \sqrt{2168}}{4}$

$w = \frac{-12 \± 46.56}{4}$

Split:

$w = \frac{-12 + 46.56}{4}$ or $w = \frac{-12 - 46.56}{4}$

$w = \frac{34.56}{4}$ or $w = \frac{-58.56}{4}$

$w = 8.64$ or $w = -14.64$

But length can't be negative

So:

$w = 8.64$

Recall that: $x = 6 + w$

$x = 6 + 8.64$

$x = 14.64$

<em>Hence, the length of the legs is 8.64cm and 14.64cm respectively</em>

5 0

3 years ago

The value of a motorbike depreciates by 32% per year. Work out the current value of a motorbike bought 5 years ago for £3600

DaniilM [7]

$\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &3600\\
r=rate\to 32\%\to \frac{32}{100}\to &0.32\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
A=3600(1-0.32)^5\implies A=3600(0.68)^5\implies A\approx 523.41601$

3 0

4 years ago

A beach ball has a radius of 9 inches. find the volume of the beachball, in cubic inches and round the answer to the nearest who

lesya692 [45]

V=4/3pi(r^3)
V=4/3pi(9^3)
V=3,054 inches^3

Think this is right

7 0

3 years ago

Read 2 more answers

At the beginning of a baking session, there were 2.26 kilograms of flour in a bag. By the end of the baking session, there were

Arisa [49]

Answer: 56.64%

Step-by-step explanation:

Given: Previous amount of flour = 2.26 kilograms

By the end of the baking session, amount of flour = 0.98 kilograms

Decrease in amount = 2.26-0.98 = 1.28 kilograms

Percent decrese = $\dfrac{\text{decrease in amount }}{\text{previous amount}}\times100$

$=\dfrac{1.28}{2.26}\times100\approx56.64\%$

Hence, the percent decrease in the amount of flour = 56.64%

6 0

3 years ago

Calculate the velocity of a baseball that travels 100 m in 5 sec.

Maslowich

Divide the distance by the time so 100/5=20 m/s.

8 0

3 years ago