A logarithmic function is the inverse of an exponential function. <br> always, sometimes, or never?

The current of a river is 4 miles per hour. A boat travels to a point 30 miles upstream and back in 4 hours. What is the speed o

Maurinko [17]

16 mph is the answer I found after doing the work

7 0

3 years ago

Please help with the following question

sasho [114]

We have:
The generic equation of the line is: y-yo = m (x-xo)
The slope is:
m = (y2-y1) / (x2-x1)
m = (- 2-0) / (3-0)
m = -2 / 3
We choose an ordered pair
(xo, yo) = (0, 0)
Substituting values:
y-0 = (- 2/3) (x-0)
Rewriting:
y = (- 2/3) x
Answer:
The equation of the line is:
y = (- 2/3) x

5 0

3 years ago

In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random,

n200080 [17]

Answer: 0.75

Step-by-step explanation:

A survey of 364 children aged 19-36 months found that 91 liked to eat potato chips.

Total children surveyed= 364

Those that like to eat potato chips= 91

Those that don't like to eat potato chips= 364 - 91 = 273

Probability that the child chosen doesn't like to eat potato chips will be children that don't like to eat potato chips divided by total number of children surveyed.

= 273/364

= 0.75

4 0

3 years ago

Work out the volume of a prism with an area of 10m squared and a length of 8m

Jobisdone [24]

Is it 80 m I think that’s the answer

4 0

4 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

A logarithmic function is the inverse of an exponential function. always, sometimes, or never?