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Leviafan [203]
3 years ago
10

Evaluate the function rule for the given value. f(x)=3^x for x=-5

Mathematics
1 answer:
FromTheMoon [43]3 years ago
6 0

Answer:

\frac{1}{243}

Step-by-step explanation:

using the rule of exponents

a^{-m} ⇔ \frac{1}{a^{m} }

f(- 5) = 3^{-5} = \frac{1}{3^{5} } = \frac{1}{243}


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Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y
Aleks [24]

Answer:

we have centre of circle as (30,40) and radius = 1

Step-by-step explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

x(t) = 10 sin(200t + 3) + 30

and

y(t) = 10 cos(200t + 3) + 40

x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40

when we square and add both the equations we get

(x-30)^2 + (y-40)^2 = 1

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1

3 0
3 years ago
Michelle can fold 4 baskets of clothes in 54 minutes, while Ruby can fold 4 baskets of clothes in 108 minutes. How long will it
Lady bird [3.3K]
Michelle can fold 4/54 baskets per minute = 8/108 baskets per minute.
Ruby can fold 4/108 baskets per minute.

Each minute Michelle and Ruby work together, they can fold
   8/108 +4/108 = 12/108 = 1/9
of a basket of clothes. For 8 baskets of clothes, it will take them
   (8 baskets)/(1/9 baskets/minute) = 72 minutes
5 0
3 years ago
Now factor the expression. 1/2 a + 6
Sophie [7]

Answer:

1a+12/2

Step-by-step explanation:

1/2a+6

1/2a+6/1

1/2a+6/1*2

1/2a+12

1a+12/2

3 0
3 years ago
Please help me solve this problem with step by step explanation.​
Kisachek [45]

Answer:

Im not rally sure but maybe 5.71 , here is my explanation :

Step-by-step explanation:

Tan 55 =x/4

tan 55 = 1/42814

1/42814 = x /4

×=5.712592027 .

3 0
3 years ago
jacob wants to buy packets of fruit juice. on tuesday, he buys 8 packets of orange and 6 packets of Apple the packets make a tot
ioda

Answer:

Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

Step-by-step explanation:

Let number of cups of juice in each packet of orange be 'x'.

Let number of cups of juice in each pack of apples be 'y'.

Given:

On Tuesday;

Number of packets of oranges = 8

Number of packets of apples = 6 packets.

Amount of fruit juice = 34 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

8x+6y=34 \ \ \ \ equation \ 1

On Wednesday;

Number of packets of oranges = 14

Number of packets of apples = 6

Amount of fruit juice = 46 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

14x+6y=46 \ \ \ \ equation \ 2

Now Subtracting equation 1 from equation we get;

14x+6y-(8x+6y)=46-34\\\\14x+6y-8x-6y=12\\\\6x=12

Now dividing both side by 6 we get;

\frac{6x}{6}=\frac{12}{6}\\\\x=2\ cups

Now we will substitute the value of 'x' in equation 1 we get;

8x+6y=34\\\\8\times2+6y=34\\\\16+6y=34

Subtracting both side by 16 we get;

16+6y-16=34-16\\\\6y= 18

Now dividing both side by 6 we get;

\frac{6y}{6}=\frac{18}{6}\\\\y=3

Hence Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

5 0
3 years ago
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