Determine the equation of the line connecting the points (0,-1) and (2,3)

Factor 5z^2+45z. The factored polynomial is _

erik [133]

Here you go
5z(z+9)

4 0

3 years ago

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

3 years ago

The graph shows the amount of money paid when purchasing bags of peanuts at the zoo:

r-ruslan [8.4K]

Answer:

B

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

--8W + 5 = -43<br> what’s this?

nataly862011 [7]

Answer:

it is the equation which you have to solve.

3 0

3 years ago

In circle A, ∠BAE ≅ ∠DAE.

kirza4 [7]

The image of circle A is missing, so i have attached it;

Answer:

x = 17

Step-by-step explanation:

In Δs EAB and EAD

We are told that;

∠BAE ≅ ∠DAE

AB = AD = AE

Now,

The Two triangles have two corresponding equal sides and the angles between them are equal, thus, we can say that the two triangles are congruent by SAS (Side Angle Side) postulate of congruence

By using the result of congruence, we can say that;

EB ≅ ED

We are given that;

EB = 3x - 24 and ED = x + 10

Thus,

3x - 24 = x + 10

∴ 3 x - 24 = x + 10

Add 24 to both sides to give;

3x = x + 34

Subtract x from both sides to give;

2x = 34

Divide both sides by 2 to give;

x = 17

5 0

4 years ago

Read 2 more answers