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sergeinik [125]
3 years ago
5

In kite WXYZ, mZWY = 41° and mXYW = 11° What is mWZY?

Mathematics
1 answer:
olchik [2.2K]3 years ago
8 0

Answer:

128°

Step-by-step explanation:

In kite WXYZ, WY and XZ are longer and smaller diagonals respectively.

Longer diagonal bisects the opposite angles.

\therefore m\angle ZYW =m\angle XYW

\because m\angle  XYW = 11\degree... (given)

\therefore m\angle ZYW =11\degree

In\: \triangle WYZ

m\angle ZYW + m\angle ZWY + m\angle WZY=180\degree

11\degree + 41\degree+ m\angle WZY=180\degree

52\degree+ m\angle WZY=180\degree

m\angle WZY=180\degree - 52\degree

\purple{\bold {m\angle WZY=128\degree}}

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Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
anzhelika [568]
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
V_{0} =(1+ i_{a} ) ^{1}
Where
V_{0} = initial investment.
i_{a} = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
V_{0} =(1+ i_{q} ) ^{4}
Where
V_{0} = initial investment.
i_{q} = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
(1+ i_{a} )=(1+ i_{q} ) ^{4}
Notice that we are not using the initial investment V_{0} since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
(1+0.07)=(1+ i_{q} ) ^{4}
1.07=(1+ i_{q} ) ^{4}
\sqrt[4]{1.07} =1+ i_{q}
 i_{q} = \sqrt[4]{1.07} -1
i_{q} =0.017
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.


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