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kotegsom [21]
3 years ago
8

What is the value of x in the figure at the right? 50 62 68 112

Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0

Step-by-step explanation:

step 1. 50° + 62° = x by means of corresponding angles.

step 2. x = 112°

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On a sunny day, a flag pole and its shadow form the sides of a right triangle. if the hypotenuse is 35 meters long and the shado
Triss [41]
We can use Pythagorean's Theorem in order to find the remaining side length
a^2+b^2=c^2
Let a be the shadow length
Let b be the height of the flagpole
Let c be the hypotenuse 
28^2+b^2=35^2
784+b^2=1225
b^2=1225-784
b^2=441
b=√441
b=21
Therefore the flagpole is 21 meters tall.
Hope this helps!
 
 
3 0
3 years ago
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
ryzh [129]

First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

t=0\implies f(10,0)=155

t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299

t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
What is the GCF of 6 and 36
Tresset [83]

Answer:

It's 6.

Step-by-step explanation:

6- 1, 2, 3, <u>6</u>

36- 1, 2, 3, 4, <u>6</u>

5 0
2 years ago
PLEASE HELP ME WITH THANKS :)
Maurinko [17]

Answer

12855.04 ft³

Step-by-step explanation:

regular Octagon consists of 8 congruent triangles

B = (13.28 x 11) / 2 x 8=584.32

V = BH = 584.32 x 22 = 12855.04

8 0
3 years ago
Read 2 more answers
The center of a circle is (0, -8). The radius is 9. What is the equation of the circle? Select all that apply.
taurus [48]

Answer:

x² + (y + 8)² = 81

Step-by-step explanation:

Centre (h,k) = (0,-8)

radius (r) = 9

(x - h)² + (y - k)² = r²

(x - 0)² + (y + 8)² = 9²

x² + (y + 8)² = 81

8 0
3 years ago
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