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3 years ago

5

Logan wants to have $130,000 to pay for a surgery on his retractable forearm claws in 30 months. If he can invest money in an ac

count right now that will give him 7.5% interest compounded monthly, how much would he have to
invest now to end up with the amount needed for the surgery later on?

1 answer:

dangina [55]3 years ago

8 0

Answer: $107,836.69 or about $107,837 (to the nearest dollar)

Step-by-step explanation:

Formula to the accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :

$A=P(1+\dfrac{r}{12})^{t}$

As per given , A = $130,000

r= 7.5% = 0.075

t= 30 months

Now,

$130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69$

Hence he need to invest $107,836.69 .

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The perimeter of the flag is 2080 ft what is the flags width and length of the length is 420 ft greater than the width

hram777 [196]

Answer:

The length of the flag is 730 ft and the width is 310 ft

Step-by-step explanation:

<u><em>The correct question is</em></u>

The perimeter of the flag is 2080 ft what is the flags width and length <u>if</u> the length is 420 ft greater than the width

Let

L ----> the length of the flag

W ---> the width of the flag

we know that

The perimeter of the flag (rectangle) is equal to

$P=2(L+W)$

we have

$P=2,080\ ft$

so

$2,080=2(L+W)$

$1,040=L+W$ ----> equation A

$L=W+420$ ---> equation B

Solve the system by substitution

substitute equation B in equation A

$1,040=(W+420)+W$

solve for W

$1,040=2W+420$

$2W=1,040-420$

$2W=620$

$W=310\ ft$

<em>Find the value of L</em>

$L=W+420$ ----> $L=310+420=730\ ft$

therefore

The length of the flag is 730 ft and the width is 310 ft

5 0

2 years ago

3 regions are defined in the figure find the volume generated by rotating the given region about the specific line

anastassius [24]

The volume generated by rotating the given region $R_{3}$ about OC is $\frac{4}{g} \pi$

<h3>Washer method</h3>

Because the given region ( $R_{3}$ ) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

$y=2(x)^{\frac{1}{4} }$

$x=(\frac{y}{2} )^{4}$

$y=2x$

$x=\frac{y}{2}$

$\int\limits^a_b {\pi } \, (R_{o^{2} } - R_{i^{2} } ) dy$

$R_{o} = x = \frac{y}{2}$

$R_{i} = x= (\frac{y}{2}) ^{4}$

$a=0, b=2$

$v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} ) dy$

$v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy$

$v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]$

$v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi$

A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095

6 0

1 year ago

What is the equation of the line in slope-intercept form?

lutik1710 [3]

The slope is negative and is -16 / 8 = -2

The y intercept is at y = 16

General form is y = mx + c
m = -2 and c = 16 so we have :-

y = -2x + 16 Answer

3 0

3 years ago

Polygon ABCD is a rectangle. What is its area? Round your answer to the

galben [10]

9514 1404 393

Answer:

26 square units

Step-by-step explanation:

Counting grid squares on the graph, we see that segment AB is the hypotenuse of a right triangle with legs 2 and 3. Its length is ...

AB = √(2²+3²) = √13

We can also see that the adjacent longer sides are twice this length, each being the hypotenuse of a triangle that is 6 wide and 4 high.

AC = √(6² +4²) = √52 = 2√13

Then the area is ...

A = LW

A = (2√13)(√13) = 2·13 = 26 . . . square units

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2 years ago

Please help ill give you points

UkoKoshka [18]

Yes, it is a function

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2 years ago

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