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lidiya [134]
3 years ago
9

Q # 1 Graph the functionY = |X + 2| - 3

Mathematics
2 answers:
Novay_Z [31]3 years ago
8 0
Do you have anymore pictures?
Svetllana [295]3 years ago
4 0
First of all we know the Absolute Value Function that is:

\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right.

This is called the Parent Function <em>of the Absolute Value Function.</em>

From the equation:

y=\left | x+2 \right |-3

The term:

\left | x+2 \right |

means that the the Parent Function is <em>shifted</em> two units <em>to the left</em>.

On the other hand, the term:

-3

means that the function \left | x+2 \right | is <em>shifted</em> three units <em>downward. </em>So the result is the graph shown below

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Natali5045456 [20]
Not 2 I think it’s a carrot
7 0
3 years ago
Read 2 more answers
Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv
Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

f_x = ycos(xy)

f_y = xcos(xy) - ze^{yz}

f_z = -ye^{yz}

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)  

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)

Where, again, the constant of integration depends on Z.

As a result,

f(x,y,z) = cos(xy) - e^{yz} + K(z)

if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0
3 years ago
100 POINTS
IgorLugansk [536]

Answer:

Step-by-step explanation:

90.9^2 - 21.2^2 = b^2

8,262.81 - 449.44 = b^2

b = 88.39326897450959189749074160142

7 0
3 years ago
there is a beaker of 3.5% acid solution and a beaker of 6% acid solution in the science lab. Mr. Larson needs 200ml of 4.5% acid
disa [49]
Below are the choices:

A. 80 mL of the 3.5% solution and 120 mL of the 6% solution 

<span>B. 120 mL of the 3.5% solution and 80 mL of the 6% solution </span>

<span>C. 140 mL of the 3.5% solution and 60 mL of the 6% solution </span>

<span>D. 120 mL of the 3.5% solution and 80 mL of the 6% solution
</span>
Let fraction of 3.5% in final solution be p. 

<span>p * 3.5 + (1 - p) * 6 = 4.5 </span>

<span>3.5p + 6 - 6p = 4.5 </span>

<span>2.5p = 1.5 </span>

<span>p = 3/5 </span>

<span>3/5 * 200 = 120 </span>

<span>Therefore the answer is B. 120 ml of 3.5% and 80 ml of 6%.</span>

6 0
3 years ago
QUESTION 25 The area of the triangle shown is 54cm. The ratio of side to side is 3:4 What is the length of side in centimetres?
AlexFokin [52]

Answer:

15

Step-by-step explanation:

Diagram would be helpful.... I am assuming this is a right triangle with legs ratio 3:4

5 0
2 years ago
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