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3 years ago

Please help!

Mathematics

1 answer:

Mrac [35]3 years ago

3 0

Answer:

Equilateral triangles are sometimes

acute triangles.

Scalene triangles are never

acute triangles.

Right triangles are never

acute triangles.

Obtuse triangles are always

isosceles triangles.

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How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 3 years? The account pays 5.9

ra1l [238]

We are asked to determine the present value of an annuity that is paid at the end of each period. Therefore, we need to use the formula for present value ordinary, which is:

$PV_{ord}=C(\frac{1-(1+i)^{-kn}}{\frac{i}{k}})$

Where:

$\begin{gathered} C=\text{ payments each period} \\ i=\text{ interest rate} \\ n=\text{ number of periods} \\ k=\text{ number of times the interest is compounded} \end{gathered}$

Since the interest is compounded semi-annually this means that it is compounded 2 times a year, therefore, k = 2. Now we need to convert the interest rate into decimal form. To do that we will divide the interest rate by 100:

$\frac{5.9}{100}=0.059$

Now we substitute the values:

$PV_{ord}=4000(\frac{1-(1+0.059)^{-2(3)}}{\frac{0.059}{2}})$

Now we solve the operations, we get:

$PV_{\text{ord}}=39462.50$

Therefore, the present value must be $39462.50

8 0

1 year ago

Newton's law of cooling is:

Mnenie [13.5K]

Answer:

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

$\frac{dw}{w} =-k dt$

IF we integrate both sides we got:

$ln |w| = -kt +C$

If we apply exponential in both sides we got:

$w = e^{-kt} *e^c$

And if we replace w = u-T we got:

$u(t)= T + C_1 e^{-kt}$

We can also express the solution in the following terms:

$u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}$

For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

$u(t) = (70-11) e^{-0.15t} +11$

And if we want that the temperature would be 32F we can solve for t like this:

$32 = 59 e^{-0.15 t} +11$

$21=59 e^{-0.15 t}$

$\frac{21}{59} = e^{-0.15 t}$

If we apply natural logs on both sides we got:

$ln (\frac{21}{59}) =-0.15 t$

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

7 0

3 years ago

3x^2- 10x - 8 please help with this

fgiga [73]

So why I now yes when she where it go to get the stuff

8 0

3 years ago

Read 2 more answers

Which triangle can be drawn as it is described?

yawa3891 [41]

Answer:

An isosceles triangle with angles measuring 20° and 80°

Step-by-step explanation:

Verify each case

case A) Scalene triangle with angles measuring 110° and 35°

Is not a scalene triangle because the third angle is (180-110°-35°=35°), therefore is an isosceles triangle

case B) An obtuse triangle with sides measuring 5,10 and 15

we know that

Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so in this problem

$5+10> 15$ -----> is not true

therefore

with these measurements can not draw any triangle

case C) An isosceles triangle with angles measuring 20° and 80°

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem the third angle is (180-20°-80°=80°),

therefore

is an isosceles triangle and can be drawn as it is described

case D) An acute triangle with sides measuring 7,4 and 2

we know that

Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so in this problem

$4+2> 7$ -----> is not true

therefore

with these measurements can not draw any triangle

8 0

3 years ago

Evaluate if x=5 what is x2 + 10 =

Minchanka [31]

Answer:

${x}^{2} + 10 \\ \\ {(5)}^{2} + 10 \\ 25 + 10 = 35$

I hope I helped you^_^

8 0

2 years ago

Read 2 more answers