Least number by which 1375 is divided to get a perfect sqaure
Answers
Answer:
55
Step-by-step explanation:
Here 5 is squared and 55 is not.
Hence, the answer is 55
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Answers
Let n represent the unknown number.
14.4 % x n= 10.4
n = 10.4 / 14.4%
n = 72.22222
n = ~72
Hope this helps!
Answers
Answer:
The slope of the line is -7/8
When the point (7, -4) is used, the point-slope form of the line is y+4=(-7/8)(x-7)
The slope-intercept form is y=(-7/8)x+(17/8)
Step-by-step explanation:
Answer:
point slope form:
y - 3 = -4/3(x- (-1))
slope intercept form:
y = -4/3x + 13/3
Step-by-step explanation:
So if the points are (7, -4) and (-1,3) then we can use those points to figure out the slope.
y2-y1/x2-x1 is the forumla for the slope
3-7/ -1 - (-4) --> -4/-1+4 --> -4/3
point slope form:
y - y1 = m(x-x1) ~ you can choose either of the two points to use, you should get the same answer
y - 3 = -4/3(x- (-1))
y - 3 = -4/3x+4/3
add 3 to both sides
y = -4/3x + 13/3 ~ slope intercept form
Answers
Answer:
"Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeroes in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients."
Explanation:
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Final answer:
The Rational Root Theorem provides possible rational roots of a polynomial while Descartes' Rule of Signs indicates the number of positive and negative roots of a polynomial. They both serve as crucial tools in understanding and solving polynomial equations.
Explanation:
The Rational Root Theorem and Descartes' Rule of Signs are both mathematical tools that can provide valuable information about the zeros (or roots) of a polynomial. The Rational Root Theorem can help us determine the possible rational roots of a polynomial equation. It states that if a polynomial has a rational root p/q (where p and q are relatively prime), then p is a factor of the trailing constant and q is a factor of the leading coefficient.
On the other hand, Descartes' Rule of Signs gives us an indication of the number of positive and negative real roots in a polynomial. It does this by considering the number of sign changes in the coefficients of the terms of the polynomial when arranged in descending power.
For example, in the polynomial + 2x - 6, by applying Descartes' Rule of Signs, we can infer there are two or zero positive roots (since there are two sign changes) and one negative root (since there are no sign changes when the terms are arranged in ascending power).
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Answers
Answer:
it is greater than ten and less than 100, the answer is 30%
Step-by-step explanation:
600*5=3000
3000/100=30%
Answers
Answer:
a. $55,390.29
b. $61,412.20
Step-by-step explanation:
a. To find the present value of your windfall, each value must be brought back to the present year at a rate of 3.5% per year. The present value is:
The present value of your windfall is $55,390.29.
b. To find the future value of your windfall at the date of the last payment, simply compound the preset value amount obtained on the previous item for three years at a rate of 3.5%:
The future value of your windfall is $61,412.20.
Final answer:
The present value and future value of an investment are calculated using formulas that account for the interest rate and the period. The present value is calculated by dividing each year's payout by the increment of the interest rate for that year and summing these values. The future value in this scenario would be the sum of the payouts.
Explanation:
This question deals with the financial concepts of present value and future value in relation to an investment payout structure over time.
a. The present value is a measure of the current worth of a future sum of money given a specified rate of return. The formula to calculate present value is PV = CF / (1 + r)^n, where CF is cash flow, r is interest rate and n is the period. To calculate the present value of your windfall:
- End of Year 1: PV = $10,000 / (1+0.035)^1
- End of Year 2: PV = $20,000 / (1+0.035)^2
- End of Year 3: PV = $30,000 / (1+0.035)^3
Add all these present values together to get the total present value.
b. The future value is how much an investment is worth at a certain time in the future. The formula to calculate future value is FV = CF * (1 + r)^n. But in this case since the last cash flow coincides with the period, the future value in three years would simply be the sum of all cash flows which is $60,000 ($10,000+$20,000+$30,000).
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Answers
Answer:
The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.
Step-by-step explanation:
Volume of the jewellery box=44cm³
The box has a square base and is to be built with silver plated sides and nickel plated top and base.
Therefore: Volume = Square Base Area X Height = l²h
l²h=44
h=44/l²
Total Surface Area of a Cuboid =2(lb+lh+bh)
Since we have a square base
Total Surface Area =2(l²+lh+lh)
The Total Surface Area of the box =2l²+4lh
Nickel plating costs $1 per cm³
Silver Plating costs $2 per cm³
Since the sides are to be silver plated and the top and bottom nickel plated:
Therefore, Cost of the Material for the jewellery box =1(2l²)+2(4lh)
Cost, C(l,h)=$(2l²+8lh)
Recall earlier that we derived:
h=44/l²
Substituting into the formula for the Total Cost
Cost, C(l)=2l²+8l(44/l²)
C=2l²+352/l
C=(2l³+352)/l
The minimum costs for the material occurs at the point where the derivative equals zero.
C'=(4l³-352)/l²
4l³-352=0
4l³=352
Divide both sides by 4
l³=88
l=4.45cm
Recall:
h=44/l²=44/4.45²=2.22cm
The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.