The ratio is 3:4:5.
Cosine by definition, is adjacent divided by hypotenuse, meaning that the value of the hypotenuse is 5. Then, we are given two other sides that are adjacent to angles A and B, which are 4 and 3 respectively.
This means that there are side lengths 3, 4, and 5, meaning that the ratio of the sides are 3:4:5.
Hope this helps.
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Use the general slicing method to find the volume of the following solid. The solid whose base is the region bounded by the curve y=38cosx and the x-axis on − π 2, π 2, and whose cross sections through the solid perpendicular to the x-axis are isosceles right triangles with a horizontal leg in the xy-plane and a vertical leg above the x-axis. A coordinate system has an unlabeled x-axis and an unlabeled y-axis. A curve on the x y-plane labeled y equals 38 StartRoot cosine x EndRoot starts on the negative x-axis, rises at a decreasing rate to the positive y-axis, and falls at an increasing rate to the positive x-axis. The region below the curve and above the x-axis is shaded. A right triangle extends from the x y-plane, where one leg is on the x y-plane from the x-axis to the curve and is perpendicular to the x-axis, and the second leg is above the x-axis and is perpendicular to the x y-plane. y=38cosx
Answer:
The volume of the solid = 1444
Step-by-step explanation:
Given that:
The region of the solid is bounded by the curves [tex]y = 38 \sqrt{cos \ x}[/tex] and the axis on [tex][-\dfrac{\pi}{2}, \dfrac{\pi}{2}][/tex]
using the slicing method
Let say the solid object extends from a to b and the cross-section of the solid perpendicular to the x-axis has an area expressed by function A.
Then, the volume of the solid is ;
[tex]V = \int ^b_a \ A(x) \ dx[/tex]
However, each perpendicular slice is an isosceles leg on the xy-plane and vertical leg above the x-axis
Then, the area of the perpendicular slice at a point [tex]x \ \epsilon \ [-\dfrac{\pi}{2},\dfrac{\pi}{2}][/tex] is:
[tex]A(x) =\dfrac{1}{2} \times b \times h[/tex]
[tex]A(x) =\dfrac{1}{2} \times(38 \sqrt{cos \ x})^2[/tex]
[tex]A(x) =\dfrac{1444}{2} \ cos \ x[/tex]
[tex]A(x) =722 \ cos \ x[/tex]
Applying the general slicing method ;
[tex]V = \int ^b_a \ A(x) \ dx \\ \\ V = \int ^{\dfrac{\pi}{2} }_{-\dfrac{\pi}{2}} (722 \ cos x) \ dx \\ \\ V = 722 \int ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}} cosx \dx[/tex]
[tex]V = 722 [ sin \ x ] ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}[/tex]
[tex]V = 722 [sin \dfrac{\pi}{2} - sin (-\dfrac{\pi}{2})][/tex]
[tex]V = 722 [sin \dfrac{\pi}{2} + sin \dfrac{\pi}{2})][/tex]
[tex]V = 722 [1+1][/tex]
[tex]V = 722 [2][/tex]
V = 1444
∴ The volume of the solid = 1444
A recipe says to use 1/5 cup of flour to make 7/10 serving of waffles. How many cups of flour are in one serving of waffles?
Don’t know the answer
What number is 0.1 less than 173.89
Answer:
173.79
Step-by-step explanation:
173.89 - 0.1 you move to the decimals place then remove that number once
The number 173.79 is 0.1 less than 173.89
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find how less is 0.1 than 173.89
In words zero point one is less than One hundred seventy three point eight nine.
To find this we have to use subtraction operator or difference.
Subtraction is an operation that represents removal of objects from a collection
Subtract 0.1 from 173.89
173.89-0.1
We get 173.79
Hence, the number 173.79 is 0.1 less than 173.89
To learn more on Equation:
https://brainly.com/question/10413253
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4.56 natural numbers or a whole numbers integers rational numbers Irrational numbers or real numbers
Answer:
it is rational number
Step-by-step explanation:
Decimals are not natural and whole numbers.
irrational numbers cannot be expressed by fraction but this question can be experssed by decimal so it is rational number not irrational
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For any question comment me
please help me on this
21.406 in standard form
21.406 in standard form
Answer:
21406 X 10^3
PLEASE HELP I WILL MARK YOU AS BRAINLEIST IF YOU GET THIS RIGHT ! ! !
Answer:
(-8, 2)
Step-by-step explanation:
Count 4 units to the right.
Point a is at (2,-8) and point c is at (-4,7). Find the coordinates of point b on ac such that the ratio of ab to bc is 2:1
Answer:(-2,2)
Step-by-step explanation:
Point S is on line segment RT. Given ST = 3x
= 3x – 8, RT = 4x, and
RS = 4x 7, determine the numerical length of RT.
Answer:
RT = 20
Step-by-step explanation:
Given that,
Point S lies on the line segment RT.
We have, ST = 3x-8, RT = 4x and RS = 4x-7
It is clear that, RT = RS+ST
Putting the values, we get :
4x = 4x-7 + 3x-8
Taking like terms together,
4x-4x-3x = -7-8
-3x = -15
x = 5
Put the value of x in RT = 4x.
So,
RT = 4(5)
RT = 20
Hence, length of RT = 20.
The price-demand equation for gasoline is 0.3d + 4p = 80, where p is the price per gallon in dollars and d is the daily demand measured in millions of gallons. Write the demand d as a function of price What is the demand if the price is $ 8 per gallon?
Answer:
The demand d as a function of price is [tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]
The demand if the price is $ 8 per gallon is 160 millions of gallons.
Step-by-step explanation:
You know that the price-demand equation for gasoline is 0.3d + 4p = 80
To write demand d as a function of price p, you must solve for or isolate demand d, remembering that:
All the terms that are multiplying on one side, go to the other side of the equality by dividing, and those that are dividing go to the other side of the equality by multiplying. The terms that are adding go to the other side of the equality by subtracting and those that are subtracting go to the other side by adding.So:
0.3d + 4p = 80
0.3d = 80 - 4p
[tex]d=\frac{80 - 4p}{0.3}[/tex]
[tex]d=\frac{80}{0.3} -\frac{4p}{0.3}[/tex]
[tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]
The demand d as a function of price is [tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]
To determine how much is the quantity demanded if the price is $ 8 per gallon, you simply plug that value into the previously determined expression and perform the corresponding calculations:
[tex]d=\frac{800}{3} -\frac{40*8}{3}[/tex]
[tex]d=\frac{800}{3} -\frac{320}{3}[/tex]
d= 160
The demand if the price is $ 8 per gallon is 160 millions of gallons.
36) A contractor built a square hall having
an area of 4489 m2. How long is the hall?
Answer:
area of square = l²= 4489m²
l=√4489 = 67m
Step-by-step explanation:
2.02 into 10 raised to 7 is the answer
what does y=-(7)/(2)x+5 look like on a graph.
Answer:
Here you go buddy.
One number is 28 less than another number. If the sum of the two numbers is 92, find the two numbers.
Answer:
The two numbers are 32 and 60.
Step-by-step explanation:
We can create two simultaneous equations to solve this problem using the information given in the question.
Let number 1 = x
Let number 1 = y
x = y - 28 -> ( 1 )
x + y = 92 -> ( 2 )
We can solve simultaneous equations using substitution or elimination. For this question, we will use substitution as it is the easier option.
Substitute ( 1 ) into ( 2 ):
x + y = 92 -> ( 2 )
( y - 28 ) + y = 92
2y - 28 = 92
2y = 120
y = 120 / 2
y = 60 -> ( 3 )
Substitute ( 3 ) into ( 1 ):
x = y - 28 -> ( 1 )
x = ( 60 ) - 28
x = 32
Therefore:
x = 32 , y = 60
p: student achieves 90 percent on the geometry final. q: student will receive a passing grade in geometry class. Which statement is logically equivalent to q → p?
Answer:
if a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class
Step-by-step explanation:
Jeremiah buys 6.5 pounds of ground beef at the grocery store. Ground beef costs $5.50 for one pound. How much does Jeremias spend?*
Answer:
35.75
Step-by-step explanation:
6.5 times 5.50 = 35.75
or
5.50+5.50+5.50+5.50+5.50+5.50=35.75
Solve each calculation. Be sure to report your answer with the correct number of decimal places. 7.365 ms 0.250 ms + 10.3 ms ms 125.010 cL 4.1023 cL – 0.30 cL cL
Answer:
1.17.9
2. 120.61
Step-by-step explanation:
Answer:
17.9
120.61
Step-by-step explanation:
If I have a 10 ft PVC pipe,how many 11/5 cuts could I make out of it?
Answer:
80
Step-by-step explanation:
Consider the Line L(t) = <2+t,5-4t>. Then L intersects:
The x- axis at the point (3.25,0) when t = 5/4
The y- axis at the point (0, 13) when t = -2
The parabola y = x^2 at the points ___ and ___ when t = ____ and ____
Answer:
The parabola [tex]y=x^{2}[/tex] at the points [tex](-2+\sqrt{17},21-4\sqrt{17})[/tex] and [tex](-2-\sqrt{17},21+4\sqrt{17})[/tex] when [tex]t=t_{1}=-4+\sqrt{17}[/tex] and [tex]t=t_{2}=-4-\sqrt{17}[/tex]
Step-by-step explanation:
We have the following line written in parametric form :
[tex]L(t)=(2+t,5-4t)[/tex] with [tex]t[/tex] ∈ IR.
In order to find the intersection between [tex]L(t)[/tex] and the parabola [tex]y=x^{2}[/tex] we know that ''[tex]2+t[/tex]'' is the x-coordinate of the line and ''[tex]5-4t[/tex]'' is the y-coordinate of the line. Now, to solve this problem we need to find the values of ''[tex]t[/tex]'' in which the intersection occurs. We can do this by replacing the components ''[tex]x[/tex]'' and ''[tex]y[/tex]'' of [tex]L(t)[/tex] in the equation of the parabola ⇒
[tex]L(t)=(2+t,5-4t)[/tex] = ( x component , y component ) = ( x , y ) ⇒
In the parabola : [tex]y=x^{2}[/tex] ⇒ [tex]5-4t=(2+t)^{2}[/tex]
Solving the equation we find that :
[tex]t^{2}+8t-1=0[/tex]
Using the quadratic formula with
[tex]a=1[/tex] , [tex]b=8[/tex] and [tex]c=-1[/tex]
We find that the two possible values for t :
[tex]t_{1}=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and [tex]t_{2}=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
are [tex]t_{1}=-4+\sqrt{17}[/tex] and [tex]t_{2}=-4-\sqrt{17}[/tex]
This values [tex]t_{1}[/tex] and [tex]t_{2}[/tex] are the values of the parameter t where the line intersects the parabola so we can find the points by replacing the values of the parameter in the equation [tex]L(t)[/tex] :
[tex]L(t_{1})=(-2+\sqrt{17},21-4\sqrt{17})[/tex] and
[tex]L(t_{2})=(-2-\sqrt{17},21+4\sqrt{17})[/tex]
The final answer is
The parabola [tex]y=x^{2}[/tex] at the points [tex](-2+\sqrt{17},21-4\sqrt{17})[/tex] and [tex](-2-\sqrt{17},21+4\sqrt{17})[/tex] when [tex]t=t_{1}=-4+\sqrt{17}[/tex] and [tex]t=t_{2}=-4-\sqrt{17}[/tex]
During a normal day, there are 280 planes taking off the airport, but the airport is a lot busier during Christmas. During the Christmas holidays, about 336 planes take off everyday from the airport
Compared with a normal day, how many more passengers depart from
the airport in a day during the Christmas holidays?
Answer:
56
Step-by-step explanation:
Answer:
6000
Step-by-step explanation:
we dont know how many people are in each plane but based on the average it should be this
Simplify. 4+5(8−10)2 Enter your answer in the box.
Answer:
-16
Step-by-step explanation:
4 + 5(8-10)2
4 + 5(-2)2
4 + 10(-2)
4 - 20
-16
The answer is: 24
I assume this is a question from k12
4 + 5(8 - 10)^2
4 + 5(-2)^2
4 + 5(4)
4 + 20
= 24
Hope this helps ^^
11. The shadow of a 10 m high pole is 6 metres. Find
the shadow of a 15 m high pole at the same time
of the day.
Answer:
25m
Step-by-step explanation:
10/6 = length of shadow per metre of pole
so 15 x 10/6 = shadow of 15m high pole
150/6 = 25m
Burgers come in packs of 10. The cost of 10 burgers is £3.45. How much does 1 burger cost?
If the probability that your DVD player breaks down before the extended warranty expires is 0.034, what is the probability that the player will not break down before the warranty expires
Answer:
0.966
Step-by-step explanation:
Given that:
Probability of DVD player breaking down before the warranty expires = 0.034
To find:
The probability that the player will not break down before the warranty expires = ?
Solution:
Here, The two events are:
1. The DVD player breaks down before the warranty gets expired.
2. The DVD player breaks down after the warranty gets expired
In other words, the 2nd event can be stated as:
The DVD does not break down before the warranty gets expired.
The two events here, have nothing in common i.e. they are mutually exclusive events.
So, Sum of their probabilities will be equal to 1.
[tex]\bold{P(E_1)+P(E_2)=1}\\\Rightarrow 0.034+P(E_2)=1\\\Rightarrow P(E_2)=1-0.034\\\Rightarrow P(E_2)=\bold{0.966}[/tex]
The first number in an ordered pair of numbers that corresponds to a point on a coordinate system is what
Answer:
"abscissa"
Step-by-step explanation:
The first number in an ordered pair of numbers in a coordinate system is generally called abscissa.
Answer:
x value is the correct answer
Step-by-step explanation:
I just took the test 2021 thank me later
Help me please because of the points
Answer:
C
Step-by-step explanation:
Because the dolphin increases his elevation, the amount he increases is added to the original elevation to get the second elevation.
Therefore:
-16 3/4 + 5x = -5 1/4
This option is not in the options but if we rearrange the left side from
- 16 3/4 + 5x
to:
5x - 16 3/4
We get the last option C.
Hope this helped!
Why is 4 + (-3) equal to 1?
Step-by-step explanation:
4+(-3)=1
because when you open brackets + and - will be -, so 4-3=1
(HELP) The point (- 8, - 2) is on the parent graph below. Where will it be on the transformed graph?
Answer:
x=[tex]\frac{y2 }{9}[/tex]
Step-by-step explanation:
2nd step: [tex]3\sqrt{x}=y[/tex]
third step: [tex]\frac{3\sqrt{x} }{3} = \frac{y}{3}[/tex]
fourth step: [tex]\sqrt{x} =\frac{y}{3}[/tex]
answer: x=[tex]\frac{y2 }{9}[/tex]
What is the answer to this?
Answer:
−6y+24
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
parenthesis come first (PEMDAS)
2×8=16
2×3y=6y
9+16-6y-1
Add like terms
9+16=25
25-6y-1
Subtract like terms
25-1=24
-6y=24
Multiple each sides by using fractions
1/(-)6×24/1=4
Sue weighed 82 kg at the start of the year, but she has lost weight at a consistent rate because she has been diligent with her exercise and diet plan. Sue weighed herself at the end of each month and tracked her progress for the full year using the graph above. How much weight did Sue lose each month? Question 5 options: A) 4 kg B) 2 kg C) 3 kg D) 1 kg
Answer:
Option (B)
Step-by-step explanation:
Sue's weight at the start of the year = 82 kg
Sue weighed herself at the end of every year, so that the straight line on the graph shows the gradual reduction in the weight every month.
Slope of the line will describe the reduction in the weight per month.
Let the two points on the given line are (1, 80) and (11, 60).
Slope of the line will be,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{60-80}{11-1}[/tex]
= -2 kg per month
(Here minus sign denotes the reduction of weight per month)
Option (B) will be the answer.
Answer:
2 kg
Step-by-step explanation:
A balloon is flcating 10 feet above the ground. How
far does the balloon need to drop to reach the
ground?
Answer:
10 feet
Step-by-step explanation:
if it is 10 feet above and needs to touch the ground it needs to drop that same amount
Answer:
10ft.
Step-by-step explanation:
if the balloon is floating 10ft from the ground the it can only drop 10ft to reach the ground.
*hope this helps. please give me brainliest, i only need four more *