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user100 [1]
3 years ago
8

Line parallel to the y-axis that passes through the point (77,88)

Mathematics
1 answer:
Step2247 [10]3 years ago
5 0

Answer:

A line which is parallel to the y-axis has form of x = a

This line passes (77, 88), then a = 77

=> The equation of this line: x = 77

Hope this helps!

:)

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The half-life of a certain radioactive substance is 45 days. There are 6.2 grams present initially. On what day
kvasek [131]

Answer:

There will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days

Step-by-step explanation:

The given parameters are;

The half life of the radioactive substance = 45 days

The mass of the substance initially present = 6.2 grams

The expression for evaluating the half life is given as follows;

N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}

Where;

N(t) = The amount of the substance left after a given time period = 1 gram

N₀ = The initial amount of the radioactive substance = 6.2 grams

t_{1/2} = The half life of the radioactive substance = 45 days

Substituting the values gives;

1 = 6.2 \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}

\dfrac{1}{6.2}  =  \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}

ln\left (\dfrac{1}{6.2} \right )  =  {\dfrac{t}{45} \times ln \left (\dfrac{1}{2} \right )

t = 45 \times \dfrac{ln\left (\dfrac{1}{6.2} \right ) }{ln \left (\dfrac{1}{2} \right )} \approx 118.45 \ days

The time that it takes for the mass of the radioactive substance to remain 1 g ≈ 118.45 days

Therefore, there will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days.

3 0
3 years ago
5y=-3+15<br><br> convert to slope intercept form
creativ13 [48]

Answer:

y=-⅗x+3

Step-by-step explanation:

5y=-3x+15. Divide 5 on both sides

5. 5

y=-⅗x+15/5

y=-⅗x+3

Hope this helps :)

8 0
3 years ago
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number
Masja [62]

Answer:

<h2>√512 by √512 </h2>

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

5 0
4 years ago
Which statement accurately describes how to perform a 90° counterclockwise rotation of point A (−1, −2) around the origin? Creat
Anastaziya [24]

Answer:

last one

Step-by-step explanation:

You are swinging A(-1,-2) around the center which in this case is the origin. Keep in mind that points on a circle all have a equal distance from the origin.  We don't want the distance from the center to change.

We want the center of that circle to be the origin.

So the answer is the last one:

"Create a circle with the origin as its center and a radius of the origin and point A, then locate a point on the circle that is 90° counterclockwise from point A. ​"

8 0
3 years ago
Read 2 more answers
Fill in the blanks to make the following rational number is equivalent 3/4=__ /24​
Andre45 [30]

Step-by-step explanation:

let the blank be x

\frac{3}{4}  =  \frac{x}{24}

x =  \frac{24 \times 3}{4}  = 6 \times 3 = 18

therefore,

\frac{3}{4}  =  \frac{18}{24}

8 0
3 years ago
Read 2 more answers
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