The maximum height would be 42.25 feet that the ball will reach.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²
Here h(t) = 52t - 16t²
Differentiate with respect to t to get maximum height
h'(t) = 52 - 2 × 16t
h'(t) = 52 - 32t
In this position, the acceleration would be zero,
So 0 = 52 - 32t
32t = 52
t = 52/ 32
t = 1.625
Substitute the value of t = 1.625 in the given function,
⇒ h = 52(1.625) - 16(1.625)²
⇒ h = 84.5 - 42.25
⇒ h = 42.25
Therefore, the maximum height would be 42.25 feet that the ball will reach.
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Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2
The approximation of the area of the region R under the graph of the function is 18.625 square units.
In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:
[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)
[tex]\Delta x = \frac{b-a}{n}[/tex] (2)
Where:
[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - IndexIf we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:
[tex]\Delta x = \frac{2-(-1)}{6}[/tex]
[tex]\Delta x = 0.5[/tex]
[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]
[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]
[tex]A = 18.625[/tex]
The approximation of the area of the region R under the graph of the function is 18.625 square units.
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What's the average of 200 and 300
Brainiest To Best Answer: Are Guidance Counselors allowed to lie or give false information about a class and force a math-genius to take an intensive math class? I took Algebra I Honors, Geometry Honors, and Algebra II Honors and scored in the 99th percentile on their EOCs and aced the classes. For my 10th grade year, my Guidance Counselor claimed that for my blank-period, I should take "Advanced Math Topics" because I would get 2 math credits that year (Pre-Calculus Honors was the other class I was taking). The Guidance Counselor did not mention it being an intensive class and this class was only for those who fail their math classes, exams, or other national math-portion of tests. It would look horrible for a math-major to have taken an intensive math class and would look weird that I was also taking a high-level math course at the same time. When we were informed about this, we were outraged and research does suggest that having such a class on your transcript will eliminate the possibility for getting into a good competitive college or getting the scholarship for out-of-state colleges in academics. I took many extra-classes and aced them online and we want to have this class removed from our transcript considering the fact that by rules, they cannot place a student performing as well as I am into a class lower than the classes previously taken. Do you agree with this? We are bringing this to the District Officer and the class was so basic, that I would be the only one in the class getting an A, "100%" every test and I would finish the questions in 5-10 minutes at most for any classwork given. Was the Guidance Counselor wrong to do this? What consequences might he face for this and will we be compensated for these troubles or have this transcript recording of this intensive class removed, exempt, or clarified?
Final answer:
Guidance counselors should not mislead students; it is worthwhile to challenge placement of a high-achieving math student in an unnecessary remedial class and seek to correct the record.
Explanation:
Guidance counselors should provide accurate information to students regarding class choices, particularly for students excelling in certain subjects like math.
It seems inappropriate for a counselor to enroll a high-achieving student in an intensive class designed for remediation without discussing the nature of the class and reviewing the student's academic history and test scores.
There may be rules or guidelines, possibly at the district level, outlining the circumstances under which a counselor can place a student in a specific class. If these procedures were not followed, bringing the issue to the attention of a District Officer is reasonable.
The aim would be to correct the student's academic record, ensuring it reflects their true capabilities and doesn't unfairly disadvantage them in future educational or scholarship opportunities. Corrective actions could include exemption, removal, or clarification of the intensive math class on the student's transcript.
The counselor in question may face a review of their practices or disciplinary action if they are found to have acted against established policies. However, the outcome will depend on the investigation conducted by the school district.
How Do You Sell More Walnuts In A Perfectly Competitive Market?
If the equilibrium price in a perfectly competitive market for walnuts
is $4.99 per pound,then an individual firm in this market can
A. Not sell additional walnuts unless the firm lowers its price.
B. Not sell additional walnuts at any price because the market is at equilibrium.
C. Sell an additional pound of walnuts at $4.99.
D. Sell more only by increasing its advertising budget.
the subject is Economics.
Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3
The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.
What is integration?It is the reverse of differentiation.
The arc length of the curve on the given interval.
Parametric equations interval
x = 6t + 5, −1 ≤ t ≤ 3
y = 7 − 7t, −1 ≤ t ≤ 3
We know that the parametric form of the arc length will be given as
[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]
Then the arc length will be
[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]
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What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?
a patient requires 30% decrease in the dosage of the medication her current dosage is 340 MGS what will the dosage be after the decrease
Answer:
The dosage will be 238 MGS after decrease.
Step-by-step explanation:
The current dosage of the medication of the patient = 340 MGS
patient requires 30% decrease in the dosage of the medication.
Now her new dosage after decrease = 340 -(30% × 340)
= 340 -(0.30 × 340)
= 340 - 102
= 238 MGS
The dosage will be 238 MGS after decrease.
how many cubic blocks of side length 1/7 inch would it take to fill a cube with a side length of 3/7 inch?
A chemist is using 353 millimeters of a solution of acid and water. If 16.5% of the solution is acid, how many millimeters of acid are there? Round your answer to the nearest tenth.
Help me please!! SOS!!
What is the slope of a line that passes through the following points (-3,8) and (2,1)
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]
Slope is -7/5
Answer is -7/5
Hope this helps!
Thanks!
-Charlie
:)
:D
HELLPP PLEASEEE ASAP
The rule for G -1(x) in G(x)=3x-5/4 is G^-1(x)=
(4x-5)/3
(4x+5)/3
(3x+5)/-4
Answer:
(4x+5)/3=y
Step-by-step explanation:
:)
5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?
Tina wants to save money for school. Tina invests 400$ in an account that pays interest rate of 8%. How many years will it take if her goal is 5500$
A company that creates model cars uses a 1.5 foot : 1 inch ration when creating the models. If a real car is 12 feet long, how long will the model car be?
With the beam being held still at a height of 40 m, the crane breaks and the beam falls to the ground. Assuming no air resistance, how much total energy will the beam have just as it hits the ground?
The total energy of the beam just as it hits the ground would be equivalent to the initial potential energy when it was held at a height of 40 m, assuming no air resistance.
Explanation:The question is about understanding the concept of conservation of energy, specifically the transformation of potential energy to kinetic energy. When the beam was held at a height of 40 m, it had potential energy given by the formula:
PE = mgh
where m is the mass of the beam, g is the acceleration due to gravity, and h is the height. Assuming no air resistance, when the beam falls, all of its potential energy will be converted to kinetic energy, which can be determined by the formula:
KE = 1/2 mv^2
However, as we don't know the exact speed of the beam just as it's hitting the ground, we don't need it because the total energy remains constant. So, just as the beam hits the ground the total energy will be the same as the initial potential energy when it was still.
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Bari Jay, a gown manufacturer, received an order for prom dresses from China. Her cost is $35 a gown. If her markup based on selling price is 79%, what is the selling price of each gown?
To calculate the selling price of a gown with a cost of $35 and a markup of 79%, convert the markup to a decimal, subtract from 1, and divide the cost by this number. The selling price is $166.67 per gown.
Explanation:Calculating the Selling Price with MarkupThe problem involves finding the selling price of a gown given the cost and the markup based on selling price. Markup based on selling price is calculated using the formula: Selling Price = Cost / (1 - Markup Percentage), where the Markup Percentage is expressed as a decimal. Here, the cost of a gown is $35, and the markup based on the selling price is 79%. Let's calculate the selling price.
Convert the markup percentage to a decimal by dividing by 100: 79% / 100 = 0.79.Subtract the markup percentage as a decimal from 1: 1 - 0.79 = 0.21.Divide the cost by the result to find the selling price: $35 / 0.21 = $166.67.The selling price of each gown is $166.67.
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If 7-y=6 then y =what
Answer:
-29
Step-by-step explanation:
The Correct Answer:
A. -29
Square both sides of the equation.
7−y−−−−√
=
6
(7−y−−−−√)2
=
(6)2
7−y
=
36
−7
−7
Subtract 7 from both sides
−y
=
29
y
=
−29
7−(−29)−−−−−−−−√
=?
6
Check your answer
7+29−−−−−√
=?
6
36−−√
=?
6
6
=
6
So m=−29 is a solution.
domain and range of x^2+x-2/x^2-3x-4
The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car, rounded to the nearest dollar.
In the middle of the page draw a equilateral triangle with 2 inch sides and the bottom parallel to the of the page
The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle. If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.
Solve for x & y. 30x−42y=−6 and 5x−7y=−1
Mick and LaToya have some shirts. The ratio of the number of shirts Mick has to the number of shirts LaToya has is 3:8. If they have a total of "k" shirts, how many fewer shirts does Mick have than LaToya?
Suppose a $75,500 mortgage is to be amortized at 6.5% interest. Find the total amount of interest that would be paid for a 40 year term. What is the amount of interest for a 40 year mortgage?
what is the point slope form of an equation with the slope of 3/5 that passes through the point (10,-2)
What is the volume of an oblique cone with radius 9 cm and height 12 cm?
972π cm3
486π cm3
648π cm3
324π cm3
Write this number in standard form. 12 ten thousands, 8 thousands, 14 hundreds and 7 ones
A firm has $100 of average inventory, operating profit of $500 and sales of $1,500. its days in inventory is:
The inventory in days is 36.5 days
Further Explanation:
Inventory Turnover Ratio: It is an activity ratio which measure of how suitably a company is handling its inventory to generates sales. The inventory turnover ratio is calculated as:
[tex]\text{Inventory Turnover Ratio}=\dfrac{\text{Cost of goods sold}}{\text{Average Inventory}}[/tex]
Calculate the days in inventory:
[tex]\begin{aligned}\text{Days in inventory}&=\dfrac{\text{365}}{\text{Inventory Turnover Ratio}}\\&=\frac{365}{10}\\ &=36.5\text{days}\end{aligned}[/tex]
Therefore, the inventory in days is 36.5 days
Working note 1:
Calculate the cost of goods sold:
[tex]\begin{aligned}\text{Cost of goods sold}&=\text{Sales}-\text{Operating profit}\\ &=\$1,500-\$500\\ &=\$1,000\end{aligned}[/tex]
Working note 2:
Calculate the inventory turnover ratio:
[tex]\begin{aligned}\text{Inventory Turnover Ratio}&=\frac{\text{Cost of goods sold}}{\text{Average Inventory}}\\ &=\frac{\$1000}{\$ 100}\\ &=\$10\end{aligned}[/tex]
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3. the sales budget
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Answer details:
Grade: High School
Subject: Financial Accounting
Chapter: Ratio Analysis
Keywords: A firm has $100 of average inventory, operating profit of $500, sales of $1,500, days in inventory.
Marisa hiked 1 3/4 miles and 3/4 hours at that rate how far can she hike in one hour
Answer:
2.33 miles/hour
Step-by-step explanation:
If Marisa hiked a distance of 1 3/4 miles in a time of 3/4 hours we can determine her speed as miles per hour. Speed is defined as the distance(d) per time(t). Let speed equal to v:
[tex]v=d/t[tex]
We can determine the decimal numbers of the distance and time:
1 3/4 = 7/4 = 1.75 miles
3/4 = 0.75 hours
∴ [tex]v=1.75/0.75=2.33[/tex]
Marisa can hike 2.33 miles per hour.
A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined