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3 years ago

Carlos bought a snowboard for $24.99 and ice skates for $19.19 how much money did he spend all together

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

3 0

Answer: $44.18

Step-by-step explanation: $24.99 + $19.99 = $44.18

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Find an equation of the line perpendicular to the graph of 14x-7y=8 that passing through the point at (-2,5).

MAXImum [283]

Answer:

2x + 4y = 16.

Step-by-step explanation:

14x - 7y = 8

Convert to slope-intercept form:

-7y = -14x + 8

y = 2x - 8/7

The slope is 2 so the line perpendicular to it has a slope of -1/2, so we have:

y = 1/2x + c

This line passes through the point (-2, 5) so:

5 = -1/2* (-2) + c

5 = 1 + c

c = 5 - 1 = 4

So our equation is y = -1/2x + 4.

Convert to standard from

4y = -2x + 16

2x + 4y = 16.

7 0

3 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

3 years ago

Assuming a soap bubble is a perfect sphere, what is the diameter of a bubble containing 500 cm of air, to the nearest tenth of a

Alex777 [14]

Answer:

9.8 cm

Step-by-step explanation:

Volume of a sphere, V = 4/3 πr³

V = 500cm³

π = 3.14

500 = 4/3 * 3.14 * r³

500 * 3 = 4 * 3.14 * r³

1500 = 12.56r³

r³ = 1500 / 12.56

r³ = 119.42675

r = (119.42675)^1/3

r = 4.9245574

Diameter = 2r

Diameter = 2 * 4.9245574

Diameter = 9.849

= 9.8cm

6 0

3 years ago

Find the sum (2x+6)+(4x-12) HELp

kotegsom [21]

Answer:

6x-6

Step-by-step explanation:

(2x+6)+(4x-12)=2x+6+4x-12

=6x-6

4 0

3 years ago

Read 2 more answers

Kelso is in charge of a bake sale. On each table, t, there will be a platter of 24 cookies and 2 bowls of brownies with b browni

Alecsey [184]

Let’s analyze the given situation:
Kelso is on a bake sale.
He needs 24 cookies per table
He also need 2 bowls of brownies per table. In where there are 12 brownies per bowl.
Thus, in every table there are also 24 brownies.
He has 7 tables.

=> 7t (24cookies + 2bowls (12brownies)) + 150 cookies
=> 7(24 + 24) + 150
=> Multiply 7 by 2 24s.
=> 168 + 168 + 150
=> 486
Therefore, Kelso have 318 cookies all in all and 168 pieces brownies or 14 bowls of brownies.

4 0

3 years ago