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3 years ago

What is the area of this figure?

Mathematics

1 answer:

Kipish [7]3 years ago

4 0

Answer:

Area is measured in "square" units. The area of a figure is the number of squares required to cover it completely, like tiles on a floor. Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared.

Step-by-step explanation: hope this helps

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Determine the open intervals on which the graph of f(x) = x - 4cos x is concave upward or concave downward

bazaltina [42]

The graph of the function $f(x)$ is

concave upward, when $f''(x)>0;$
concave downward, when $f''(x)$

Find $f''(x):$

$f'(x)=(x-4\cos x)'=1+4\sin x;$

$f''(x)=4\cos x.$

Now:

1. when $4\cos x>0,$ the graph of the function is concave upward and this is for

$x\in \left(-\dfrac{\pi}{2}+2\pi k,\dfrac{\pi}{2}+2\pi k\right), \text{ where } k\in Z.$

2. when $4\cos x$ the graph of the function is concave downward and this is for

$x\in \left(\dfrac{\pi}{2}+2\pi k,\dfrac{3\pi}{2}+2\pi k\right), \text{ where } k\in Z.$

6 0

2 years ago

Salma and coron broomall have reached an agreed upon price of $197,000. They plan to make a 30 percent down payment and finance

Sladkaya [172]

Answer:

1. The monthly payment is $689.5

2. The total amount to be paid is

$224,580.

Step-by-step explanation:

Salsa and Corn Broom all reached an agreement upon the price of $197,000.

- The plan on making a 30 percent down payment. This implies that the will pay 0.3 × $197,000 = $59,100

This leaves them with

$197,000 - $59,100

= $137,900 to pay.

The plan on financing this remaining amount at 6 percent for 20 years.

This means they will pay

0.06 × $137,900 = $8,274 for 20 years. This translates to the payment of $8,274 × 20 = $165,480 across the 20 years.

1. The monthly payment is the yearly payment divided by 12.

Which is $8,274 ÷ 12 = $689.5

2. The total amount to be paid is

$165,480 + $59,100

= $224,580.

6 0

3 years ago

Simplify the expression 3/2 (5/3) -1 1/4 + 1/2 Given the answer as a simplified fraction. The simplified expression is a/b.

ella [17]

<h2>Hello!</h2>

The answer is:

The simplified fraction is:

$\frac{7}{4}$

To solve this problem we must remember the following:

- Addition or subtraction of fractions, we add or subtract fractions by the following way:

$\frac{a}{b}(+-)\frac{c}{d}=\frac{ad(+-)bc}{bd}$

- Product of fractions, the multiplication of fraction is linear, meaning that we should multiply the numerator by the numerator and denominator by denominator, so:

$\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}$

- Convert mixed number to fraction,

$a\frac{b}{c}=a+\frac{b}{c}=\frac{ac+b}{c}$

So, solving we have:

$\frac{3}{2}*\frac{5}{3}-1\frac{1}{4}+\frac{1}{2}=\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{3*5}{2*3} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}\\\\\frac{15}{6} -1\frac{1}{4}+\frac{1}{2}=\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}\\\\\frac{15}{6} -(1+\frac{1}{4})+\frac{1}{2}=\frac{15}{6}-(\frac{4+1}{1*4})+\frac{1}{2}\\\\\frac{15}{6}-(\frac{4+1}{4})+\frac{1}{2}=\frac{15}{6}-\frac{5}{4}+\frac{1}{2}$

$\frac{15}{6}-\frac{5}{4}+\frac{1}{2}=(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}\\\\(\frac{5}{2}-\frac{5}{4})+\frac{1}{2}=(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}\\\\(\frac{(4*5)-(2*5)}{8})+\frac{1}{2}=(\frac{20-10}{8})+\frac{1}{2}\\\\(\frac{20-10}{8})+\frac{1}{2}=(\frac{10}{8})+\frac{1}{2}\\\\(\frac{10}{8})+\frac{1}{2}=\frac{5}{4}+\frac{1}{2}\\\\\frac{5}{4}+\frac{1}{2}=\frac{(5*2)+(4*1)}{2*4}\\\\\frac{(5*2)+(4*1)}{2*4}=\frac{10+4}{8}=\frac{14}{8}\\\\\frac{14}{8}=\frac{7}{4}$

Hence, the simplified fraction is:

$\frac{7}{4}$

Have a nice day!

8 0

2 years ago

Read 2 more answers

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$

Now, we differentiate the profit function to get the marginal profit function (P'):

$P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530$

This is the marginal profit function , P'.

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

$P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194$

and

$P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268$

6 0

3 years ago

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 is the area of this figure?​

What is the area of this figure?