A (0, 2), B (–2, 6), and C (4, 0). Find the coordinates of the orthocenter

How many midsegments does a triangle have?

GREYUIT [131]

The midsegments the triangle have is three

4 0

3 years ago

Read 2 more answers

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

What's another way to do this cuz I'm SAD rn cuz I got a virus on my computer

emmainna [20.7K]

You need to add them all.

3 0

3 years ago

Read 2 more answers

The graph shows a proportional relationship between the cost of grapes, in dollars, and the number of pounds of grapes.

andreyandreev [35.5K]

Answer:

where is the picture

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

Artist 52 [7]

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $44,500

Sample mean, $\bar{x}$ = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s = $9,500

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}$

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37$

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income than the national average

5 0

3 years ago