PLEASE HELP ME TO ANSWER THIS QUESTION.
A right pyramid PQRST has a rectangular base QRST. Given
that W is the midpoint of QS and RT, the lengths of QT = 8 cm,
TS = 6 cm and point P is vertically above point W, calculate
(a) PT, in cm, if PW = 12 cm
(b) the value of < PTR [angle PTR]
THANK YOU!!!
Answers
Answer:
(a) PT = 13 cm
(b) <PTR = [tex]39.7^{o}[/tex]
Step-by-step explanation:
(a) Applying the Pythagoras theorem to QST, we have;
[tex]QS^{2}[/tex] = [tex]ST^{2}[/tex] + [tex]QT^{2}[/tex]
= [tex]6^{2}[/tex] + [tex]8^{2}[/tex]
[tex]QS^{2}[/tex] = 36 + 64
100
QS = [tex]\sqrt{100}[/tex]
= 10
QS = 10 cm
Since QS = TR, then;
WT = [tex]\frac{1}{2}[/tex] TR
= [tex]\frac{1}{2}[/tex] x 10
WT = 5 cm
Thus, applying Pathagoras theorem to PWT;
[tex]PT^{2}[/tex] = [tex]PW^{2}[/tex] + [tex]WT^{2}[/tex]
= [tex]12^{2}[/tex] + [tex]5^{2}[/tex]
= 144 + 25
[tex]PT^{2}[/tex] = 169
PT = [tex]\sqrt{169}[/tex]
= 13
PT = 13 cm
(b) To determine <PTR, TR = 10 cm. Apply the required trigonometric function;
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos θ = [tex]\frac{10}{13}[/tex]
= 0.7692
θ = [tex]Cos^{-1}[/tex] 0.7692
= 39.7179
θ = [tex]39.7^{o}[/tex]
Therefore, <PTR = [tex]39.7^{o}[/tex]
Related Questions
Carl buys seven 5-gallon jugs of water for the water cooler. How many liters of water did Carl buy? (1 gal= 3.785 liters)
Answers
Answer:
Carl buys 132.475 liters of water.
Step-by-step explanation:
Since Carl buys seven 5-gallon jugs of water multiply 7 by 5 to know how many gallons of water Carl bought in total.
7(5) = 35 Gallons
Now that you have the total amount of gallons of water Carl bought you have to convert 35 gallons to liters given that 1 gallon = 3.785 liters by multiplying 35 by 3.785.
35(3.785) = 132.475
So Carl bought 132.475 liters of water.
Though that is the answer based on what is given a gallon is actually equal to 3.78541 liters so the exact answer would be 132.489 liters of water.
Ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r=0.02 . Money can be withdrawn from the account at regular intervals, and no additions to the account can be made. The function P models the balance of the account, in dollars, at time t. Assume that Ana withdraws money from the account continuously at a rate of N dollars per year.
Required:
Write down the differential equations that best describes the relationship between P and t?
Answers
Answer:
dp/dt = 0.02P-N
Step-by-step explanation:
[tex]\frac{p(t+t)}{nt}[/tex]
The differential equation that describes the relationship between P and t is:
dP/dt = rP - N
where P is the balance in dollars, t is time in years, r is the annual interest rate, and N is the rate of withdrawals in dollars per year.
What is a differential equation ?A differential equation is an equation that relates an unknown function to its derivatives (or differentials) with respect to one or more independent variables. In other words, it is an equation that involves derivatives of an unknown function.
The rate of change of the balance P in the bank account is equal to the difference between the rate of interest earned on the account and the rate at which money is withdrawn from the account.
The rate of interest earned on the account is given by the continuous compounding formula:
dP/dt = rP
where r is the annual interest rate, P is the balance in dollars, and dP/dt is the rate of change of P with respect to time.
On the other hand, the rate at which money is withdrawn from the account is given by the expression:
dN/dt = N/T
where N is the rate of withdrawals in dollars per year, and T is the time interval in years between withdrawals.
If we assume that Ana withdraws money from the account continuously at a rate of N dollars per year, we can write:
N = dN/dt
Substituting this into the first equation, we get:
dP/dt = rP - dN/dt
Substituting the expression for dN/dt, we get:
dP/dt = rP - N/T
Simplifying, we get:
dP/dt = rP - N
which is the differential equation that describes the relationship between P and t.
The differential equation
dP/dt = rP - N
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In QRS the measures of S = 90° and the measures of Q = 64° and RS = 16 feet find the length of QR to the nearest 10th of a foot
Answers
Answer:
vfd
Step-by-step explanation:
ddf
I need help I need the answer
Answers
Answer:
(4,4)
Step-by-step explanation:
because it's right in between the school and bank therefore equal distance to both
Answer:
(6,8)
Step-by-step explanation:
the same distance from bank to school (sorry if im wrong)
Can someone please actually help with with this problem?
Answers
Answer:
(a)
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ {P(x)} & {0} & {4} & {8} & {12} & {16}& {20} & {24} \ \end{array}[/tex]
(b)
[tex]P(x) = 4x[/tex]
(c)
See attachment for graph
Step-by-step explanation:
Given
P(x) = Perimeter of square
Solving (a): Complete the table
The perimeter of a square is:
[tex]P =4x[/tex]
so, the table will be completed by multiplying each value of x by 4.
So, we have:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ {P(x)} & {0} & {4} & {8} & {12} & {16}& {20} & {24} \ \end{array}[/tex]
Solving (b): The equation
This has already been stated in (a)
[tex]P(x) = 4x[/tex]
Solving (c): The graph
See attachment for graph
Given f(x) = 5 - x?, find f(3).
Answers
Answer:
the answer is 2
Step-by-step explanation:
just plug in the 3 for x and perform the neccessary calculation.
Answer:
2
Step-by-step explanation:
if x is 2 that means 2 + 3 = 5
Give me brainllest Plz
(d) Work out
1
4 of 28 kg.
Answers
Step-by-step explanation:
[tex]here \: is \: your \: soution \\ \\ (1 \div 4) \times 28 \\ \\ 28 \div 4 = 7 \\ \\ 7 \: is \: your \: answer \\ \\ hope \: it \: help[/tex]
14x+5y=31
2x−3y=−29
Answers
Answer:
x = -1, y = 0=9
Step-by-step explanation:
Multiply the second equation by 7 and subtract the two.
14 x + 5 y = 31
- (14 x - 21 y = -203)
This gives 26 y = 234. Divide both sides by 26. y = 9
Then substitute y into any equation. I'll use
2 x - 3 y = -29
2 x -3(9) = -29
2 x - 27 = -29
2 x = -2
x = -1
What is the probability of choosing a heart or a spade from a deck of cards? Type your answer as a fraction.
Answers
Answer:
26/52 or 1/2
Step-by-step explanation:
There are 13 cards per suit therefore there must be 26
Answer:
Step-by-step explanation:
13/52
Triangle ABC is inscribed in a circle O. What is the measure of Angle A?
Answers
Angle A=40
Answer:
answer is 40 degree
Step-by-step explanation:
hope it helps!!!
Which of the following is NOT an example of a random sample? A. Placing the names of 500 people in the target population in a box and drawing 50 names without looking. B. Choosing a name at random from a list of 500 people in the target population and then choosing every fifth person on the list after that. C. Dividing a list of names in the target population by age and randomly selecting a proportional sample from each group. D. Starting with a list of 500 names in the target population and choosing the first 50 names on the list.
Answers
Answer:
B
Step-by-step explanation:
If it's not D, and I also learned it isn't C, then It's more than likley gonna be B. I think bc they vote every 5th person after the random.
Hope It Help :)
B. Choosing a name at random from a list of 500 people in the target population and then choosing every fifth person on the list after that.
What is random sample?In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a method of choosing a sample at random.
To learn more about the random sample refer to:
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help me pls i have been stuck on this for the past hour
Answers
Answer:
-4, -6, -3, -5, -1. The inequality solved for n is n ≥ -6.
Step-by-step explanation:
Substitute all the values in the equation.
n/2 ≥ -3
-10/2 ≥ -3
-5 is not ≥ -3.
n/2 ≥ -3
-7/2 ≥ -3
-3.5 is not ≥ -3.
n/2 ≥ -3
-4/2 ≥ -3
-2 is ≥ -3.
n/2 ≥ -3
-9/2 ≥ -3
-4.5 is not ≥ -3.
n/2 ≥ -3
-6/2 ≥ -3
-3 is ≥ -3.
n/2 ≥ -3
-3/2 ≥ -3
-1.5 is ≥ -3.
n/2 ≥ -3
-8/2 ≥ -3
-4 is not ≥ -3.
n/2 ≥ -3
-5/2 ≥ -3
-2.5 is ≥ -3.
n/2 ≥ -3
-2/2 ≥ -3
-1 is ≥ -3.
To solve the inequality n/2 ≥ -3 for n, do these steps.
n/2 ≥ -3
Multiply by 2.
n ≥ -6.
A new pair of shoes is advertised for $110. The sales tax is 7.5%. What is the total cost of the shoes?
Answers
Answer:
$118.25
Step-by-step explanation:
Always convert the percentage to a decimal by moving the decimal two points to the right/dividing by 100. So 7.5 % = 0.075
110 x 0.075 = 8.25 (the amount of tax added)
110 + 8.25 = 118.25
You can also multiply 110 by 1.075, where the "1" is the $110 and the ".075" is the tax, and save the step of adding. 110 x 1.075 = 118.25
Beth wants to buy a radio for $36. She
gives the cashier $40. What is her
change?
Answers
40-36=4
Answer:
4
Step-by-step explanation:
Micah is flying a kite and has used all of the 50 meters of the string. If the kite is 13 meters above the ground, what is the angle of elevation that
the boy has when looking up at the kite?
Sketch a picture and solve. Round to the nearest degree.
ILL MARK YOU THE BRANLIEST ANSWER IF YOU ANSWER FAST PLEASE
Answers
Answer:
37
Step-by-step explanation:
I believe you subtract the meters to the meters above the ground
What is the area of the real object that the scale drawing models?
Scale factor: 1:4
Area =
6 square cm
Scale drawing
Object
O A. 24 square cm
O B. 96 square cm
O C. 64 square cm
O D. 48 square cm
Answers
Answer:
96
Step-by-step explanation:
I just did it on a p 3 x
Y-Coordinate
What is the Y-coordinate for each point below? The
y-coordinates are your code. (Use decimals where applicable.)
D
A
B
-2
]]]]
A
D
2 3
4
The numbers together form your code
Answers
Answer:
A = -2
B = 2
C = 2
D = 3
Step-by-step explanation:
those are the y- coordinates
A recent hailstorm caused $1200 worth of body damage to Karen's car. Based
on Karen's insurance policy given below, how much money will Karen receive
after she files her claim?
Summary
Comprehensive Deductible: 333
Collision Deductible: 5550
Premium of $625 for 4 months
A. $625
B. $825
O C. $375
Ο Ο
D. $1200
Answers
Answer:B
Step-by-step explanation:
$825
Asking for help again
Answers
Answer: D. (7, 0)
Step-by-step explanation:
[tex]4x+9y=28\\-4x-y=-28[/tex] The xs can already cancel since 4x is positive for the first equation, but negative on the second.Add the equations together8y=0Divide both sides by 8 y=0Plug y into one of the equations4x + 9(0)=28Distribute 04x=28Divide both sides by 4x= 7So your answer is (7, 0)
I need help with this math problem
Answers
What is the reciprocal of 14?
Answers
Reciprocal of 14 is 1/14.
Please help with this question it is due today I will give 20 points. Thank you and may God bless you! :)
Answers
I would say A but please wait for someone else to answer to make sure it's not wrong I would hate for you to get this wrong
If l || m, determine what type of angles they are and find the value of x.
Answers
3x=51
x=17
The angles are obtuse angles.
Answer the question asked. When necessary, round to the nearest hundredth.
A boat moves 6 kilometers upstream in the same amount of time it moves 20 kilometers
downstream. If the rate of the current is 6 kilometers per hour, find the rate of the boat in still water.
Answers
Answer:
0.555km p/h
shown as 555m p/h
Step-by-step explanation:
First we convert km to meters
6k = 6000m
Time = distance / rate.
20/6 = 3.33333333 = 3hr + ( 0.33 x 60 = 19.8) - 3.20hr
then 3.33 / 6 = 0.555 km = 555 meters p/h
Amy spent $42 on breakfast for her family. She gave the waiter an 18% tip. What is the tip?
Answers
18% of 42 is 7.56
You roll a six-sided die. How likely is it that you roll a number greater than 6?
impossible
impossible
likely
likely
Answers
Answer:
Impossible (0/6)
Step-by-step explanation:
A single six-sided die has:
1, 2, 3, 4, 5, 6.
It is impossible to roll a number greater than 6 because there is no number greater than 6 on a six-sided die.
Please solve using the tangent formula(real answers only no links)
Answers
Answer:
x = 21.06 units
Step-by-step explanation:
Given that,
Base, b = 20
Height, h = x
Angle = 36
We need to find the value of x. Trigonometric formulas are used to solve such problems such that,
[tex]\tan(36)=\dfrac{x}{29}\\\\x=29\times \tan(36)\\\\x=21.06[/tex]
So, the value of x is equal to 21.06 units.
What did E=MC squared stand for
Answers
Answer:
[tex]{\huge\red{\fbox{{E = mc² }}}}[/tex]
✏ E = mc² stands for -> Energy equals mass times the speed of light squared.
✏ On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.
Answer:
✏ E = mc² stands for -> Energy equals mass times the speed of light squared.
✏ On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.
4x<-2 como se desarrolla esta desigualdad
Answers
Answer:
x<-0.5
Step-by-step explanation:
The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption. You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water. In this case you would want to _____.
Answers
Question Completion:
Suppose that
H subscript o : mu less or equal than 0.01
H subscript alpha : mu greater than 0.01
The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption. You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water. In this case you would want to _____.
A. maximize the power of the test
B. maximize beta
C. minimize mu
D. maximize the significance, alpha
E. maximize 1 minus alpha
Answer:
In this case you would want to _____.
D. maximize the significance, alpha
Step-by-step explanation:
The alpha (α) denotes the significance level or the probability of rejecting the initial or null hypothesis when it is true.
A higher alpha (α) reduces the probability of committing a Type II error or not rejecting the null hypothesis. On the other hand, a higher alpha (α) makes it more probable to reject a null hypothesis when it is true (Type I error).