Prove: cot x (tan x + sin x) =1+ cos x

If f(x) = -7x + 5x2 + 10, what does f(-2) equal?

aksik [14]

Answer:

f(-2) = 44

Step-by-step explanation:

Hello there! Lets get started solving this function!

For a function, whenever we see f(x) = ... , the function is simply asking the value of the equation at x! So, if replace f(x) with f(-2), we simply substitute x with -2 in the equation! Lets get started!

$f(x) = -7x + 5x^{2} + 10\\f(-2) = -7(-2) + 5(-2)^{2} + 10\\f(-2) = 14 + 20 + 10\\f(-2) = 44\\$

First, we can write the original function. Next, we substitute in -2 for x. Then, we find our final terms. Finally, we are given that f(-2) = 44.

Hope this helps! Remember, math is fun!

7 0

3 years ago

The graph of f is given in the figure to the right. Let A(x)equals=Integral from 0 to x f left parenthesis t right parenthesis

Tpy6a [65]

Answer:

$A(4)=-4\pi$

$A(8)=-4\pi +8$

$A(12)=-4\pi +16$

$A(14)=-4\pi +15$

Step-by-step explanation:

we are given

$A(x)=\int\limits^x_0 f{x} \, dx$

Calculation of A(4):

we can plug x=4

$A(4)=\int\limits^4_0 f{x} \, dx$

Since, this curve is below x-axis

so, the value of integral must be negative

and it is quarter of circle

so, we can find area of quarter circle

radius =4

$A(4)=-\frac{1}{4}\times \pi \times (4)^2$

$A(4)=-4\pi$

Calculation of A(8):

we can plug x=8

$A(8)=\int\limits^8_0 f{x} \, dx$

we can break into two parts

$A(8)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx$

now, we can find area and then combine them

$A(8)=-4\pi +\frac{1}{2}\times 4\times 4$

$A(8)=-4\pi +8$

Calculation of A(12):

we can plug x=12

$A(12)=\int\limits^12_0 f{x} \, dx$

we can break into two parts

$A(12)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx$

now, we can find area and then combine them

$A(12)=-4\pi +\frac{1}{2}\times 8\times 4$

$A(12)=-4\pi +16$

Calculation of A(14):

we can plug x=14

$A(14)=\int\limits^14_0 f{x} \, dx$

we can break into two parts

$A(14)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx+\int\limits^14_12 f{x} \, dx$

now, we can find area and then combine them

$A(14)=-4\pi +\frac{1}{2}\times 8\times 4-\frac{1}{2}\times 1\times 2$

$A(14)=-4\pi +16-1$

$A(14)=-4\pi +15$

8 0

2 years ago

Which of the following has a solution set of {x | x = 0}?

Burka [1]

It is B
(x+1<1)this mark(x+1>1)

8 0

3 years ago

Read 2 more answers

What is the number whose 4/5 is 144

Savatey [412]

We want 4/5 of a number to be 144. This means that

$\dfrac{4}{5} \cdot x = 144$

Multiplying both sides by 5/4, we have

$x = \dfrac{144\cdot 5}{4} = 180$

4 0

3 years ago

The ratio of boys to girls in a group is 5:3. If there are 18 more boys than girls, work out how

zmey [24]

<h3>Answer: 72 people total</h3>

45 boys, 27 girls

============================================================

Explanation:

g = number of girls

g+18 = number of boys, since there are 18 more boys than girls

For example, if g = 7, then g+18 = 7+18 = 25. In this example, we have 7 girls and 25 boys. The problem with this example is the ratio of boys to girls is 25:7 which is not equal to 5:3

We could use trial and error until we land on the solution, or we can use algebra as shown in the next section.

-------------------

The ratio of boys to girls is 5:3, meaning

(number of boys)/(number of girls) = 5/3

which turns into

(g+18)/g = 5/3

after we make the proper substitutions

Let's solve for g

(g+18)/g = 5/3

3(g+18) = 5g

3g+54 = 5g

54 = 5g-3g

54 = 2g

2g = 54

g = 54/2

g = 27

There are 27 girls.

This leads to,

g+18 = 27+18 = 45

So there are 45 boys

In total, we have 27+45 = 72 people

-----------------------------

Checking the answer:

The claim is that 45/27 is the same as 5/3

For now assume that claim is true. Set the fractions equal to each other and use cross multiplication like so

45/27 = 5/3

45*3 = 27*5

135 = 135

The third equation has the same thing on both sides, so it's a true equation. This must mean the first equation is true as well. Therefore, 45:27 and 5:3 are the same ratio and the answer is confirmed.

You could also use your calculator to note that

45/27 = 1.667

5/3 = 1.667

both decimal values are approximate.

8 0

2 years ago