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3 years ago

If you earned $32,000 this year at your job and know you will receive a 4% raise every year,

Mathematics

1 answer:

Maksim231197 [3]3 years ago

6 0

Answer:

$38,400

Step-by-step explanation:

Find 4 percent of $32,000, which is 1280.

Multiply 1280 by 5 as for 5 years which will become 6400 and then add 32,000 and 6400 and you get your answer which is $38,400

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f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

5 0

2 years ago

!!!!PLEASE HELP!!!

DaniilM [7]

Answer:

a^2 + b^2 = c^2

a^2 + 32^2 = 58^2

a^2 + 1024 = 3364

a^2 = 2340

a = 48.37

Step-by-step explanation:

5 0

3 years ago

1)Evaluate 2A - 3B for A = 7 and B = -2.

Gnom [1K]

Hey Brion,

1) Evaluate 2A - 3B for A = 7 and B = -2.
To solve this start by filling in the variables.
2(7) - 3(-2)

Now multiply, remember that a positive times a negative is a negative.
14 - (-6)

Finally, subtract. Remember, Keep, Change, Change (KCC). Keep the first number, change symbol (for subtraction use addition), and change the negative number to a positive number.
14 + 6 = 20

2) If x = -3, then x 2-7x + 10 equals
Start by filling in the variables.
-3(2) - 7(-3) + 10

Now follow PEMDAS (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction) to solve. Remember K.C.C (no. 1 above)
-3(2) - 7(-3) + 10
(-6) - (-21) + 10
(-6) + (21) + 10
15 + 10
25*****See NOTE!***
_____________________________________________________________
Note: For #2 you may be missing a symbol between the first "x" and "2" because the answer I got above (25) is not one of your choices. Let me know what symbol is missing in the equation: x 2-7x + 10, and I will help you solve it.

5 0

2 years ago

Reynaldo drew square EFGH. Then, he drew the image of it, square E'F'G'H', 4 centimeters to the left of the original figure. Lin

OLEGan [10]

Answer:

6 centimeters

Step-by-step explanation:

Square E'F'G'H' is just square EFGH translated to the left.

It is still the same size, just in a different location.

Line segment EF is the same length as segment E'F'.

6 centimeters

3 0

2 years ago

Which Property is illustrated?

GalinKa [24]

A + (b + c) = (a + b) + c.....what u have here is the associative property of addition

6 0

3 years ago