Answer:
T= 2.35 seconds
Step-by-step explanation:
⇒The question is on the time of flight.
⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile
Given;
Initial velocity of ball= 110ft./sec.
The projectile angle= 20°
Acceleration due to gravity, g=32 ft./s²
⇒Formulae for time of fright T= (2×u×sin Ф)/g
Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.
Substituting values
T= (2×u×sin Ф)/g
T=( 2×110×sin 20°) / 32
T= 2.35 seconds
Answer:
Option B - Time taken for the ball to hit the ground is 2.47 seconds.
Step-by-step explanation:
Given : A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.
To find : How long does it take for the ball to hit the ground?
Solution :
According to question,
The equation that models the height of the ball in feet as a function of time is
[tex]h(t) = h_0 + v_0t -16t^2[/tex]
Where, [tex]h_0[/tex] is the initial height,
[tex]v_0[/tex] is the initial velocity and
t is the time in seconds.
We have given,
Initial height, [tex]h_0=4.5 ft.[/tex]
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees.
The initial speed, [tex]v_0=110\times \sin(206\circ)[/tex]
[tex]v_0=37.62ft/s[/tex]
We have to find the time for the ball to hit the ground i.e. h(t)=0
Substitute all the values in the formula,
[tex]0 =4.5+ 37.62t -16t^2[/tex]
Applying quadratic formula to solve the equation,
The solution of quadratic general equation [tex]ax^2+bc+c=0[/tex] is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where, a=-16 , b=37.62 , c=4.5
Substituting in the formula,
[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]
[tex]t=\frac{-37.62\±\sqrt{1703.2644}}{-32}[/tex]
[tex]t=\frac{-37.62\±41.270}{-32}[/tex]
[tex]t=\frac{-37.62+41.270}{-32},\frac{-37.62-41.270}{-32}[/tex]
[tex]t=-0.114,2.47[/tex]
neglecting the negative value
t=2.47 seconds
Therefore,Option B is correct.
Time taken for the ball to hit the ground is 2.47 seconds.
Please answer fast!!! Will give brainliest!!!
given: m∠EYL= 1/3 m arc EHL Find: m∠EYL.
Answer:
The measure of angle EYL is [tex]45\°[/tex]
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
Let
x-----> the measure of arc EVL
y----> the measure of arc EHL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
[tex]m<EYL=\frac{1}{3}(y)[/tex]
so
[tex]\frac{1}{3}y=\frac{1}{2}(x-y)[/tex]
Multiply by 6 both sides
[tex]2y=3x-3y[/tex]
[tex]3x=5y[/tex]
[tex]x=\frac{5}{3}y[/tex] -----> equation A
[tex]x+y=360\°[/tex] -----> equation B ( is a complete circle)
substitute equation A in equation B
[tex]\frac{5}{3}y+y=360\°[/tex]
[tex]\frac{8}{3}y=360\°[/tex]
[tex]y=(360\°)*(3)/8=135\°[/tex]
Find the value of x
[tex]x=\frac{5}{3}(135\°)=225\°[/tex]
Find the measure of angle EYL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
substitute the values
[tex]m<EYL=\frac{1}{2}(225\°-135\°)=45\°[/tex]
16.4
19.6
10.6
21.2
question 45
Answer: FIRST OPTION
Step-by-step explanation:
You need the formula for calculate the arc lenght:
[tex]arc\ length=2\pi r(\frac{C}{360})[/tex]
Where "r" is the radius and and "C" is the central angle in degrees.
You know that the radius is:
[tex]r=7.5[/tex]
And the central angle ∠CAT is:
[tex]C=\angle CAT=125\°[/tex]
Then, you need to substitute these values into the formula [tex]arc\ length=2\pi r(\frac{C}{360})[/tex] to calculate the length of CT.
Then, this is:
[tex]arc\ length=CT=2\pi (7.5)(\frac{125\°}{360})[/tex]
[tex]arc\ length=CT=16.4[/tex]
Which is the graph of f(x) = (x – 1)(x + 4)?
Answer:
The fourth graph (last graph)
Step-by-step explanation:
Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:
[tex]f(x)=(x-1)(x+4)[/tex]
[tex](x-1)(x+4)=0[/tex]
[tex]x-1=0,x+4=0[/tex]
[tex]x=1,x=-4[/tex]
Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.
Since both x values inside the parenthesis are positive, our parabola is opening upwards.
The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.
We can conclude that the graph of [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.
ANSWER
See attachment.
EXPLANATION
The given function is
f(x) = (x – 1)(x + 4).
This parabola will open upwards because the leading coefficient is positive.
The x-intercepts can be found by equating the function to zero.
[tex](x - 1)(x + 4) = 0[/tex]
By the zero product property;
[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]
This implies that,
[tex]x = 1 \: or \: x = - 4[/tex]
The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.
The correct choice is D.
Use the function below to find F(4)
[tex]F(x) = 5 *(\frac{1}{2})^x[/tex]
[tex]
f(4)=5\times(\frac{1}{2})^4 \\
f(4)=\frac{5\times1^4}{2^4} \\
f(4)=\boxed{\frac{5}{16}}
[/tex]
Hope this helps.
Brainliest would be great.
For this case we have a function of the form[tex]y = f (x)[/tex]
Where:
[tex]f (x) = 5 * (\frac {1} {2}) ^ x[/tex]
We must find the value of the function when x = 4, that is, f (4):
Substituting we have:
[tex]f (x) = 5 * (\frac {1} {2}) ^ 4\\f (x) = 5 * \frac {1} {2} * \frac {1} {2} * \frac {1} {2} * \frac {1} {2}\\f (x) = 5 * \frac {1} {16}\\f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]
ANswer:
[tex]f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]
Edward wants to have $50,000 in 10 years for college. What single deposit would he need to make now into
an account that pays 4.3% interest, compounded daily, to meet his goal?
Answer:
[tex]\$32,526.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$50,000\\ r=0.043\\n=365[/tex]
substitute in the formula above
[tex]\$50,000=P(1+\frac{0.043}{365})^{365*10}[/tex]
[tex]P=\$50,000/[(1+\frac{0.043}{365})^{3,650}]=\$32,526.28[/tex]
Majel is making batches of trail mix. Each batch uses 3/4 cup of granola. How many batches of trail mix can Majel make from 6 1/2 cups of granola
Answer: 8 2/3
Step-by-step explanation:
During a weekend sale, a store sold 85 DVDs for $19 each. What is the total amount of money, rounded to the nearest hundred, the store made by selling DVDs?
Answer:
$1615.00
Step-by-step explanation:
When solving the equation log7 (x+1) + log7x = log7 12 a student arrives at a verifiable solution and an extraneous solution. The value of the extraneous solution is
3
-4
-3
5.5
Answer:
[tex]-4[/tex]
Step-by-step explanation:
The given logarithmic equation is:
[tex]\log_7(x+1)+\log_7x=\log_712[/tex]
Recall and apply product rule of logarithms.
[tex]\log_aM+\log_aN=\log_aMN[/tex]
We apply this property to the left side of the equation to get;
[tex]\log_7x(x+1)=\log_712[/tex]
We take the antilogarithm of both sides to get:
[tex]x(x+1)=12[/tex]
We expand to obtain:
[tex]x^2+x=12[/tex]
We rewrite in the standard quadratic form:
[tex]x^2+x-12=0[/tex]
We factor to obtain:
[tex](x-3)(x+4)=0[/tex]
Either [tex](x-3)=0[/tex] or [tex](x+4)=0[/tex]
Either [tex]x=3[/tex] or [tex]x=-4[/tex]
But the domain is[tex]x\:>\:0[/tex].
Hence [tex]x=-4[/tex] is an extraneous solution.
A cylinder has a diameter of 22 cm and a height of 9 cm. Identify the volume of the cylinder to the nearest tenth. HELP PLEASE!!
Answer: 3421.19
Step-by-step explanation:
look up cylinder formula and r= radius which is just the diameter cut in half
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 3421.1944 cm³.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
Given the diameter of the cylinder is 22 cm, therefore, the radius of the cylinder is 11cm, Also, given the height of the cylinder is 9 cm.
The volume of the cylinder = πR² × H
= π × (11cm)² × 9cm
= 1089π cm³
= 3421.1944 cm³
Hence, the volume of the cylinder is 3421.1944 cm³.
Learn more about Cylinder:
https://brainly.com/question/12248187
#SPJ2
Write the equation of the circle in general form. Show all of your work.
Answer:
x^2 + y^2 + 6x - 8y + 21= 0.
Step-by-step explanation:
The center of this circle is (-3, 4) and the radius id 2.
So in Standard form, the equation is:
(x + 3)^2 + ( y - 4)^2 = 2^2
Converting to General form we have:
x^2 + 6x + 9 + y^2 - 8y + 16 = 4
x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0
x^2 + y^2 + 6x - 8y + 21= 0.
Jesse wants to go skydiving. Each skydive is 14,000 feet high. Jesse wants to do 2 jumps which will cost him $400. In addition, Jesse must pay a $100 training fee. What is the price per foot of skydive if the training fee is added to the final price?
Answer:
Price per foot of skydive is 31.11 repeated, or 31 1/9
Step-by-step explanation:
Jesse is going on 2 jumps, which is 14000*2=28000.
Each Skydive is $400, and two jumps would be $800. Plus a $100 training fee, it would cost $900 for 2 jumps.
28000/900=31.1111 repeated.
math question! please help!
Answer:
the correct choice is marked
Step-by-step explanation:
The red line has intercept -3 and slope 1/3, so is ...
y = 1/3x -3
The blue line has intercept +1 and slope -1, so is ...
y = -x +1
The graph solves this system of equations, which can also be written as the single equation ...
y = y
1/3x -3 = -x +1
In a game a die numbered 9 through 14 is rolled. What is the probability that the value of a roll will be a multiple of two or ten?
Answer:
Step-by-step explanation:
This is a special die. Its six sides bear the numbers {9, 10, 11, 12, 13, 14}.
There are three possibilities for getting a multiple of two: {10, 12, 14}, and
there is only one possibilities for getting a multiple of ten: {10, 12, 14}
The probability here of getting a multiple of two is 3/6, and that of getting a multiple of ten is 1/6. But one of the outcomes is found in both result sets: 10. Getting a multiple of 10 is already included in the event that the outcome is a multiple of two. My answer here would be 3/6, or 1/2.
the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.
The probability of rolling a multiple of two or ten on a die numbered 9 through 14 can be calculated as follows:
Numbers that are multiples of two in the given range are 10, 12, and 14, which are 3 possibilities.Numbers that are multiples of ten in the given range are 10, which is 1 possibility.Therefore, the total favorable outcomes are 3 (for multiples of two) + 1 (for a multiple of ten) = 4. The total possible outcomes from 9 through 14 are 6.Hence, the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.\
Jacob will pay a monthly payment of $650.12 on a fixed rate mortgage over 20 years. What is the total principal and interest for the life of this mortgage rounded to the nearest dollar? I think maybe D.
A. $234,043
B. $13,002
C. $195,036
D. $156,029
I believe the answer is d. 156,029
I think the answer is D
Can a translation and a reflection map QRS to TUV? Explain why or why not. No, the triangles are not congruent. Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV. No, the triangles are obtuse. Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map △QRS to △TUV.
Answer:
The answer is B
Step-by-step explanation:
just took the answer on e2020
Answer:
B:
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.
The residuals for data set X and data set Y were calculated and plotted on separate residual plots. If the residuals for data set X do not form a pattern and the residuals for data set Y form a pattern, what can be concluded?
A. Data set X is not linear, and data set Y is not linear.
B. Data set X is not linear, and data set Y is linear.
C. Data set X is linear, and data set Y is linear.
D. Data set X is linear, and data set Y is not linear.
Answer:
B. Data set X is not linear, and data set Y is linear.
Step-by-step explanation:
We assume here that "form a pattern" means "roughly forms a line"... because a pattern doesn't necessarily equal a line, it would be a curve that would easily be interpreted too, but it wouldn't be linear.
Since you cannot form a pattern, and based on your choices for answer, we have have to say that data set X is NOT linear.
On the opposite, since the data set Y produces a pattern, it has to be linear.
So, X = NOT linear, Y = linear.
Answer:
(Data set x is linear, and data set y is not linear.) This is the correct answer 100%...
When i put the answer in from the other person which was (x is not linear, and y is linear) it said incorrect and gave me this answer x is linear, and y is not linear. So be careful what you put down.
Step-by-step explanation:
Misty has the choice of taking out a 25-year loan for $105,000 at 3.8% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. If she would pay a total of $57,810 in interest on the 25-year loan, how much in total would she pay in interest on the 20-year loan?
Without more information, we cannot give a specific numerical answer for the total interest on a 20-year loan. As a rule, total interest paid will be less on a shorter loan, despite higher monthly payments.
Explanation:The question is asking how much total interest would Misty pay on a 20-year loan, given she knows the total interest paid on a 25-year loan to be $57,810. We're not given enough information to provide a specific numerical answer for this - the loan interest for a 20-year loan and a 25-year loan involve different payment schedules and amounts - so we can't directly compare or convert the total interest paid.
However, generally speaking, the total interest paid over a shorter loan term (i.e. 20 years) is expected to be less than that of a longer term (i.e. 25 years), assuming all else (loan amount, interest rate) remains equal - this is because the principal balance is being paid down more rapidly, leaving less time for interest to accrue. The trade-off is that monthly payments would be higher on the shorter term loan.
Learn more about Interest Calculation here:https://brainly.com/question/29011216
#SPJ12
20. what is the missing value to the nearest hundredth
tan _ = 15
• 0.97°
• 0.27°
• 88.09°
• 86.19°
Answer:
86.19°
Step-by-step explanation:
Let x represent the missing value.
The given trigonometric equation becomes:
[tex]\tan x=15[/tex]
We take the inverse tangent of both sides to obtain:
[tex]\tan^{-1}(\tan x)=\tan^{-1}(15)[/tex]
This implies that;
[tex]x=\tan^{-1}(15)[/tex]
We use at least a scientific calculator to evaluate this and obtain:
[tex]x=86.18592517\degree[/tex]
To the nearest hundredth, the missing value is [tex]x=86.19\degree[/tex]
A city in the country determines public servants different than usual. The city asks citizens to rank candidates and the person with the highest point total wins. First place votes get 4 points, second place votes get 2 points and third place votes get 1 point. If John Tyler received 867 first place votes, 301 second place votes and 432 third place votes, how many total points did he obtain?
A) 1600
B) 2467
C) 3370
D) 4502
First Place Vote: 4x867= 3468
Second Place Vote: 2x301= 602
Third Place Vote: 1x432= 432
3468+602+432= 4502.
Your answer is therefore D.
I hope this helps! :)
Answer:
D) 4502
Step-by-step explanation:
It is given that,
Points for first place = 4 points
Second place = 2 points
Third place = 1 point
Thus, First Place Vote : 4 × 867 = 3468
Second Place Vote: 2 × 301= 602
Third Place Vote: 1 × 432= 432
Thus, Total Points = 3468 + 602 + 432 = 4502.
Hence, last option is correct.
calculate the value of A
Answer:
Second Option
[tex]a=1.46[/tex]
Step-by-step explanation:
The triangle of the figure is a straight triangle.
We know the length of the hypotenuse, h = 2, and we know the angle A = 43°. We need to find the length a. Side a is the side adjacent to the 43° angle
By definition we know that
[tex]cosx = \frac{adjacent}{hypotenuse}[/tex]
Then
adjacent = a
hypotenuse =2
x =43°
[tex]cos(43\°) = \frac{a}{2}[/tex]
[tex]a= 2cos(43\°)[/tex]
[tex]a= 1.46[/tex]
Solve the equation of e^x-2=(1/e^6)^x+3.
Answer:
x = -16/7
Step-by-step explanation:
The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...
x ≈ 1.60945071137
_____
Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...
e^(x-2) = (1/e^6)^(x+3)
x -2 = -6(x +3) . . . . . . . . take the natural log of both sides
x -2 = -6x -18 . . . . . . . . . eliminate parentheses
7x -2 = -18 . . . . . . . . . . . add 6x
7x = -16 . . . . . . . . . . . . . add 2
x = -16/7
Question 6 Gradpoint Math Question Please Help
Answer:
The right answer is 3a - 11 ≤ 7 ⇒ 4th answer
Step-by-step explanation:
* Lets study the problem
- From the figure
# The blue line started from 6 and the point is bold that means
the inequality sign is ≤ or ≥
# The blue line started from 6 and moved to the negative numbers
that means the inequality is less than or equal
∴ a ≤ 6
* Now lets look to the answers
- There is only one answer has the sign ≤ , the last answer
* Now lets solve it to be sure
∵ 3a - 11 ≤ 7 ⇒ add 11 to the both sides
∴ 3a ≤ 18 ⇒ divide the both sides by 3
∴ a ≤ 6
* The right answer is 3a - 11 ≤ 7
Help Me PLZZZZZZZ
Raoul's taxable income is $38,438. He is filling as head of household, and he has already paid $4428 in federal taxas.
What will he receive or pay after he figueres his taxas for the year?
Options:
A. He will receive a refund of $908
B. He will pay $908
C.He Will receive a Refund of $916
D.He will pay $916
Answer:
He will pay 916
Step-by-step explanation:
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
The wide would be 7.2 cm
Step-by-step explanation:
Let
x------> the wide of the proportional wall map
we know that
Using proportion
45/27=12/x
x=27*12/45
x=7.2 cm
Find the Area of the circle
Answer: 530 cm^2
Step-by-step explanation:
A = 3.14 * r^2
A = 3.14 * 13 * 13
A = 3.14 * 169
A = 530 cm ^2
Which of the following is equal to sqrt. (50(a^6) (b^7))
Answer:
5 · a³ · b³ · √5b
Step-by-step explanation:
Start with √(50a^6b^7). Rewrite 50 as the product of the largest possible perfect square and a multiplier: 50 = 25 · 2. Then √50 = 5√2.
a^6 is already a perfect square, so find its square root: √a^6 = a^3.
b^7 = b · b^6, so √b^7 = b^3√b
Now rewrite (50(a^6) (b^7)) as √(50a^6b^7).
Then rewrite √(50a^6b^7) as 5√2 · a³ · b³ · √b.
This latter result can be simplified to 5 · a³ · b³ · √5b
This matches possible answer #1.
Identify the surface area of the composite figure. HELP PLEASE!!
The total surface area for the figures aee;
1) 128 m²
2) 714 in²
How to find the surface area?1) To find the surface area, we need to find the area of each surface that makes up the object and add together.
Thus:
T.S.A = 4(4 * 4) + (4 * 4) + 4(½ * 4 * 6)
T.S.A = 128 m²
2) The total surface area here is;
T.S.A = 2(15 * 10) + 2(10 * 7) + 2(15 * 7) + 4(4 * 4)
T.S.A = 714 in²
Read more about surface area at: https://brainly.com/question/30794567
#SPJ3
math help !! will mark brainliest
Answer:
y = 2 x - 1
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
When x = 1 , y= 1
x = 2 , y=3
The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas. True or false
Answer:
True
Step-by-step explanation:
The area of a regular polygon is found by multiplying 1/2 times the apothem times the perimeter. The area for a single triangle is 1/2 times the height (which is the same as the apothem of a regular polygon) times the base (which is one of the sides of the regular polygon which you are multiplying by to find the perimeter of the polygon).
Answer:
The given statement is true.
Step-by-step explanation:
The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas.
This is true.
Breaking down in 7 triangles and adding separately the areas of these triangles, will give the complete area of the heptagon. We can also find the area of one triangle and multiply that by 7 to get the same result.
50 POINTS PLEASE HELP!!
Which values of a, b, and c represent the answer in simplest form?
5/8 divided by 3/8= a b/c
a. a=1, b=3, c=2
b. a=1, b=40, c=24
c. a=1, b= 16, c=24
d. a=1. b=2, c=3
Answer:
d. a=1. b=2, c=3
multiply by the Reciprocal.
Answer:
D
Step-by-step explanation:
(5/8) / (3/8)
(5/8) * (8/3)
5/3
1 ⅔
a = 1, b = 2, c = 3
Answer D.