MATHEMATICS HIGH SCHOOL

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Answers

Answer 1

Answer:

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(MN)/(MP)\n \nMN=MP\sin \angle P\n \nMN=4\sin 21^(\circ)\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}=(MH)/(MN)\n \nMH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^(\circ)-m\angle P=90^(\circ)-21^(\circ)=69^(\circ)$

Thus,

$MH=1.43\cos 69^(\circ)\approx 0.51\ cm$

Related Questions

How to solve this problem?
"12 cool dinits and 10 pizza15 cool daries and 5 pizzas. 20 cool driris and 5 pirzer 2 2e cool diniks and simal"
(4/3)d^2+5=2a). d= -2/3 or d= 2/3b). d= -3/2 or d= 3/2c). d= -36 or d=36d). NO REAL SOLUTION
Find d^4y/dx^4 given dy/dx = x^4 + x^3 + x^2 + x
Ted throws an object into the air with an initial vertical velocity of 54 feet per second from a platform that is 40 feet above the ground. About how long will it take the object to hit the ground?

Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, the principal of the loan will be $19,450, and Dahlia will make monthly payments. Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly, and assesses a service charge of $925.00. Bank Q offers a ten-year loan with an interest rate of 5.5%, compounded monthly, and assesses a service charge of $690.85. Which loan will have the greater total finance charge, and how much greater will it be? Round all dollar values to the nearest cent.a.
Loan Q’s finance charge will be $83.73 greater than Loan P’s.
b.
Loan Q’s finance charge will be $317.88 greater than Loan P’s.
c.
Loan P’s finance charge will be $20.51 greater than Loan Q’s.
d.
Loan P’s finance charge will be $234.15 greater than Loan Q’s.

Answers

To solve this, we are going to use the loan payment formula: $P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

where

$P$ is the payment

$PV$ is the present debt

$r$ is the interest rate in decimal form

$n$ is the number of payments per year

$t$ is the time in years

For Bank P

We know from our problem that the the principal of the loan will be $19,450, so $PV=19450$ . We also know that Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly , so $t=9$ and $r=(5.8)/(100) =0.058$ . Since Dahlia will make monthly payments, and a there are 12 months in a year, $n=12$ . Lets replace the values in our formula:

$P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

$P= ( (0.058)/(12)(19450))/(1-(1+ (0.058)/(12))^(-(12)(9)) )$

$P=231.59$

Now we know that the monthly payment of Dahlia is $231.59. Since we know that she is going to make 12 monthly payments for 9 years, we can calculate the future value of the loan multiplying the amount of the monthly payments ($231.59) by the number of monthly payments (12) by the number of years (9):

$FV=(231.59)(12)(9)$

$FV=25011.72$

Now we know that she is is going to pay $25,011.72 for her loan. Finally, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,011.72), and then, we are going to add the service charge ($925.00):

$FinanceCharge=(25011.72-19450)+925$

$FinanceCharge=6486.72$

The total finance charge of bank P is $6,486.72

For Bank Q

We are going to repeat the same procedure as before.

$P=19450$ , $r=(5.5)/(100) =0.055$ , $n=12$ , and $t=12$ . Lets replace the values in our formula:

$P= ( (0.055)/(12)(19450))/(1-(1+ (0.055)/(12))^(-(12)(10)) )$

$P=211.08$

Now that we have our monthly payment, we can calculate the future value of the loan multiplying the amount of the monthly payments ($211.08) by the number of monthly payments (12) by the number of years (10):

$FV=(211.08)(12)(10)$

$FV=25329.6$

Just like before, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,329.6), and then we are going to add the service charge ($690.85):

$FinanceCharge=(25329.6-19450)+690.85$

$FinanceCharge=6570.45$

The total finance charge of bank Q is $6570.45

Notice that the finance charge of ban Q is greater than the finance charge of bank P, so we are going to subtract the finance charge of bank Q from the finance charge of bank P:

$6570.45-6486.72=83.73$

We can conclude that Loan Q’s finance charge will be $83.73 greater than Loan P’s. Therefore, the correct answer is a.

Answer:

a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.

Step-by-step explanation:

Given that 23°=√k,determine the value of each of the following in terms of k,without using a calculator1.sin203°
2.cos23°
3.tan(-23°)
Please
Answer any question you know

Answers

Hello,

In order to exist ,k>=0

1) sin (180°+x)=-sin (x) ==>sin(203°)=-√k

2) cos² x +sin² x=1==>cos x=√(1+sin² x)=√(1+k)

3)tan (-x)=-tan (x) =-sin (x)/cos (x) =- √k/√(1+k)=√(k/(1+k))

What are the zeros of the function below? Check all that apply. F(x) = x(x+7)(x+2)/(x-4)(x+4)

Answers

The zeros of a function are the values of x that equates the function to 0

The zeros of the function are: 0, -7 and -2

The function is given as:

$\mathbf{f(x)= (x(x + 7)(x + 2))/((x - 4)(x + 4))}$

Equate to 0

$\mathbf{ (x(x + 7)(x + 2))/((x - 4)(x + 4)) = 0}$

Cross multiply

$\mathbf{ x(x + 7)(x + 2) = 0}$

Split

$\mathbf{ x= 0\ or\ (x + 7) = 0\ or\ (x + 2) = 0}$

Solve for x

$\mathbf{ x= 0\ or\ x = -7\ or\ x = -2}$

Hence, the zeros of the function are:

F. 0

D. -7

C. -2

Read more about zeros of a function at:

brainly.com/question/16633170

question: What are the zeros of the function below? Check all that apply.

F(x)= x(x+7)(x+2) / (x-4)(x+4)

answer:

c. -2
d. -7
f. 0

explanation: The "0" you are looking for are the x's. They equal the F(x) to 0.

F(x)= x(x+7)(x+2) / (x-4)(x+4)

Step 1- Set equal to 0.

x(x+7)(x+2) / (x-4)(x+4) = 0

Step 2- Multiply.

x(x+7)(x+2) = 0

Step 3- Separate.

x = 0
(x+7) = 0
(x+2) = 0

Step 4-Simplify.

x = 0

x + 7 = 0

- subtract 7 from both sides.

- x = -7

x + 2 = 0

- subtract 2 from both sides.

- x = -2

summary: The zeros in the function F(x)= x(x+7)(x+2) / (x-4)(x+4) are 0 , -7 , or -2.

I need help on this question

Answers

4.2% means 0.042 .

4.2% more than some amount is 1.042 of it.

Interest compounded annually means that a year after you deposit some money
into your bank account, the bank looks to see how much of your money has been
there for a year, and they add 4.2% of that into your account. Another way to
look at it is that they change the balance in your account, from the amount it was
a year ago, to 1.042 of that amount. That's right. They just give you free money !

Why that's so good is: Now the new amount in your account is 1.042 of
the amount you originally deposited, and after another year, they'll give you
another 4.2% of that larger amount. Then you'll have (1.042)² = about
8.6% more than your original deposit, 2 years earlier.

At the end of any number of years ... call it 't' years ... the amount in your
account is the amount you deposited, multiplied by (1.042)^'t' power.

If you just put some money into this particular bank, and forget about it
and never touch it, you'll have double the amount in 17 years.

Now we can go and take care of Rhonda.

She put $3000 into a new account at the the bank, and then she forgot
about it and never touched it. How much is in that account after 't' years ?
The amount that's in that account at any time is called the 'balance'.
How much is it after 't' years ?

Balance = 3,000 (1.042)^'t' power .

The Sine and Cosine RulesRight-angled triangle Trigonometry
Please note your working out with your answer, thank you.

Q11) A lifeguard on top of an observation tower 12.5m high notices a surfer in trouble at an angle of depression of 8 degrees. How far, correct to one decimal place, is the surfer from the tower?

Q13) A boat is 420m from the base of the cliff. The angle of depression of the boat from the top of the cliff is 28 degrees. Find the height of the cliff to the nearest metre.

Answers

Hello,
I am not doing that with sin, cos and pythagorean theorem.

DEFINITION: we call TAN x=sin x / cos x
This means that in a right triangle the tangent of an angle is the ration of opposed side by adjacent side.

11: tan 8°=12.5/d
==>d=12.5/tan 8°=12.5/0.14054...=88.942121...m≈88.9 (m)

12:
tan 28°=h/420
==>h=420*tan 28°=420*0.5317...=223.3179...≈223.3 (m)

The bull’s-eye on a target has diameter 2 in. What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for π.