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3 years ago

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Quincy deposits $400 in a new bank account that earns 4 simple interest per year. What is the total amount in the account after

3 years? Apply the markup or markdown to each item and then find the retail sale price of the following items. Round to two decimal places

1 answer:

Kobotan [32]3 years ago

6 0

Ÿū tj Yates tu hamase de Beas

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Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

1. Ella has 7 rolls and 6 loose medium shirts. Each shirt costs $10. What is the value of her

weqwewe [10]

Answer:

the value of her medium shirts is $60 if Ella makes 100 more shirts her new value is $600

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2 years ago

The measures of three parts of ABC are given in the diagram. What is AC, correct to two decimal places?

miskamm [114]

There is no link or photo, so no person will be able to help... sorry!

6 0

3 years ago

PLEASE HELP!!!! I will mark brainliest

strojnjashka [21]

Answer:

I think B.

Step-by-step explanation:

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3 years ago

Read 2 more answers

HELP any1 good at math?

valentina_108 [34]

Step-by-step explanation:

the equations are :-

=》d = 40m + 200

=》d = 50m

here, by equalising both equations.

( since, d = d )

=》40m + 200 = 50m

=》50m - 40m = 200

=》10m = 200

=》m = 200 ÷ 10

=》m = 20

now,

=》d = 50m

=》d = 50 × 20

=》d = 1000

6 0

2 years ago