A small pool is leaking water from a hole. After 2 1/2 minutes, 3 1/2 liters of water leaked out.

The hike to the campsite is 4 km long if we take turns carrying the tents for 4/5 of a kilometer meter how many times will the t

andrey2020 [161]

Total Distance = 4km

Each person takes 4/5km

Calculate the number of times the tent has to change hands:

$4 \div \dfrac{4}{5} = \dfrac{4}{1} \times \dfrac{5}{4} = \dfrac{5}{1} = 5$

$\boxed {\boxed { \text {Answer: The tent will have to change hands 5 times.} } \\ \\ }$

6 0

2 years ago

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Peter placed an order with an online nursery for 6 apple trees and 5 azaleas and the order came to $147. The next order for 3 ap

Setler79 [48]

Answer:

$243

Step-by-step explanation:

The first order you made :

6 apple

5 azaleas

And total cast was:

$147

The secant order you order was:

3 apples

4 azaleas

And total cast was:

$96

The total cast of both orders is:

$243

5 0

2 years ago

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A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed

Olegator [25]

Answer:

The length of shadow decrease at 0.48 m/s.

Step-by-step explanation:

The distance of man from building = x

Thus initially, x = 12

It is given that dx/dt= -1.3 m/s

Let the shadow height = Y

Now solve for the $dy/dt$ when x=4

from the diagram (triangle) it can be seen similar triangles with similar base/height ratios.

$\frac{2}{12-x} = \frac{y}{12} \\Y = \frac{24}{12 - x} \\ \frac{dy}{dt} = \frac{24}{(12-x)^{2}} \times \frac{dx}{dt} \\at x=4, dy/dt \ becomes: \\\frac{24}{(12-4)^2} \times -1.3 \\= -0.48 m/s$

8 0

3 years ago

Lol help What is 3.5 × 1.2 =

Aleks04 [339]

Answer:

4.2

Step-by-step explanation:

3.5 x 1.2 = 4.2

7 0

2 years ago

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The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago