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3 years ago

The growth of bacteria in a dish is modeled by the function f(t)=2 to the power of t/3. For which value of t is f(t)=32?

Mathematics

1 answer:

Juliette [100K]3 years ago

6 0

Answer:

$\boxed{t=15}$

Step-by-step explanation:

Function: $f(t)=2^{t/3}$

You need to replace f(t) for 32 and isolate "t", like this:

$f(t)=2^{t/3}\\ 32=2^{t/3}\\ 2^5=2^{t/3}$

Since both bases are 2, we only take the powers:

$5=\dfrac{t}{3}\;\Longrightarrow 5\cdot3=t=15$

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You solve for x and get x<-2 or x>= -1/2 and then graph

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3 years ago

White and black shapes are used in a game Some of the shapes are circles All the other shapes are squares The ratio of white to

PIT_PIT [208]

Answer:

The fraction of all shapes which are square in shape is $\frac{23}{32}$ .

Step-by-step explanation:

Given that , in a game , white and black shapes are used. Some of them are circle in shape and remains are square in shape.

The ratio of white to black shapes are 5:11.

Consider 5x= the number of shapes which are white in color.

11x= The number of shapes which are black in color.

There are (5x+11x)= 16x shapes in the game.

The white circle and white square are in the ratio 3:7.

The number of white square is

$=(\textrm{The number of white shape})\times (\frac{7}{3+7})$

$=(5x)\times (\frac{7}{10})$

$=\frac{7x}{2}$

The black circles and black square are in the ratio 3:8

The number of black square is

$=(\textrm{The number of black shape})\times (\frac{8}{3+8})$

$=(11x)\times (\frac{8}{11})$

=8x

Therefore the total number of shape which are square is

$=\frac{7x}{2}+8x$

$=\frac{7x+16x}{2}$

$=\frac{23x}{2}$

The fraction of all shape are square is

$=\frac{\textrm{shape in square}}{\textrm{Total number shape}}$

$=\frac{\frac{23x}{2}}{16x}$

$=\frac{23}{32}$

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3 years ago

Tan^2 x+sec^2 x=1 for all values of x.<br> True or False

gogolik [260]

False

because tan^2 45 = 1^2 = 1
and sec^2 x = 1/ cos^2 45 = (sqrt2)^2 = 2

so the sum = 3

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3 years ago

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You are cutting a rectangular piece of fabric in half along a diagonal. The fabric measures 28 inches wide and 1 1/4 yards long.

liubo4ka [24]

Answer:

45.61 inches

Step-by-step explanation:

Use the pythagorean theorem.

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3 years ago

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What is the sequence of transformations that maps △ABC to △A′B′C′ ? Select from the drop-down menus to correctly identify each s

torisob [31]

<h3>Answer:</h3>

Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).

<h3>Step-by-step explanation:</h3>

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.

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3 years ago