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maxonik [38]
3 years ago
10

A 6 ft tall petrified stump standing next to a car casts a 12 ft shadow. If the car casts a shadow that is 6 ft long, then how t

all is it?
Mathematics
1 answer:
sveta [45]3 years ago
4 0

Answer:

3 feet tall

Step-by-step explanation:

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Eli walk from her house to a friends house in one hour. She can travel the same Distance on her bicycle in 15 minutes. If she ri
lord [1]

Answer: her speed on the bicycle is 8 mph

Step-by-step explanation:

Let x represent the speed at which she walks. If she rides 6 mph faster than she can walk, then the speed at which she rides is (x + 6) mph

Distance = speed × time

Eli walk from her house to a friends house in one hour. This means that the distance covered is 1 × x = x miles.

Distance on her bicycle in 15 minutes. Converting 15 minutes to hours, it becomes 15/60 = 0.25 hour. Distance covered while riding is 0.25(x + 6) = 0.25x + 1.5

Since the distance is the same,then

x = 0.25x + 1.5

x - 0.25x = 1.5

0.75x = 1.5

x = 1.5/0.75

x = 2

her speed on the bicycle is

x + 6 = 2 + 6 = 8 mph

3 0
3 years ago
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just fini
mel-nik [20]

Answer:

The next step is;

Label the two intersection points

Step-by-step explanation:

To make a copy of an angle, the steps are;

1) Draw the rays of the original angle passing through the point B

2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays

3) Label the point of intersection of both rays points C and D

4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J

5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M

6) Draw a line from B passing through M to complete the second ay of the copied angle.

5 0
4 years ago
How to differentiate ?
Bas_tet [7]

Use the power, product, and chain rules:

y = x^2 (3x-1)^3

• product rule

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}

• power rule for the first term, and power/chain rules for the second term:

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}

• power rule

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3

Now simplify.

\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) =  \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)

Differentiate both sides and you end up with the same derivative:

\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2

7 0
3 years ago
Heather paid $1,493.30 for a computer. If the price paid includes a 9% sales tax, which of the following equations can be used t
aliina [53]
A because x is the original price, so you multiply by the tax (9%) which would convert to 1.09 which you would multiply to the x

3 0
3 years ago
I need help because I didn't understand and I don't know how to do and I don't know plz help me and if you help me I would like
zepelin [54]
Umm what do you need helo with?
3 0
4 years ago
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