Mara ran 3 km north and then 4 km east. she will finish her run by running directly home. what was the total distance of her run? a right triangle with side lengths 8 kilometers and 4 kilometers. a point at intersection of the side with length 3 kilometers and the hypotenuse is labeled mara's house. 5 km 7 km 12 km 14 km

Answer:

25 to 3 power ÷ 3 = 69

The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

[tex]\rm x^2 + y^2=25[/tex]

Differentiate with respect to time

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]

Substitute all the values in the equation

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]

Hence, the value of dy/dt at this time is -9/2.

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The number of tops on the 6th day based on the exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

First day class collected = 2 tops

Third day class collected = 8 tops

The exponential function can be modelled:

[tex]\rm D(N) = 2^N[/tex]

D(1) = 2  (first day)

D(3) = 8  (third day)

D(6) = 64 (sixth day)

The linear function can be modeled:

D(N) = 3N -1

D(1) = 2  (first day)

D(3) = 8 (third day)

D(6) = 17 (sixth day)

Thus, the number of tops on 6th day based on exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

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Answer:

-13f

Answer:

0.32

Step-by-step explanation:

3/10=0.3

2/5=0.4

0.32 is between these two numbers.

Hope this Helps

Answer:

[tex]P(X=3)\approx27\%[/tex]

Step-by-step explanation:

Use the binomial distribution

[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^{4-3}\\\\P(X=3)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]

Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%

Answer:

its 3

Step-by-step explanation:

id ont know the formula but im certain im a very smart 6th grader!

Answer:

750 mL

Step-by-step explanation:

Unit Conversion Rate

Solving

Answer:

750

Step-by-step explanation:

.75 x 1000 = 750

multiply volume value by 1000

hope this helps!

A first step in solving the equation 1/4 x + 1/2 = 3/4x will be answer A multipllied by 4 on both sides.

What is an equation?

The equation is actually a relationship between the numbers and the variables.The given equation is  1/4 x + 1/2 = 3/4x

Now the solution of the equation will be:-

1/4 x + 1/2 = 3/4x

By multiplying with 4 the equation will become:-

x+2=3x

3x-x=2

2x=2

x=1

Hence the solution of the given equation will be x=1

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Answer:A

Step-by-step explanation:

Multiplying each by 1/4.We have;4x1/4 + 4x1/2 = 4x3/44/4 + 4/2 = 12/41 + 2 = 33=3This is the most effective way.

The area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

r=6sin(6θ)

First we have to find the limits:

r = 0

6sin(6θ) = 0

θ = nπ/6

n = 0 to n = 1

θ = 0 to  θ = π/6

[tex]\rm Area = \int\limits^{\dfrac{\pi}{6}}_0 {6sin6\theta} \, d\theta[/tex]

After calculating the above definite integral, we will get:

Area = 3π/2

Thus, the area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. Convert both mixed numbers into improper fractions:

[tex]\frac{15}{4} x = \frac{5}{4}[/tex]

2. Multiply both sides by 4:

4 · [tex]\frac{15}{4} x=\frac{5}{4}[/tex] · 4

15x = 5

3. Isolate x:

x = 1/3

hope this helps!

Answer:

24

Step-by-step explanation:

6/2 = x/8

x=24

24 oil changes

The completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

Program or programming is the combination of codes. These codes are used to generate the program such that a machine can understand the inputs given to it.

The program is written to allow a user to guess a number. This number should be between the number 0 to 10.

Here, the input is needed to a machine or computer, for which it's process the number and show if the guessed number is correct or not.

Hence, the completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

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Answer:

6

Step-by-step explanation:To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set. If n is an odd number, the median lies at the position (n + 1) / 2. If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1.

Answer:

6

Step-by-step explanation:

The value of the expressions (-0.3)⁴ equal to 0.0081.

A mathematical expression is the representation of numbers in the form of powers or mathematical signs.

Here we have the (-0.3)⁴

Now by evaluating the expression we will get:

(-0.3)⁴=(-0.3x-0.3x-0.3x-0.3)

Hence the value of the given expression will be 0.0081

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Answer:

Step-by-step explanation:

The mode is the number of most repeated data in the set.

Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).

If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.

There is no change in mode, so the mode decrease is zero.

Answer:

The mode would not decrease

Step-by-step explanation:

Given set of numbers:  2, 1, 4, 7, 1

The mode is most frequently occurring data value.

Therefore, 1 is the mode of the given data set as there are two of this data value.

If we add 1 to the data set, the set becomes:  2, 1, 4, 7, 1, 1

Therefore, 1 is still the mode since there are now three of this data value.

In conclusion, the mode would stay the same.

Answer:

45.5 m²

Step-by-step explanation:

Area (Shaded) = Area (Rectangle) - Area (Trapezoid)

Area of trapezoid:-

Area of triangle:-

Which part is shaded not said so both shaded regions area calculated

The positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

The function f of (x) is used to denote a linear algebra that can be represented on the graph.

Given that:

We are to determine a positive integer for which g(x) first exceeds f(x). Using the following option;

Therefore, we can conclude that the positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

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The length of the hypotenuse will be equal to H=122.25 when value of x=14.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.

It is given that:

Value of x=14

The perpendicular is  =6x+5=6x14+5=89

The base is  =6x=84

So by using the Pythagorean theorem:-

[tex]H^2=P^2+B^2\\\\\\H^2=89^2+84^2\\\\\\H=\sqrt{89^2+84^2}\\\\\[/tex]

Hence the value of hypotenuse will be H=122.25

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Answer: 113 ( 34x3+11

Step-by-step explanation:

34x 3 on top + 7 + 24/6

34 x 3 on top + 7 = 4

34 x 3 on top + 7 + 4

34 x 3 on top + 11

34 x 3 on top + 11

Answer:

10 times

Step-by-step explanation:

4 in 547 is equal to 40

4 in 84 is equal to 4

When you separate that number into smaller parts

Ex: 547 = 500 + 40 + 7

You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;

We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^

Where A is the magnitude of the resultant

x is the value of the x-component

y is the value of the y-component

We are given;

Magnitude of vector = 84 units

Y-component of the vector = -67 units

Thus,

[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]

From A above, let us take the positive value of the x-component and as such our original vector will be;

A = 56.68i^ - 66j^

The direction of the vector V is;

[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]

Since it points entirely to the negative x-axis, then the angle is;

180 - (-27.15) = 207.15°

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Answer:

B is the correct answer from my understanding

Step-by-step explanation:

The region outside the circle r = 3 and inside the circle r = - 6cos θ is given below.

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region outside the circle r = 3 and inside the circle r = - 6cos θ

Then the value of the θ will be

[tex]\begin{aligned} -6\cos \theta &= 3\\\\\cos \theta &= -\dfrac{1}{2}\\\\\theta &= -\dfrac{2\pi}{3}, \dfrac{2\pi}{3} \end{aligned}[/tex]

Then the area will be given as

[tex]\rm Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [-6 \cos \theta)^2 - 3^2 ] d \theta \\\\\\Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [18 (2\cos ^2 \theta ) - 9]d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2(1 + \cos 2\theta ) - 1] d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2 \cos 2\theta ) + 1] d \theta \\\\[/tex]

[tex]\rm Area = \dfrac{9}{2} [ \sin 2\theta + \theta ] _{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} \\\\\\ Area = \dfrac{9}{2} [ \sin 2( \frac{2\pi}{3}) +\frac{2\pi}{3} - \sin 2 (\frac{2\pi}{3}) - \frac{2\pi}{3}] \\\\\\[/tex]

On simplifying, we have

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

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Step-by-step explanation:

cubic root(56) + cubic root(189) =

= cubic root(7×8) + cubic root(27×7) =

= 2×cubic root(7) + 3×cubic root(7) = 5×cubic root(7) =

= 9.564655914...

Answer:

[tex]\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the sides, and [tex]C[/tex] is the included angle)

[tex]\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2[/tex]

(where [tex]\theta[/tex] is the angle in degrees and [tex]r[/tex] is the radius)

Therefore, using the above formulas:

[tex]\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}[/tex]

Given:

Substitute the given values into the formula and solve for r:

[tex]\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}[/tex]

Answer:

X intercepts are (-4,0) and (2,0)

Step-by-step explanation:

use the desmos graphing calculator for a simple answer

Answer:

Step-by-step explanation

the figure is composed of a square with an isosceles right triangle inside, we find the area of ​​the square and we take away the area of ​​the triangle.

Triangle area = lxl, right-angled triangle area side by side divided by two.

8 * 8 = 64cm²

6 * 6 : 2 = 18 cm²

Area of the shaded region

64 - 18 = 46 cm²

The Solution of -x +y = 84, x + 3y = 12, x - 7y + z = 15 be [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

The correct option is (C)

The inverse of matrix is another matrix, which on multiplying with the given matrix gives the multiplicative identity.

Given equation are:

-x +y = 8

4x + 3y = 12

x - 7y + z = 15

So,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right] \;*\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

then,

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

Now, Calculating the inverse of Matrix we have,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \;[/tex] =      [tex]\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right][/tex]

so, [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \;\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-12/7\\44/7\\425/7\end{array}\right][/tex]

 [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

Hence ,[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

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