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amm1812
3 years ago
9

Make t the subject of the formula. Please help.

Mathematics
1 answer:
Digiron [165]3 years ago
5 0

Answer:

t = \frac{2-3q}{q+4}

Step-by-step explanation:

q = \frac{2-4t}{t+3}\\\\

Cross multiply,

q(t+3) = 2 - 4t        

Use distributive property: a*(b + c) =(a*b) + (a*c)

qt + 3q = 2- 4t

qt + 4t + 3q = 2

  qt + 4t     = 2 - 3q

    t(q + 4)  = 2 -3q

               t = \frac{2-3q}{q+4}

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Evaluate the difference quotient for the given function.
kherson [118]

Assuming you mean f(t) = g(t) × h(t), notice that

f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)

Then the difference quotient of f is

\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}

Recall the angle sum identity for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

Then we can write the difference quotient as

\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}

or

\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}

(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)

7 0
2 years ago
2. Given the equation of a circle in standard form, identify the center, radius, and graph the circle.
Varvara68 [4.7K]

Answer:

Center: ( -1 , 2 )

Radius: 6

Step-by-step explanation:

The equation for a circle is given as follow:

(x-h)^{2} +(y-k)^{2} =r^{2}

Where,

the Center is: ( h , k ) (note that the signs of the number are different)

and the radius is: r

So if we compare the original circle equation to the equation in the question we can see that:

(x+1)^{2} +(y-2)^{2} =36

the Center is: (-1,2)

and the radius is: \sqrt{36} = 6

2. To draw the graph find points that lay on the circle, it's better to take the values of x and y from the Center:

first sub y=2 in the equation to find the values for x:

(x+1)^{2} +(y-2)^{2} =36

(x+1)^{2} +(2-2)^{2} =36

(x+1)^{2} +(0)^{2} =36

(x+1)^{2}  =36

x+1 =±\sqrt{36}

x=6-1    AND    x=-6-1

x=5          AND    x=-7

  • The points are A(5,2)  and  B(-7,2)

second sub x= -1 in the equation to find the values for y:

(x+1)^{2} +(y-2)^{2} =36

(-1+1)^{2} +(y-2)^{2} =36

(0)^{2} +(y-2)^{2} =36

(y-2)^{2} =36

y-2=±\sqrt{36}

y=6+2    AND    y=-6+2

y=8          AND    y=-4

  • The points are D(-1,8)  and  E(-1,-4)      

After finding the points write them in the graph and match them together to get the like the circle in the picture below:

8 0
3 years ago
Please Answer ASAP According to the table, which ordered pair is a local maximum of the function, f(x)? (0, 64) (3, –35) (5, 189
Katarina [22]
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Nadusha1986 [10]

Answer:

1. Yes

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Step-by-step explanation:

1. Two triangles are the same if they share two side lengths with the same angle between them.

2. Since the triangles are equal if they share two side lengths with the same angle between them, if they changed the angle between 3 and 5, it'd no longer be the same triangle.

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Answer:

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Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

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3 years ago
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