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4 years ago

Prove that the altitude to the base of an isosceles triangle is also the angle bisector of the angle from which it is drawn

Mathematics

1 answer:

andriy [413]4 years ago

5 0

Step-by-step explanation:

To prove- Altitude to the base of an isosceles triangle bisects the angle from which it is drawn.

In the given figure ΔABC (isosceles triangle) whose sides AB=AC

From ∠A an altitude is drawn to base (BC) which meets BC at X

∠AXB=90 and ∠AXC =90

∴We need to prove ΔXAB= ΔXAC for altitude to bisect the ∠ BAC

In Δ AXB and Δ AXC

AB=AC (same hypotenuse)

AX= common altitude (serve as the common leg of the hypotenuse)

ΔAXB ≅ ΔAXC

Hence, we can conclude that the corresponding angle∠ XAB = ∠XAC. QED

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D) Use your knowledge of scale drawings and image sizes to fill in the missing

astraxan [27]

Answer:

Your table is filled in below.

Step-by-step explanation:

The scale factor is the ratio of image size to original size. In part (d), the image height is "blocks" while the original height is "feet". So, the units of the scale factor are "blocks/ft".

Sometimes a scale factor has units, like this, and sometimes it is expressed as a pure number. A map scale factor might be the pure number ratio 1 : 62500, or it could also be expressed with units as 1 in : 1 mile.*

* actually, these are slightly different scales. 1:62500 is about 0.98643 inches per mile.

7 0

3 years ago

Read 2 more answers

What is the scale factor use to create this dilation?

andrezito [222]

Given Info: "The dashed triangle is the image of the solid triangle"

So the "before" is the large solid triangle and the "after" is the smaller dashed triangle.

The horizontal side of the solid triangle is 15 units. The corresponding side for the dashed triangle is 3 units. Dividing the two values gives: 3/15 = 1/5 = 0.2

Make this value negative. The reason why is due to the fact that we have a sort of reflection going on as we're scaling down the figure.

So the final answer is -0.2

3 0

3 years ago

Find T5(x) : Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0 . (You need to enter function.) T5(x)= Find all va

Burka [1]

Answer:

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

The polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

Step-by-step explanation:

According to Taylor's theorem

$\bf f(x)=f(0)+f'(0)x+f''(0)\displaystyle\frac{x^2}{2}+f^{(3)}(0)\displaystyle\frac{x^3}{3!}+f^{(4)}(0)\displaystyle\frac{x^4}{4!}+f^{(5)}(0)\displaystyle\frac{x^5}{5!}+R_6(x)$

with

$\bf R_6(x)=f^{(6)}(c)\displaystyle\frac{x^6}{6!}$

for some c in the interval (-x, x)

In the particular case f

f(x)=cos(x)

we have

$\bf f'(x)=-sin(x)\\f''(x)=-cos(x)\\f^{(3)}(x)=sin(x)\\f^{(4)}(x)=cos(x)\\f^{(5)}(x)=-sin(x)\\f^{(6)}(x)=-cos(x)$

therefore

$\bf f'(x)=-sin(0)=0\\f''(0)=-cos(0)=-1\\f^{(3)}(0)=sin(0)=0\\f^{(4)}(0)=cos(0)=1\\f^{(5)}(0)=-sin(0)=0$

and the polynomial approximation of T5(x) of cos(x) would be

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that

$\bf R_6(x)=-cos(c)\displaystyle\frac{x^6}{6!}$

for some c in (-x,x). So

$\bf |R_6(x)|\leq|\displaystyle\frac{x^6}{6!}|=\displaystyle\frac{|x|^6}{6!}$

and we must find the values of x for which

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652$

Working this inequality out, we find

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652\Rightarrow |x|^6\leq1.90944\Rightarrow\\\\\Rightarrow |x|\leq\sqrt[6]{1.90944}\Rightarrow |x|\leq1.113826815$

Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

8 0

3 years ago

A tire company paid $4,992 for 64 tires. Which is the most reasonable estimate for the cost of each tire?

4vir4ik [10]

$78 for each tire
4,992 divided by 64 is 78

7 0

3 years ago

The local farmers market has oranges on sale for 5 for 1.80 What is the cost of one orange ?

lara [203]

Answer:.36 cent

1Step-by-step explanation:1.80 divided by 5

5 0

3 years ago