The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
Answer:
3.2 feet
Step-by-step explanation:
The equation [tex]f(x)=-0.3x^{2}+2x[/tex] shows the height of water [[tex]f(x)[/tex]] and horizontal distance [[tex]x[/tex]].
Given the horizontal distance is 4 feet, they want to know the height.
Simply put 4 in [tex]x[/tex] of the equation and solve for [tex]f(x)[/tex]. So,
[tex]f(x)=-0.3(4)^{2}+2(4)\\f(x)=3.2[/tex]
So, the height of the water was 3.2 feet above the ground.
in the decimal number .98703, the 0 holds what place value
Answer:
it is in the 10 thousansth place.
Step-by-step explanation:
.98703
9=10nth place
8=100th place
7=thousandth place
0=ten thousandth place
3=hundred thousandth place
I hope this helps.
sin^2(75)-cos^2(75)=?
a rectangeler field is twice as long as it is wide a golf cart travrling at 12 miles per hour takes 7.5 minutes to travel the perimeter of the field what is the length (in miles) of the field
If i drove 34 times over a 7 mile bridge. how many miles in all did i drive?
Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. ...?
What unit of measurement would Guatemalans typically use to measure the weight of flour?
How do i write an akgebaric expression? Carrisa divided 40 grapes equally amoung f friends. How many grapes did each friend get?
How many friends?
40
____
X
40/ x
What is the length of segment LM?
Answer:
Step-by-step explanation:
From the given figure, we have
[tex]KN=NM[/tex]
⇒[tex]14x-3=25[/tex]
⇒[tex]14x=28[/tex]
⇒[tex]x=2[/tex]
Also, a is the angle bisector of ∠KNM and also it bisects the side KM such that KL=LM, thus
[tex]KL=LM[/tex]
Also, [tex]KL=9x+5[/tex]
Substituting the value of x in the above equation, we get
[tex]KL=9(2)+5[/tex]
[tex]KL=18+5[/tex]
[tex]KL=23[/tex]
Therefore, [tex]KL=LM[/tex]
[tex]LM=23[/tex]
Thus, the value of the segment LM is 23.
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
A)
19 cubic feet of snow
B)
31 cubic feet of snow
C)
511 cubic feet of snow
D)
1022 cubic feet of snow ...?
Answer:
A
Step-by-step explanation:
Final answer:
To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.
Explanation:
To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.
The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.
The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.
The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.
The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.
Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Write an equation to describe this situation where x is the number of bananas Tommy eats and y is the total number of pieces of fruit the monkey eats.
Answer:
The required equation is : [tex]2x+4[/tex]
Step-by-step explanation:
Tommy's monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Let Tommy eats x bananas, then the monkey eats 2x bananas.
Then, the required equation will be :
[tex]2x+4[/tex]
Express x in terms of the other variables in the diagram below:
From the diagram below , x = t ( r - h ) / h
Further explanationFirstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenusecos ∠A = adjacent / hypotenusetan ∠A = opposite / adjacentThere are several trigonometric identities that need to be recalled, i.e.
[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]
[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]
[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]
[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]
Let us now tackle the problem!
Look at ΔADE in the attachment.
We will use the following formula to find relationship between variable t and h:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{DE}{AD}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{h}{t} } }[/tex] → Equation 1
Look at ΔABC in the attachment.
We will use the following formula to find relationship between variable r , t and x:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{BC}{AB}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{r}{x + t} } }[/tex] → Equation 2
Next we can substitute equation 1 to equation 2 :
[tex]\tan \angle A = \frac{r}{x+t}[/tex]
[tex]\frac{h}{t} = \frac{r}{x+t}[/tex]
[tex](x + t)h = r ~ t[/tex]
[tex](x + t) = \frac{(r ~ t)}{h}[/tex]
[tex]x = \frac{(r ~ t)}{h} - t[/tex]
[tex]x = \frac{(r ~ t)}{h} - \frac{(h ~ t)}{h}[/tex]
[tex]\large {\boxed {x = \frac{t(r - h)}{h}} }[/tex]
Learn moreCalculate Angle in Triangle : https://brainly.com/question/12438587Periodic Functions and Trigonometry : https://brainly.com/question/9718382Trigonometry Formula : https://brainly.com/question/12668178Answer detailsGrade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
How much of the circle is shaded? Write your answer as a fraction in simplest form?
Answer:
[tex]5/14[/tex]
Step-by-step explanation:
Let
x-----> the shaded area
we know that
[tex]x+\frac{1}{7}=\frac{1}{2}[/tex]
solve for x
Multiply by [tex]14[/tex] both sides
[tex]14x+2=7[/tex]
[tex]14x=7-2[/tex]
[tex]14x=5[/tex]
Divide by [tex]14[/tex] both sides
[tex]x=5/14[/tex] ----> fraction irreducible
Write the equation of a line in slope-intercept form from the graph below.
Write the equation of a line in slope-intercept form from the graph below.
Answer: Y=x or y=1x
Step-by-step explanation:
Slope of 1 y-intercept of (0,0)
My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just started it today and she my teacher gave us 3 pages of the math.
Solve the problem. Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? a. $13,500 in bonds; $5500 in certificates of deposit b. $5500 in bonds; $13,500 in certificates of deposit c. $13,000 in bonds; $6000 in certificates of deposit d. $6000 in bonds; $13,000 in certificates of deposit
...?
Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.
Explanation:To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:
x + y = $19,000 (Total investment amount)
0.07x + 0.09y = $1,590 (Total annual income from investments)
Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:
7x + 9y = 159,000
Next, we can multiply the first equation by 7 to help us eliminate one variable:
7x + 7y = 133,000
Subtracting the modified first equation from the second equation:
9y - 7y = 159,000 - 133,000
2y = 26,000
y = $13,000
Using y = $13,000 in the first equation:
x + 13,000 = 19,000
x = $6,000
Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.
Regarding the bond investment scenario:
a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.
b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:
The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.
Using the market interest rate of 9%, the present value (PV) formula is:
PV = Payment / (1 + market interest rate)
PV = $10,600 / (1 + 0.09)
PV = $10,600 / 1.09
PV ≈ $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond.
in DEF DE=17 m angle =32 Find DF nearest tenth
Answer:
(A) 32.1
Step-by-step explanation:
It is given that in ΔDEF, DE=17 and m∠F=32, thus
Using the trigonometry, we have
[tex]sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}[/tex]
⇒[tex]sin32^{\circ}=\frac{17}{DF}[/tex]
⇒[tex]DF=\frac{17}{sin32^{\circ}}[/tex]
⇒[tex]DF=\frac{17}{0.529}[/tex]
⇒[tex]DF=32.1[/tex]
Therefore, the value of DF is 32.1.
Hence option A is correct.
1000 millimeters equals what =
The following is a correspondence one is
A.{(a,1),(b,1),(c,1)}
B.{(1,a),(2,c),(3,d)
C.{(1,b),(2,c),(3,b)
D.{(a,b),(c,d),(b,d)
Harry’s team has won 13 less than 6 times as many games as it has lost. The team lost n games. What expression could you use to find the number of games the team has won?
2 1/7 into a improper fraction
What does x equal
8=3+x/-6
The measures of each exterior angle in a regular hexagon is (4x + 15)°. Find the value of x. Show equations and all work that leads to your answer.
...?
if you drive your car constant speed of 45 miles per hour, how long will it take to travel 378 miles
can someone explain how to find two positive numbers such that their product is 192 and the sum of the first plus three times the second is a minimum?
(only subject im bad at) What is the Least Common Denominator (LCD) of 7/8 and 1/6 ?
i need work shown write .569 as a percent
alice leaves her house and walks to school she walks 45 meters south and 336 meters east. how far is Alice from her house?
Alice's distance from her home is 339 meters.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Alice leaves her house and walks to school she walks 45 meters south and 336 meters east.
We can write the Alice's distance from her home as -
{x} = √(45)² + (336)²
{x} = √(2025 + 112896)
{x} = 339 meters
Therefore, Alice's distance from her home is 339 meters.
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ6
A heart beats 8 times in 3 seconds.About how many times will a cats heart beat in 2 minutes
What is the product? enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)?
yeah it would be 3/11 i just did the test