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3 years ago

Can yall help me pls?

Mathematics

1 answer:

vlada-n [284]3 years ago

6 0

Figure A maps to figure B with a scale factor of 2/3 -> Every single side of figure B equal to 2/3 of its corresponding side on triangle A.

So, we can find x by taking 10.5 x 2/3 = 7

-> x = 7

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What is the inverse of y=^x3

Rashid [163]

Answer:

Inverse of y=x^3 is f^-1(x) = ∛x

Step-by-step explanation:

We need to find the inverse of y=x^3

Step 1:

Interchange the variables:

x= y^3

Step 2: Now solve to find the value of y

=> y^3 = x

taking cube root on both sides of the equation

∛y^3 = ∛x

y=∛x

Step 3: Replace y with f^-1(x)

f^-1(x) = ∛x

So inverse of y=x^3 is f^-1(x) = ∛x

4 0

3 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

3 years ago

(x+5)(x+1)+(x+5)(x+8)

gtnhenbr [62]

Answer:

2x² + 19x + 45

Step-by-step explanation:

(x + 5)(x + 1) + (x + 5)(x + 8) ← expand both sets of factors using FOIL

= x² + 6x + 5 + x² + 13x + 40 ← collect like terms

= 2x² + 19x + 45

5 0

3 years ago

Graph the line with slope -2 passing through the point (1,-4)

lorasvet [3.4K]

the equation for the line is:

y = -2( x + 1 )

4 0

3 years ago

the graph below shows a linear relationship. The points shown have a whole number. Which function models the linear relationship

Nitella [24]

Answer:

y=2/3 x+2

Step-by-step explanation:

The equation of a linear graph is given as

y=mx+c

m is the slope of the line while c is the y intercept

As shown from the graph, the y-intercept is 2

The slope can be calculated by diving the height by the length:

2/3

y=2/3 x+2

3 0

4 years ago