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ZanzabumX [31]
3 years ago
6

WILL MARK BRAINLIEST AND WORTH 30 POINTS

Mathematics
1 answer:
BabaBlast [244]3 years ago
5 0

Answer:

The growth factor of <em>f(x)</em> is <em>less</em><em> </em><em>than</em><em> </em>the growth factor of <em>g(x)</em>.

Explanation:

\displaystyle g(x) = 3(4)^x \\ \\ f(x) = 4(3)^x

<em>x</em><em> </em> | <em>f(x)</em>

_____

0 | 4

1 | 12

2 | 36

You can tell because the <em>g</em><em>(</em><em>x</em><em>)</em><em> </em>function is multiplying by 4, while the <em>f</em><em>(</em><em>x</em><em>)</em><em> </em>function is multiplying by 3.

I am joyous to assist you anytime.

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre
andrew-mc [135]

Answer:

The area function is

A=\frac{135}{2}x-\frac{9}{2}x^2.

The domain and range of A is (0,15m) and (0, 253.125 m^2].

Step-by-step explanation:

The given length of fencing is 90 m.

Let the length and width of each pen be x and y respectively as shown in the figure.

As there are 3 pens, so, the total area,

A= 3 xy \;\cdots (i)

From the figure the total length of fencing is 6x+4y.

Here, for a significant area for the animals, x>0 as well as y>0 as x and y are the sides of ben.

From the given value:

6x+4y=90\;\cdots (ii)

\Rightarrow  y=\frac {45}{2}-\frac{3x}{2}

Now, from equation (i)

A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)

\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)

This is the required area function in the terms of variable x.

For the domain of area function, from equation (ii)

x=15-\frac{2y}{3}

\Rightarrow x [as y>0]

So, the domain of area function is (0,15m).

For the range of area function:

As x \rightarrow 0 or y\rightarrow 0, then A\rightarrow 0 [from equation (i)]

\Rightarrow A>0

Now, differentiate the area function with respect to x .

\frac {dA}{dx}=\frac{135}{2}-9x

Equate \frac {dA}{dx}  to zero to get the extremum point.

\frac {dA}{dx}=0

\Rightarrow \frac{135}{2}-9x=0

\Rightarrow x=\frac{15}{2}

Check this point by double differentiation

\frac {d^2A}{dx^2}=-9

As,  \frac {d^2A}{dx^2}, so, point x=\frac{15}{2} is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2

\Rightarrow A=253.125 m^2

Hence, the range of area function is (0, 253.125 m^2].

4 0
3 years ago
Suppose you flip 3 quarters, one at a time. What is the probability that you will
Semenov [28]

Answer:

The probability of the combination {H, T and H} is 0.125.

Step-by-step explanation:

The sample space of flipping a quarter is:

S = {H and T}

The probability of both outcomes is same, i.e. P (H) = P (T) = 0.50.

It is provided that three quarters are flipped one at a time.

The outcomes of all the three quarters are independent of each other.

Compute the probability of the combination {H, T and H} as follows:

P(\text{H},\text{T and H}) = P(\text{H})\times P(\text{T})\times P(\text{H})

                        =0.50\times 0.50\times 0.50\\=0.125

Thus, the probability of the combination {H, T and H} is 0.125.

7 0
3 years ago
Line segment XY is tangent to circle Z at point U. Circle Z is shown. Line segment U V is a secant. Line segment X Y is a tangen
Yuri [45]

Answer:

138°

Step-by-step explanation:

∠YUV creates arc YV. Circle Z is made up of arc UV (84°) and arc YV. Solve for the measure of arc YV. (A circle equals 360°)

84° + x = 360°

arc YV = 276°

arc YV is formed from a secant and a tangent. Because of this ∠YUV is half of arc YV.

276° ÷ 2 = 138°

∠YUV = 138°

3 0
2 years ago
Read 2 more answers
Find the volume of a cone with a diameter of 5.5 km
vagabundo [1.1K]

Answer:

volume =  \frac{1}{3} \pi {r}^{2} h \\  =  \frac{1}{3}  \times  \frac{22}{7}  \times  {( \frac{5.5}{2}) }^{2}  \times 11.2 \\  = 88.7 \:  {km}^{3}

4 0
2 years ago
A party mix is made by adding nuts that sell for $2.50 per kg to a cereal mixture that sells for $1 per kg. How much of each sho
sesenic [268]

Answer:

The amount of nuts is 16 kg and cereal mixture is 44 kg to obtain 60 kg of a mix that will sell for $1.40 per kg

Step-by-step explanation:

Let

x=nuts at $2.50 per kg

y=cereal at $1 per kg

x+y=60 kg (1)

2.50x+y=1.40(60) (2)

From (1)

x=60-y

Substitute x=60-y into (2)

2.50x+y=1.40(60)

2.50(60-y)+y=84

150-2.5y+y=84

-1.5y=84-150

-1.5y=-66

Divide both sides by -1.5

y=44 kg

Substitute y=44 into (1)

x+y=60

x+44=60

x=60-44

=16

x=16 kg

3 0
3 years ago
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