All categories

3 years ago

Becky's ship is 43 miles west all the harbor.

Mathematics

1 answer:

pishuonlain [190]3 years ago

5 0

Answer:

Clyde is 49.74 away from the harbor

Step-by-step explanation:

Here in this question, we are interested in knowing the distance of Clyde from the harbor.

The key to answering this question is having a correct diagrammatic representation. Please check attachment for this.

We can see we have the formation of a right angled triangle with the distance between Clyde’s ship and the harbor the hypotenuse.

To calculate the distance between the two, we shall employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides.

Let’s call the distance we want to calculate h.

Mathematically;

h^2 = 25^2 + 43^2

h^2 = 625 + 1849

h^2 = 2474

h = √2474

h = 49.74 miles

You might be interested in

One man is three times as old as another. Fifteen years ago the first was six times as old as the second. Find their ages now.

alex41 [277]

Answer:

error

Step-by-step explanation:

4 0

3 years ago

Merlin worked these hours during the week: 4.5, 8.75, 9.5, 10, and 4.25 hours. What was his gross pay for the week, if he makes

mart [117]

The answer is $361.86

7 0

3 years ago

Read 2 more answers

liubo4ka [24]

<u>Answer:</u>

3/5

<u>Step-by-step explanation:</u>

We are to find the similarity ratio of a cube with volume $729 m^3$ to a cube with volume $3375 m^3$ .

We know the formula for the ratio of two cubes:

$\frac{V_1}{V_2} =k^3$

where $k$ is the similarity ratio of the two cubes.

Substituting the given values in the formula to find $k$ :

$k^3 = \frac {729} {3375}$

$k^3 = \frac {27} {125}$

$k^3 = (\frac {27} {125})^3$

$k=\frac{3}{5}$

Therefore, the similarity ratio of the two cubes is 3/5.

8 0

3 years ago

Read 2 more answers

Is this the correct answer?

Step2247 [10]

Step-by-step explanation:

Close. You correctly set up the integrals. When integrating e²ˣ:

∫ e²ˣ dx

½ ∫ 2 e²ˣ dx

½ e²ˣ + C

So the coefficient should be ½, not 2.

[eˣ − ½ e²ˣ]₋₁⁰ + [½ e²ˣ − eˣ]₀¹

[(e⁰ − ½ e⁰) − (e⁻¹ − ½ e⁻²)] + [(½ e² − e) − (½ e⁰ − e⁰)]

1 − ½ − e⁻¹ + ½ e⁻² + ½ e² − e − ½ + 1

-e⁻¹ + ½ e⁻² + ½ e² − e + 1

8 0

3 years ago

Read 2 more answers

In Exercises 3–10, use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent varia

sashaice [31]

I'll use subscript notation for brevity, i.e.

$\dfrac{\partial f}{\partial x}=f_x$

$f(x,y,z)=xy+z^2\implies\begin{cases}f_x=y\\f_y=x\\f_z=2z\end{cases}$

$x(r,s)=s^2\implies\begin{cases}x_r=0\\x_s=2s\end{cases}$

$y(r,s)=2rs\implies\begin{cases}y_r=2s\\y_s=2r\end{cases}$

$z(r,s)=r^2\implies\begin{cases}z_r=2r\\z_s=0\end{cases}$

By the chain rule,

$f_r=f_xx_r+f_yy_r+f_zz_r=2xs+4zr=2s^3+4r^3$

$f_s=f_xx_s+f_yy_s+f_zz_s=2ys+2xr=6rs^2$

$x(r,s,t)=r+s-2t\implies\begin{cases}x_r=1\\x_s=1\\x_t=-2\end{cases}$

$y(r,s,t)=3rt\implies\begin{cases}y_r=3t\\y_s=0\\y_t=3r\end{cases}$

$z(r,s,t)=s^2\implies\begin{cases}z_r=0\\z_s=2s\\z_t=0\end{cases}$

By the chain rule,

$f_r=f_xx_r+f_yy_r+f_zz_r=y+3xt=3rt+3r+3s-6t^2$

$f_s=f_xx_s+f_yy_s+f_zz_s=y+4zs=3rt+4s^3$

$f_t=f_xx_t+f_yy_t+f_zz_t=-2y+3xr=3r+3s-12rt$

8 0

2 years ago