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Ira Lisetskai [31]

2 years ago

15

Alexis invests $475 in a bank account that earns 1.25% interest compounded annually. Which function models the growth of her inv

estment over x years?

1 answer:

olchik [2.2K]2 years ago

8 0

Answer: The function that modes this situation would be: y = 475(1 + .0125)^x.

This is an example of an exponential equation. These equations are always in the form y = ab^x.

The a value is the starting value. The b value is the interest rate. The x value is the number of years.

The only thing to be careful about is the rate. We are adding 1.25% or 0.125. Make sure that you are adding 1 whole to the 1.25% and don't just use 0.125.

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Please answer all of them need this

VikaD [51]

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area= $\frac{1}{2}\times 218.5\times 224.5\times sin(58.2^0)\approx20845$ $m^2$

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the $\Delta ABC$ given to us.

Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

$\frac{17}{Sin(25^0)}=\frac{a}{Sin(45^0)}$

This gives $a$ to be:

$a\approx28.44$

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

$AC=\sqrt{(AB)^2+(BC)^2-2(AB)(BC)\times Cos(\angle B)}$

$\therefore AC=\sqrt{(172.20)^2+(111.64)^2-2(172.20)(111.64)\times Cos(177.29^0)}\approx283.8$ miles.

Thus, Option D is the answer.

8 0

2 years ago

Read 2 more answers

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

3 0

2 years ago

Lian invested an amount of money at an interest rate of 5.2% per year.

Zigmanuir [339]

Answer:

$6500

Step-by-step explanation:

Let the amount of money invested by Lian be $x

Interest rate = 5.2% per year

interest earned in first year will be 5.2% of amount of money invested by Lian .

(note: since in first year there will be no interest accrued on interest so interest for first year is simple interest )

interest earned in one year if money invested by Lian is $x

= 5.2% of $x (1)

But , it is given in one year she received interest of 338 dollars

so, 338 dollars must be equal to 5.2% of $x

equating $338 with 5.2% of $x , we have

5.2% of x = 338

=> (5.2/100) * x = 338

=>5.2 x = 338*100

=> x = 33800/5.2 = 6500.

Thus, amount of money Lian invested is $6500.

7 0

1 year ago

The typical college freshman spends an average of μ=150 minutes per day, with a standard deviation of σ=50 minutes, on social me

Rashid [163]

Answer: The proportion of students spending at least 2 hours on social media equals 0.7257 .

Step-by-step explanation:

Given : The typical college freshman spends an average of μ=150 minutes per day, with a standard deviation of σ=50 minutes, on social media.

The distribution of time on social media is known to be Normal.

Let x be the number of minutes spent on social media.

Then, the probability that students spending at least 2 hours (2 hours = 120 minutes as 1 hour = 60 minutes) on social media would be:

$P(x\geq120)=1-P(x$

Hence, the proportion of students spending at least 2 hours on social media equals 0.7257 .

4 0

2 years ago

The point (Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction)

Ierofanga [76]

Answer:

$\cot(x) = - 1 \: and \: \cos(x) = - \frac{ \sqrt{2} }{2}$

Step-by-step explanation:

The given point is :

$( - \frac{ \sqrt{2} }{2}, \frac{ \sqrt{2} }{2})$

This point is in the second quadrant.

This means:

$\cos(x) = - \frac{ \sqrt{2} }{2}, \sin(x) = \frac{ \sqrt{2} }{2})$

Cotangent is cosine/sine

$\cot(x)=\frac{ \frac{ \sqrt{2} }{2} }{ - \frac{ \sqrt{2} }{2} } = - 1$

5 0

2 years ago

Read 2 more answers