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Nezavi [6.7K]
3 years ago
12

4x + 1 = 2x - 5 ; x =

Mathematics
1 answer:
jenyasd209 [6]3 years ago
8 0

Answer:

x=-3

Step-by-step explanation:

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Derek found a function that approximately models the population of iguanas in a reptile garden, where x represents the number of
serious [3.7K]

Answer:

i(x)=12 \times (1+\frac{0.9}{12})^{12x} and growth rate factor is 0.075

Step-by-step explanation:

The function that models the population of iguanas in a reptile garden is given by i(x)=12 \times (1.9)^{x}, where x is the number of years.

Since, i(x)=12 \times (1.9)^{x}

i.e. i(x)=12 \times (1+0.9)^{x}.

Therefore, the monthly growth rate function becomes,

i.e. i(x)=12 \times (1+\frac{0.9}{12})^{x \times 12}.

i.e. i(x)=12 \times (1+\frac{0.9}{12})^{12x}.

Hence, the monthly growth rate is i.e. i(x)=12 \times (1+\frac{0.9}{12})^{12x}.

Also, the growth factor is given by \frac{0.9}{12} = 0.075.

Thus, the growth factor to nearest thousandth place is 0.075.

4 0
3 years ago
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
PUZZLE #2
Maksim231197 [3]
I have no clue I don’t understand this
4 0
2 years ago
Alana has 100 mL of water in her water bottle. She needs to share it with 3 other students so that all 4 of them have the same a
elena-14-01-66 [18.8K]

Answer:

each person (including Alana) gets 25mL of water

Step-by-step explanation:

since there is 4 ppl, and 100mL of water, you divide 100/4. Therefore, each person gets 25mL of water:)

6 0
3 years ago
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What are the like terms in the expression 8+x²-4x³+5x+2x²​
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X^2 and 2x^2 are alike.
They both have variables and the same exponent
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