0.002 is 1/100of what decimal?

Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.

KATRIN_1 [288]

Answer:

The translation is $1$ unit to the left and $5$ units down

Step-by-step explanation:

we have

$g(x)=\sqrt{x+1}-5$

$f(x)=\sqrt{x}$ -----> parent function

we know that

The transformation

f(x)-----> g(x) has the following rule

$(x,y)-------> (x-1,y-5)$

That means

The translation is $1$ unit to the left and $5$ units down

see the attached figure to better understand the problem

6 0

2 years ago

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Marginal cost At a certain factory the marginal cost is 3(q-4)^2 dollars per unit when the level of production is q units.

viktelen [127]

Answer:

a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k

where k is a constant.

The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k

C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k

Thus:

C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH

(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170

7 0

2 years ago

Match the following items.

Margarita [4]

Answer:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

Step-by-step explanation:

Given:

$\angle DBC=40$ °

From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

$m\textrm{ arc CD}=2\times \angle DBC\\m\textrm{ arc CD}=2\times 40=80$

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°,

$m\angle BCD=90$

From the Δ BCD, which is a right angled triangle,

$m\angle DBC+m\angle BDC=90\textrm{ (right angled triangle)}\\40+m\angle BDC=90\\m\angle BDC=90-40=50$

Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.

Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles $m\angle DBC\textrm{ and }m\angle BDC$ and EF is a tangent to the circle at point C.

Therefore, $m\angle DCF=m\angle DBC=40\\m\angle ECB=m\angle BDC=50$

Again, using the same theorem as above,

$m\angle DCF=50\\\therefore m\textrm{ arc BC}=2\times m\angle DCF=2\times 50=100$

Hence, all the angles are as follows:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

6 0

2 years ago

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.