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2 years ago

Using the diagram below, what is the measure of ZE?

Mathematics

1 answer:

matrenka [14]2 years ago

7 0

The measure of angle E is (b) 50°

<h3>How to determine the angle measure?</h3>

The given parameters are:

ΔCAB is similar to ΔCED
AB and ED are parallel

The similarity of the triangles implies that:

angle C = angle C
angle A = angle E
angle B = angle D

From the figure, we have:

angle A = 50

Substitute angle A = 50 in angle A = angle E

angle E = 50

Hence, the measure of angle E is (b) 50°

Read more about similar triangles at:

brainly.com/question/14285697

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5. Find the general solution to y'''-y''+4y'-4y = 0

CaHeK987 [17]

For any equation,

$a_ny^(n)+\dots+a_1y'+a_0y=0$

assume solution of a form, $e^{yt}$

Which leads to,

$(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0$

Simplify to,

$e^{yt}(y^3-y^2+4y-4)=0$

Then find solutions,

$\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}$

For non repeated real root y, we have a form of,

$y_1=c_1e^t$

Following up,

For two non repeated complex roots $y_2\neq y_3$ where,

$y_2=a+bi$

and,

$y_3=a-bi$

the general solution has a form of,

$y=e^{at}(c_2\cos(bt)+c_3\sin(bt))$

Or in this case,

$y=e^0(c_2\cos(2t)+c_3\sin(2t))$

Now we just refine and get,

$\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}$

Hope this helps.

r3t40

5 0

3 years ago

Number 5 and 6 please?

GuDViN [60]

Answer:

5. Profit of Rs 1 per lemon

6. Rs 20

Step-by-step explanation:

5. Buy Rs 60 per 12 lemons = Rs 5 per lemon

Sell Rs 30 per 5 lemons = Rs 6 per lemon

Profit Rs 1 per lemon

6. Sell Rs 2500 per 100 pens = Rs 25 per pen

Profit per pen is 20% = (20/100)25 = 5

Cost price of a pen = 25 - 5 = 20

6 0

3 years ago

Find the simplified product<br> ^3V9x^4 x ^3V3x^8

Kay [80]

$\sqrt[3]{9x^4}\cdot \sqrt[3]{3x^8}\implies \sqrt[3]{(9x^4)(3x^8)}\implies \sqrt[3]{27x^{4+8}}\implies \sqrt[3]{27x^{12}} \\\\\\ \sqrt[3]{3^3(x^4)^3}\implies 3x^4$

8 0

3 years ago

The area of a trapezium is 35cm2.find its altitude if the bases is 6cm and 8cm

r-ruslan [8.4K]

Answer: altitude: 5 cm

Explanation:

$\sf \dfrac{1}{2} ( a + b) h = Area \ of \ trapezium$

[ <u>a and b are bases, h is the altitude</u> ]

Here given:

Area = 35

a = 6

b = 8

h = ?

Solve for altitude:

$\sf \rightarrow \sf \dfrac{1}{2} ( 6 + 8) h = 35 \ \ \ \Rightarrow \ \ \ \dfrac{1}{2} ( 14) h = 35 \ \ \ \ \Rightarrow \ \ \ \ 7 h = 35 \ \ \ \ \Rightarrow \ \ h = \dfrac{35}{7} \ = \ 5$

7 0

2 years ago

the window of a room is 20m long and 14m wide. if the carpenter works to put a metallic frame around it which cost Rs.120 per me

notka56 [123]

Answer:

33,600

Step-by-step explanation:

length=20m

wide=14m

area= 28m²

1m= 28

cost = 120*28= rs33600 per m²

3 0

2 years ago