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3 years ago

WILL MARK BRAINIEST

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

3 0

A) (0,1), (1,-2), (-1,4), (2,-5)
b) (0,4), (-1,2), (-2,0), (1,6)
c) (-2,-7), (-1, -7), (0,-7), (1, -7)

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How much more interest will Maria receive if she invests $1,000 for one year at x percent annual interest, compounded semiannual

notka56 [123]

Answer:

$0.025x² . . . where x is a number of percentage points

Step-by-step explanation:

The multiplier for semi-annual compounding will be ...

(1 + x/2)² = 1 + x + x²/4

The multiplier for annual compounding will be ...

1 + x

The multiplier for semiannual compounding is greater by ...

(1 + x + x²/4) - (1 + x) = x²/4

Maria's interest will be greater by $1000×(x²/4) = $250x², where x is a decimal fraction.

If x is a percent value, as in x = 6 when x percent = 6%, then the difference amount is ...

$250·(x/100)² = $0.025x² . . . where x is a number of percentage points

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<u>Example</u>:

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3 years ago

(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13

jolli1 [7]

Answer:

$y(x)=3e^{5x}-2xe^{5x}$

Step-by-step explanation:

The given differential equation is $y''-10y'+25y=0$

The characteristics equation is given by

$r^2-10r+25=0$

Finding the values of r

$r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5$

We got a repeated roots. Hence, the solution of the differential equation is given by

$y(x)=c_1e^{5x}+c_2xe^{5x}...(i)$

On differentiating, we get

$y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)$

Apply the initial condition y (0)= 3 in equation (i)

$3=c_1e^{0}+0\\\\c_1=3$

Now, apply the initial condition y' (0)= 13 in equation (ii)

$13=5(3)e^{0}+0+c_2e^{0}\\\\13=15+c_2\\\\c_2=-2$

Therefore, the solution of the differential equation is

$y(x)=3e^{5x}-2xe^{5x}$

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3 years ago

Mark is making a decoration for a rally, using a string of triangular strips. Each strip is an isosceles triangle when flattened

inysia [295]

B) 40 because if you add the two angles at the bottom which are shown to be congruent, then subtract 180 from the sum of those two, then you are left with your answer

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Can someone help me with this question?

andre [41]

The y-intercept (where x = 0) of the equation is at -20.

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