Compare using <, >, or =. 4 5/8

What is an equation of the tangent line at x = 4, assuming that f(4) = 3 and f '(4) = 2? (enter your answer as an equation using

Margaret [11]

The general equation for a line in the case where the slope and one point on the line are known is y-b = m(x-a), where m is the slope and (a,b) is the point.

Here f(4) = 3 corresponds to the point (4,3), and f '(4) = 2 corresponds to the slope of the tangent line at that point.

Thus the equation of the tangent line here is

y - 3 = 2(x - 4).

An alternative form of this equation would be y = 3 + 2x - 8, or

y = 2x - 5

3 0

3 years ago

PLEASE HELP ASAP TRIGONOMETRY

valentinak56 [21]

Answer:

9). x = 36.9°

10). x = 18.3°

Step-by-step explanation:

9). By applying tangent rule in the given triangle,

tan(x) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(x) = $\frac{9}{12}$

x = $\text{tan}^{-1}(\frac{3}{4})$

x = 36.87°

x = 36.9°

10). By applying sine rule in the given triangle,

sin(x) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

sin(x) = $\frac{11}{35}$

x = $\text{sin}^{-1}(\frac{11}{35})$

x = 18.32

x ≈ 18.3°

3 0

3 years ago

What is the total resistance of a parallel circuit that has three loads? Load one has a resistance of 6 ohms. Load two has a res

gizmo_the_mogwai [7]

Answer:

The total resistance of these three resistors connected in parallel is $1.7143\Omega$

Step-by-step explanation:

The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: $R_1=6\Omega$ , $R_2=3\Omega$ and $R_3=12\Omega$ .

First step: to find the source current

The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ( $R_1$ , $R_2$ and $R_3$ ).

$I_{R_1}=\frac{V_S}{R_1}$

$I_{R_2}=\frac{V_S}{R_2}$

$I_{R_3}=\frac{V_S}{R_3}$

The total current is:

$I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}$

$I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}$

The total resistance ( $R_T$ ) is the source voltage divided by the source current:

$R_T=\frac{V_S}{I_S}$

Now, replace $I_S$ by the previous expression and the total resistance would be:

$R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}$

Simplify the expression and you must get:

$R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}$

The last step is to replace the values of the resistors:

$R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega$

Thus, the total resistance of these three resistors connected in parallel is $1.7143\Omega$

4 0

3 years ago

An is mathematical sentence that compares expression that are not equal

Flura [38]

Answer:

Inequality

Step-by-step explanation:

An inequality is mathematical sentence that compares expression that are not equal.

Instead of using an equal sign = , you use an inequality symbol (>, <, ≥, ≤, ≠) with an inequality.

7 0

4 years ago

What is p(4,4) on two consecutive rolls of a number cube

Fiesta28 [93]

The probability of rolling 1 number, a four, on a 6-sided number cube, is 1/6.
On the second roll, the probability of rolling 1 number, a four, is again 1/6 (remember theoretical probability for one event does not consider previous rolls).
But the probability of rolling a four on 2 on consecutive rolls will be the probability of the first event times the probability of the second event. Think of it as rolling a four on the first time and the second time, and whenever there is "and" you need to multiply the probabilities. The probability of rolling a four on two consecutive rolls is
(1/6)*(1/6) = 1/36.

5 0

3 years ago

Compare using <, >, or =. 4 5/8 _ 4 2/3