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3 years ago

Use the triangle below and the given trigonometric ratio to determine which angle in the triangle below is

Mathematics

1 answer:

MrRa [10]3 years ago

7 0

Answer: Angle 2

The 7.5 cm side is opposite angle 2, so opposite = 7.5
The 18 cm side is adjacent to angle 2, so adjacent = 18

Therefore, tan(angle 2) = opposite/adjacent = 7.5/18
Replace "angle 2" with "A" and we have tan(A) = 7.5/18

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IRINA_888 [86]

Answer:

$- \frac{1}{2} {n}^{2} + 18 = 0 \\ - \frac{1}{2} {n}^{2} = - 18 \\ {n}^{2} = - 18 \times - 2 \\ {n}^{2} = 36 \\ n = + - \sqrt{36} \\ n = + - 6$

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3 years ago

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For the quadratic function shown below, find (a) the direction of the opening, (b) the vertex, and (c) the axis of symmetry.

Angelina_Jolie [31]

Answer:

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2 years ago

Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

$k=0$

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

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2 years ago

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maria [59]

Number 5 is 135 because angle 3 is congruent to 7 and 7 is 135

5 0

3 years ago

Please help me with this question

mihalych1998 [28]

Answer:

John and Pam are paid $8.5 for each hour worked. John's share of the money is $29.75.

Step-by-step explanation:

Let x = the hourly salary. John worked for 3.5 hrs, and Pam for two. We can represent this using the equation:

3.5x + 2x = 46.75, where the coefficients equals the amount of hours.

Let's solve for x!

5.5x=46.75

x = 46.75/5.5 = 17/2 = 8.5

John and Pam are paid 8.5 dollars per each hour worked.

To figure out John's share of the money, we will multiply the wage by the hours he worked.

8.5 x 3.5 = 29.75

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3 years ago