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3 years ago

What is f(4) is says to determine the input of the function when X=4.)

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

Answer:

f(4) is called function notation.

typically you are given a function and need to evaluate it. As I believe you are trying to state, the 4 will be the input. See the example.

Step-by-step explanation:

f(x) = 3x + 4 This called a function, it has an input (the x) and a output

which is f(x). The question might look like this:

f(x) = 3x + 4, find f(4)

What this is basically saying is: find the output, f(x), when the input is 4

f(4) = 3(4) + 4

f(4) = 16

For the function f(x) = 3x + 4, the output is 16 when the input is 4

Hope this helps

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It took 3.5 hours for an airplane traveling at a constant speed of 550 miles per hour to reach its destination. What distance di

Nata [24]

The formula that we want to use here is S = D/T.

S = Speed
D = Distance
T = Time

So, we know that S = 550 and T = 3.5, so we can plug them in.

We get 550 = D/3.5
Multiply by 3.5 on each side, and you figure out that the plane has traveled 1925 miles.

7 0

3 years ago

Find cot and cos <br> If sec = -3 and sin 0 > 0

Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given $\displaystyle \large{\sec \theta = -3}$ and $\displaystyle \large{\sin \theta > 0}$ . What we have to find are $\displaystyle \large{\cot \theta}$ and $\displaystyle \large{\cos \theta}$ .

First, convert $\displaystyle \large{\sec \theta}$ to $\displaystyle \large{\frac{1}{\cos \theta}}$ via trigonometric identity. That gives us a new equation in form of $\displaystyle \large{\cos \theta}$ :

$\displaystyle \large{\frac{1}{\cos \theta} = -3}$

Multiply $\displaystyle \large{\cos \theta}$ both sides to get rid of the denominator.

$\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}$

Then divide both sides by -3 to get $\displaystyle \large{\cos \theta}$ .

Hence, $\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}$

__________________________________________________________

Next, to find $\displaystyle \large{\cot \theta}$ , convert it to $\displaystyle \large{\frac{1}{\tan \theta}}$ via trigonometric identity. Then we have to convert $\displaystyle \large{\tan \theta}$ to $\displaystyle \large{\frac{\sin \theta}{\cos \theta}}$ via another trigonometric identity. That gives us:

$\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}$

It seems that we do not know what $\displaystyle \large{\sin \theta}$ is but we can find it by using the identity $\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}$ for $\displaystyle \large{\sin \theta > 0}$ .

From $\displaystyle \large{\cos \theta = -\frac{1}{3}}$ then $\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}$ .

Therefore:

$\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}$

Then use the surd property to evaluate the square root.

Hence, $\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}$

Now that we know what $\displaystyle \large{\sin \theta}$ is. We can evaluate $\displaystyle \large{\frac{\cos \theta}{\sin \theta}}$ which is another form or identity of $\displaystyle \large{\cot \theta}$ .

From the boxed values of $\displaystyle \large{\cos \theta}$ and $\displaystyle \large{\sin \theta}$ :-

$\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}$

Then rationalize the value by multiplying both numerator and denominator with the denominator.

$\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}$

Hence, $\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}$

Therefore, the second choice is the answer.

__________________________________________________________

Summary

Trigonometric Identity

$\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}$

Surd Property

$\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}$

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

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2 years ago

I need help to find the volume

alexira [117]

Answer:

224ft^3

Step-by-step explanation:

l*w*h= volume

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3 years ago

Read 2 more answers

Fabric length: 3 7/8 yd.

RUDIKE [14]

3 x $9.25 = 27.75
4/8 = 9.25/2 = 4.6 so 27.75+ 4.6 equals 32.37 (so I’ve only done 4/8 so far but it states it’s 7/8 so we’re gonna go ahead and add 2/8 of it more so that it’s 6/8) therefore we know 4/8 is 4.6 we’ll divide that by 2 to get 2/8 and that would be 2.3 so 32.37 + 2.3 equals 34.67 Nd we do the same again with the remainder additional 1/8 since we know 2/8 is 2.3 then we divide it by two that would 1.15 so 34.67+ 1.15 equals 35.81 and the closest answer is D

6 0

3 years ago

Read 2 more answers

(0,1),(2,5),(3,7) in an equation

12345 [234]

The equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.

Step-by-step explanation:

Step 1; We need to determine the equation relating the x to the f(x) values from the given coordinates. y is the dependent value whereas x is the independent value i.e. y's value depends on x's value.

Step 2; If we multiply the x value with 2 and add the resulting answer with 1 we get the y value.

y = 2x + 1 is the equation that relates the values in the table.

Step 3; Now we substitute the values in the equation to see if it's correct.

For x = 0, y = 2(0) + 1 = 0 + 1 = 1,

For x = 2, y = 2(2) + 1 = 4 + 1 = 5,

For x = 3, y = 2(3) + 1 = 6 + 1 = 7.

So the equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.

7 0

3 years ago

What is f(4) is says to determine the input of the function when X=4.)​

What is f(4) is says to determine the input of the function when X=4.)