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Paladinen [302]
3 years ago
7

TWO QUESTIONS BELOW:

Mathematics
1 answer:
alekssr [168]3 years ago
4 0

Answer:

Measure angle 2 is 70 degrees (question 1)

Measure angle 1 is 115 degrees (question 2)

Step-by-step explanation:

assume the other 2 angles sum up to 180 degrees

Subtract measure angle 3 by 180 degrees to find measure angle 2

Hope this helped :) comment if you need more help or clarification

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Given g(x) = 10x + 2, find x when g(x) = 2.
Elan Coil [88]

Answer:

x=0    

Step-by-step explanation:

We are given:

g(x) =10x +2

and

g(x)=2

g(x) is equal to both 10x+2 and 2. Therefore, by substitution, we can set them equal to each other

10x+2=2

Now, we need to solve for x. First, move all the numbers to the same side. Subtract 2 from both sides

10x+2-2=2-2

10x=0

To solve for x, we have to get x by itself. x and 10 are being multiplied. To get x alone, divide both sides by 10.

10x/10=0/10

x=0

8 0
2 years ago
Someone help me with this
Alenkasestr [34]

Answer:

70°

Step-by-step explanation:

ABC is the center angle that sees the arc and is twice as angle ADC so the measure of ABC is e × 35 = 70

3 0
3 years ago
Read 2 more answers
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw
vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0

<em>x</em> ² - 10<em>x</em> + 25 + <em>y </em>² = 25

(<em>x</em> - 5)² + <em>y</em> ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

<em>x</em> = <em>r</em> cos(<em>θ</em>)

<em>y</em> = <em>r</em> sin(<em>θ</em>)

Then

<em>x</em> ² + <em>y</em> ² = 100   →   <em>r </em>² = 100   →   <em>r</em> = 10

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0   →   <em>r </em>² - 10 <em>r</em> cos(<em>θ</em>) = 0   →   <em>r</em> = 10 cos(<em>θ</em>)

<em>y</em> = 5   →   <em>r</em> sin(<em>θ</em>) = 5   →   <em>r</em> = 5 csc(<em>θ</em>)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to <em>y</em> = 5 at the point (0, 5).

Split up the region at 3 angles <em>θ</em>₁, <em>θ</em>₂, and <em>θ</em>₃, which denote the angles <em>θ</em> at which the curves intersect. They are

<em>θ</em>₁ = 0 … … … by solving 10 = 10 cos(<em>θ</em>)

<em>θ</em>₂ = <em>π</em>/6 … … by solving 10 = 5 csc(<em>θ</em>)

<em>θ</em>₃ = 5<em>π</em>/6  … the second solution to 10 = 5 csc(<em>θ</em>)

Then the area of the region is given by a sum of integrals:

\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)

=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta

To compute the integrals, use the following identities:

sin²(<em>θ</em>) = (1 - cos(2<em>θ</em>)) / 2

cos²(<em>θ</em>) = (1 + cos(2<em>θ</em>)) / 2

and recall that

d(cot(<em>θ</em>))/d<em>θ</em> = -csc²(<em>θ</em>)

You should end up with an area of

=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta

=\boxed{25\sqrt3+\dfrac{125\pi}3}

We can verify this geometrically:

• the area of the larger circle is 100<em>π</em>

• the area of the smaller circle is 25<em>π</em>

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line <em>y</em> = 5, has area 100<em>π</em>/3 - 25√3

Hence the area of the region of interest is

100<em>π</em> - 25<em>π</em> - (100<em>π</em>/3 - 25√3) = 125<em>π</em>/3 + 25√3

as expected.

3 0
2 years ago
Good afternoon, please help me with this question and if u get it correct ill give u the brainlest
Luden [163]

Answer:

3/5

Step-by-step explanation:

Hope that this helped :)

3 0
2 years ago
Haley's car gets at least 17 miles per gallon. If she plans a trip that is 250 miles, what is the minimum number of gallons she'
icang [17]
Divide 250 miles by 17 mpg:

250 miles
-------------- = 14.7 gallons (absolute mininum).  Go for 15 gallons.
  17 mpg
4 0
3 years ago
Read 2 more answers
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