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3 years ago

PLZ HELP ASAP SOLID GEOMETRY WORD PROBLEMS

Mathematics

1 answer:

yan [13]3 years ago

8 0

The volume of the candle initially is:
V=Ab*h
Area of the base of the cylinder: Ab=pi*r^2
pi=3.14
Radius of the base: r=4 cm
Height of the cylinder: h=6 cm

Ab=pi*r^2
Ab=3.14*(4 cm)^2
Ab=3.14*(16 cm^2)
Ab=50.24 cm^2

V=Ab*h
V=(50.24 cm^2)*(6 cm)
V=301.44 cm^3

The candle melts at a constant rate of:
r=(60 cm^3)/(2 hours)=(120 cm^3)/(4 hours)=(180 cm^3)/(6 hours)
r=30 cm^3/hour

The amount of candle melted off after 7 hours is:
A=(30 cm^3/hour)*(7 hours)
A=210 cm^3

The percent of candle that is melted off after 7 hours is:
P=(A/V)*100%
P=[(210 cm^3)/(301.44 cm^3)]*100%
P=(0.696656051)*100%
P=69.66560510%
Rounded to the nearest percent
P=70%

Answer: 70%

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Find the percent of increase from 40 gallons to 89 gallons. Round to the nearest tenth of a percent if necessary.

fredd [130]

Solution

- 89 gallons contains 40 gallons twice such that:

$89=40+40+9$

- This means that we can find at least 200% of 40 gallons in 89 gallons. This gives us what to expect.

- To get the percentage we are looking for, we should use the formula:

$\frac{\text{new}}{\text{old}}\times100\text{ \%}$

New, in this case, is 89 gallons, Old is 40 gallons.

- Thus, we can calculate the percentage as follows:

$\begin{gathered} \frac{89}{40}\times100 \\ =2.225\times100 \\ =222.5\text{ \%} \end{gathered}$

Thus, the answer is 222.5%

8 0

1 year ago

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

Which linear system of equations does the matrix represent 4 -7 -14 4 -12 4

Novosadov [1.4K]

The given matrix represent the following linear system

4x - 7y = -12
-14x + 4y = 4

Good luck!!!

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3 years ago

If f(x)= 3x squared - 2x + 1 what is f(x+2)

Crazy boy [7]

2x squared would be you final answer

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3 years ago

Sketch a quadratic function with the given characteristics.

xeze [42]

Answer:

See photo below

Add arrows to the two ends of the parabola.

Step-by-step explanation:

To sketch this quadratic function, we to connect three dots: the two roots and a vertex.

The given roots are -1 and 1.

Draw two dots at the x-intercepts, which are (-1, 0) and (1, 0).

Vertex dot: V (x, y)

The vertex x-coordinate always in the middle of the two roots. The middle of -1 and 1 is 0. That's the same as the y-axis.

V (0, y)

Since the function increases when x < 0, the parabola will open up.

We read from left to right. The greater numbers are towards the top of the page.

You can put the vertex anywhere on the y-axis that is below the x-axis.

7 0

3 years ago