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2 years ago

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What property is being used in 2a+5a=(2+5)a

1 answer:

Tems11 [23]2 years ago

5 0

Answer:

distributive property

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Write an equation of the cosine function with amplitude pi/2 and period 3

juin [17]

Answer:

$y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)$

Step-by-step explanation:

Given

$Amplitude = \frac{\pi}{2}$

$Period = 3$

Required

Write the equivalent cosine function

The general formula is:

$y = acos(bx)$

Where

$amplitude = |a|$

$period = \frac{2\pi}{b}$

Substitute $\frac{\pi}{2}$ for amplitude in $amplitude = |a|$

$|a| = \frac{\pi}{2}$

$a = \frac{\pi}{2}$

Substitute 3 for period in $period = \frac{2\pi}{b}$

$\frac{2\pi}{b} = 3$

<em>Multiply both sides by b</em>

$2\pi = 3b$

<em>Divide through by 3</em>

$b = \frac{2\pi}{3}$

Hence;

$y = acos(bx)$ becomes

$y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)$

5 0

3 years ago

Find the absolute maximum and minimum values of the following function in the closed region bounded by the triangle with vertice

alukav5142 [94]

$f(x,y)=2x^2-8x+y^2-8y+2$

$f_x(x,y)=4x-8=0\implies x=2$

$f_y(x,y)=2y-8=0\implies y=4$

There is one critical point at (2, 4), but this point happens to fall on one of the boundaries of the region. We'll get to that point in a moment.

Along the boundary $x=0$ , we have

$f(0,y)=y^2-8y+2=(y-4)^2-14$

which attains a maximum value of

$f(0,4)=-14$

Along $y=44$ , we have

$f(x,44)=2x^2-8x+1586=2(x-2)^2+1578$

which attains a maximum of

$f(2,44)=1578$

Along $y=2x$ , we have

$f(x,2x)=6x^2-24x+2=6(x-2)^2-22$

which attains a maximum of

$f(2,4)=-22$

So over the given region, the absolute maximum of $f(x,y)$ is 1578 at (2, 44).

8 0

2 years ago

Fiona divided 3x2 5x – 3 by 3x 2. the expression represents the remainder over the divisor.what is the value of a?

Pavel [41]

If Fiona is to divide the first expression by the second one, clearly only the first term of the first expression is divisible. The remaining terms of the fist expression will remain as the remainder. The remainder from the division done by Fiona should be 5x - 3.

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3 years ago

Match each description with the expression containing terms that model it

Paul [167]

Answer:

?

Step-by-step explanation:

8 0

2 years ago

The number of visitors to a certain Web site triples every month. The number of visitors is modeled by the expression 900 * 3^m

kipiarov [429]

Answer:

$900\times 3^m$ = 100

Step-by-step explanation:

The number of visitors is modeled by the expression $900\times 3^m$

Where m is the number of months after the number of visitors was measured.

We need to evaluate the above expression for m = -2.

So,

$900\times 3^m=900\times 3^{-2}\\\\=900\times \dfrac{1}{3^2}\\\\=900\times \dfrac{1}{9}\\\\=100$

At m = -2, the value of the above expression is equal to 100.

5 0

3 years ago