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3 years ago

Point R is located at (1, 2) on a coordinate grid. Point S is located at (4, 5) on the same

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

6 0

Answer:

4.2 units

most likely answer choice B

Step-by-step explanation:

(1, 2) and (4, 5)

To find the distance between two points, we use the distance formula:

$d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }$

Let's plug in what we know.

$d = \sqrt{(4 - 1)^2 + (5 - 2)^2 }$

Evaluate the parentheses.

$d = \sqrt{(3)^2 + (3)^2 }$

Evaluate the exponents.

$d = \sqrt{(9) + (9) }$

Add.

$d=\sqrt{18}$

Evaluate the radical.

d = 4.24

Round to the nearest tenth.

d = 4.2 units

*note: The answer choice is 4.6. I'm not sure if that is a typo on someone's end, but the distance between these two points is exactly 4.24264068712 units.

Hope this helps!

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

Alonzo and Miguel scored a total of 54 points in a basketball game. Miguel scored 4 more points than Alonzo. How would I graph t

Liono4ka [1.6K]

A + m = 54, m = a + 4 and, a + m = 54, - a + m = 4,

Combine the equations: 2m = 58

Now solve: 2m = 58, 2m/2 = 58/2, m = 29, therefore a = 24

4 0

3 years ago

A committee is formed consisting of one representative from each of the 4 departments (CS-IS-IT-SW) in the computer science coll

alexandr1967 [171]

Step-by-step explanation:

each department has 3 options for their representative.

and each of these options can be associated with the 3 options of the next department. and so on.

so, we have

3×3×3×3 = 3⁴ = 81

possibilities to firm that committee overall.

7 0

3 years ago

I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions.

Brums [2.3K]

Given that the area is equal to twice the perimeter and the dimensions are:
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)

Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft

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4 years ago

Evaluate -1(5)(2)(-4)

wariber [46]

Answer:

Step-by-step explanation:

-1 × 5 = -5

-5 × 2 = -10

-10 × -4 = 40

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3 years ago