A circle has a diameter of 12 inches. What is its area in terms of π?<br> help please

in a study 44 of adults questioned reported that their health was excellent. a researcher wishes to study the health of people l

dlinn [17]

Where's the question? We have some data...but no question

6 0

3 years ago

a boat travels upstream on the allegheny river for 2 hours. the return trip only takes 1.7 hours because the boat travels 2.5 mi

Gre4nikov [31]

To solve this we are going to use the speed equation: $S= \frac{d}{t}$
where
$S$ is speed
$d$ is distance
$t$ time

We know from our problem that the upstream trip takes 2 hours, so $t_{u}=2$ . We also know that the downstream trip takes 1.7 hours, so $t_{d}=1.7$ . Notice that the distance of both trips is the same, so we are going to use $d$ to represent that distance.
Now, lets use our equation to relate the quantities:

For the upstream trip:
$S_{u}= \frac{d}{t_{u} }$
$S_{u}= \frac{d}{2}$ equation (1)

For the downstream trip:
$S_{d}= \frac{d}{t_{d} }$
$S_{d}= \frac{d}{1.7}$ equation (2)

We know that the boat travels 2.5 miles per hour faster downstream, so the speed of the boat upstream will be the speed of the boat downstream minus 2.5 miles per hour:
$S_{u}=S_{d}-2.5$ equation (3)

Replacing (3) in (1):
$S_{u}= \frac{d}{2}$
$S_{d}-2.5= \frac{d}{2}$ equation (4)

Solving for $d$ in equation (2):
$S_{d}= \frac{d}{1.7}$
$d=1.7S_{d}$ equation (5)

Replacing (5) in (4):
$S_{d}-2.5= \frac{d}{2}$
$S_{d}-2.5= \frac{1.7S_{d}}{2}$
$2(S_{d}-2.5)=1.7S_{d}$
$2S_{d}-5=1.7S_{d}$
$0.3S_{d}=5$
$S__{d}= \frac{5}{0.3}$
$S_{d}= \frac{50}{3}$ equation (6)

Replacing (6) in (5)
$d=1.7S_{d}$
$d=1.7( \frac{50}{3} )$
$d= \frac{85}{3}$ miles

We can conclude that the boat travel $\frac{85}{3}$ , which is approximately 28.3 miles, in one way.

5 0

3 years ago

Which equation is TRUE?

lubasha [3.4K]

The answer is C as 4x+7 = 4x+7

8 0

3 years ago

A rectangle has one of its sides on the x-axis and corners of the opposite side on the piece of the parabola y = 12 − x 2 above

saw5 [17]

Answer:

$A(x) = 24x - 2x^3$

Step-by-step explanation:

first we need to visualize what the question is trying to represent

A rectangle with one of its sides on the x-axis
The corners of the opposite two sides of the rectangle intersect with a parabola

the equation of the parabola is $y = 12 - x^2$

the equation of the parabola can also be written as

$y = -x^2 + 12$ this shows that the parabola has a $\cap$ shape and the turning point (peak) lies at the y-axis at y = 12. The parabola is symmetric along the y-axis!

right corner of the lower side of the rectangle has the coordinates (x,0)

we can also say that the coordinates of the lower left side are (-x,0). This is because the parabola is symmetric along the y-axis.

Solution:

We have enough information to express the sides lengths of the rectangle:

1) Lower side, (L)

We'll name the lower side 'L' and since this is a rectangle, this side length is the same as the upper side.

The lower side coordinates are (-x,0) and (x,0). Hence the side length is the difference of the two coordinates.

$L = x-(-x)$

$L = 2x$

2) The Left and Right side have the same height (H)

since the the lower side is on the x-axis (y=0), the only side moving is the upper one, i.e the coordinates of the upper corners are (0,y) where $y = 12- x^2$ . The side length of either the left or right sides is $y$