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4 years ago

5

Solve for a.g= 1+2a ------- a

1 answer:

vladimir2022 [97]4 years ago

8 0

Subtract g add 1 divide by 2a

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In the two functions fand g, fog and go fare both equivalent to x. Which of the following statements must be TRUE?

garik1379 [7]

F Must be the inverse of g

8 0

2 years ago

The local museum had 20,000 visitors in 1990. The number of visitors has decreased by 3% each year since 1990. Enter a function

Volgvan

Answer:

m(x) = 20000(0.97)^x

Step-by-step explanation:

Given that :

Initial population, population in 1990, P = 20,000

Rate, r = 3% = 0.03

Number of visitors to the museum x years after 1990

Since population decreases, Decay formula

m(x) = Initial population * (1 - r)^x

m(x) = 20000(1 - 0.03)^x

m(x) = 20000(0.97)^x

8 0

3 years ago

Circular tracts of land with diameters 900 meters, 700 meters and 600 meters are tangent to each other externally. There are hou

Rudik [331]

Answer:

$\alpha=69.28^o$

$\beta=61.26^o$

$\gamma=49.46^o$

<em /> $A=227980.26\ m^2$ <em />

Step-by-step explanation:

<u>Triangle Solving</u>

If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.

The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are

$x=450+350=800$

$y=450+300=750$

$z=350+300=650$

The internal angles can be computed by using the cosine's law

$x^2=y^2+z^2-2yzcos\alpha$

$y^2=x^2+z^2-2xzcos\beta$

$z^2=x^2+y^2-2xycos\gamma$

Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:

$\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}$

$\displaystyle cos\alpha=\frac{750^2+650^2-800^2}{2\cdot 750\cdot 650}$

$cos\alpha=0.3538$

$\alpha=69.28^o$

Similarly

$\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}$

$\displaystyle cos\beta=\frac{800^2+650^2-750^2}{2\cdot 800\cdot 650}$

$cos\beta=0.4808$

$\beta=61.26^o$

The other angle is computed now

$\displaystyle cos\gamma=\frac{x^2+y^2-z^2}{2xy}$

$\displaystyle cos\gamma=\frac{800^2+750^2-650^2}{2\cdot 800\cdot 750}$

$cos\gamma=0.65$

$\gamma=49.46^o$

The area can be found by

$\displaystyle A=\frac{1}{2}x.y.sin\gamma$

$\displaystyle A=\frac{1}{2}\cdot 800\cdot 750\cdot sin49.46^o$

$A=227980.26\ m^2$

8 0

3 years ago

For a quadrilateral to be a square, the diagonals must be ________________.

DENIUS [597]

Answer:

congruent and perpendicular

4 0

3 years ago

Find the average rate of change for f(x) = x2 − 8x + 15 from x = −3 to x = 2.

zimovet [89]

Answer:

its -9

Step-by-step explanation:

7 0

3 years ago