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3 years ago

Please help its eighth math!

Mathematics

1 answer:

Margaret [11]3 years ago

3 0

Answer:

t and u are parallel lines

s and t are also parallel lines

Step-by-step explanation:

If two parallel lines are cut by a transversal ,

then in it

pair of alternate angle are equals, similarly vice versa

if pair of alternate angle are equals then lines are parallel

pair of corresponding angles are equal and vice-versa

for example

in the given problem

if line t and u are parallel (note we have assumed this to give example of parallel lines)

then angle 7 and 9 are called alternate angles

pair of angles 5 and 9 are corresponding angles.

________________________________________________

given

∠8 = ∠10 which are alternate angles for line t and u and s is transversal for it,

thus t and u are parallel lines

___________________________

∠1 = ∠3 as they vertically opposite angles

and we know that pair of vertically opposite angles are equal

given

∠1 = ∠7

thus

∠3 = ∠7

as pair of angles ∠3 and ∠7 are corresponding angles. and are equal and hence line s and t are also parallel.

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Please explain how they plugged the removable discontinuity in this question.

kondor19780726 [428]

In the limit

$\displaystyle \lim_{x\to c} f(x)$

we're interested in the value that $f(x)$ converges to as $x$ gets closer to $c$ . So in fact $x\neq c$ .

In the given example, $f(x)$ is factorized to reveal a common factor of $x-1$ in the numerator and denominator. We have $x\neq1$ if $x\to1$ , so $x-1\neq0$ so we can simplify

$\dfrac{x-1}{x-1} = 1$

and *remove* the discontinuity.

Then

$\displaystyle \lim_{x\to1} \frac{2(x-1)}{(x+1)(x-1)} = \lim_{x\to1} \frac2{x+1} = \frac2{1+1} = 1$

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=45%3D9%5E%7B%5Csqrt%7Bx%7D%20%7D" id="TexFormula1" title="45=9^{\sqrt{x} }" alt="45=9^{\sqrt{x

timama [110]

Answer:

Step-by-step explanation:

a= b^c << === >> logb(a) = c

a b c

Convert 45 = 9^√x << === >> log9 (45) = √x

1.7324867604 = √x

3.0 = x squared both sides

I used a log calculator on the internet when a Gaggled log calculators

8 0

3 years ago

Find the given derivative by finding the first few derivatives and observing the pattern that occurs. d103 dx103 (sin(x))

aleksandrvk [35]

To find $\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)$ , we find the first few derivatives and observe the pattern that occurs.

$\frac{d}{dx} (\sin{(x)})=\cos{(x)} \\ \\ \frac{d^2}{dx^2} (\sin{(x)})= \frac{d}{dx} (\cos{(x)})=-\sin{(x)} \\ \\ \frac{d^3}{dx^3} (\sin{(x)})= -\frac{d}{dx} (\sin{(x)})=-\cos{(x)} \\ \\ \frac{d^4}{dx^4} (\sin{(x)})= -\frac{d}{dx} (\cos{(x)})=-(-\sin{(x)})=\sin{(x)} \\ \\ \frac{d^5}{dx^5} (\sin{(x)})= \frac{d}{dx} (\sin{(x)})=\cos{(x)}$

As can be seen above, it can be seen that the continuos derivative of sin (x) is a sequence which repeats after every four terms.

Thus,

$\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)= \frac{d^{4(25)+3}}{dx^{4(25)+3}} \left(\sin{(x)}\right) \\ \\ = \frac{d^3}{dx^3} \left(\sin{(x)}\right)=-\cos{(x)}$

Therefore,

$\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)=-\cos{(x)}$ .

8 0

3 years ago

Jacob has 96 books to stack on library shelves. Each shelf can hold 9 books. How many shelves will he need to stack all the book

weeeeeb [17]

Answer:

11 book shelves

Step-by-step explanation:

All you have to do is divide 69/9 =10.66

round up and get 11 book shelves

7 0

3 years ago

The number of defective components produced by a certain process in one day has a Poisson

kakasveta [241]

Answer:

Step-by-step explanation:

Let X be the no of defective components produced by a certain process in one day

X is Poisson with parameter = 20

Y = no of components that can be repaired

Since each component to be repaired is independent of the other Y is Binomial with p =0.60

a) $P(x=15) = 0.051649$

b) P(Y = 10)= Binomial prob (15,0.6) for y =10

= $0.1859$

Here no of repairables X is binomial.

c) Prob for 15 produced and 10 repairable = product of a and b

= 0.009603

6 0

4 years ago