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Lerok [7]
3 years ago
10

Find the tangent line to the graph of f(x)=x at point (0,0)

Mathematics
1 answer:
ratelena [41]3 years ago
4 0

Given:

The function is

f(x)=x

To find:

The tangent line to the graph of f(x)=x at point (0,0).

Solution:

We have,

f(x)=x

It is a linear function because the highest power of the variable is 1.

We know that the tangent line to a linear function at any point is the line itself.

Derivative of given function is

f'(x)=1

So, slope of the tangent line is 1. It is given table the tangent line passes through the point (0,0). The equation of tangent line is

y-0=1(x-0)

y=x

Therefore, the tangent line to the graph of f(x)=x at point (0,0) is y=x.

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HELP!
KonstantinChe [14]

Answer:

1 and 4 are vertical angles

2 and 3 are vertical angles

Step-by-step explanation:

Vertical angles are across from one another, share the same point (vertex) and are made by intersecting lines

1 and 4 are vertical angles

2 and 3 are vertical angles

5 0
3 years ago
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How do you do this problem
Fudgin [204]
A triangle is 180°; therefore:
x = 180-52-43
x = 85
x° = 85°
7 0
3 years ago
how many liters of glycerin should be added to 12 Liters of an 8% glycerin solution so that the resulting solution contains 16%
mojhsa [17]

Answer:

1.14 liters

Step-by-step explanation:

We have 8% glycerin solution and we need to make it 16%  glycerin solution [more concentration].

When we add "x" liters, we add glycerin as well as changes the total. in 12 Liters, there is 12 * 0.08 = 0.96Liters of glycerin. How much we need to add to this??

Note, 16% = 0.16

We can write a Ratio as shown below, cross multiply and solve for x:

\frac{0.96+x}{12+x}=0.16\\(12+x)(0.16)=0.96+x\\1.92+0.16x=0.96+x\\1.92-0.96=x-0.16x\\0.96=0.84x\\x=1.14

We need to add around 1.14 liters

4 0
3 years ago
Read 2 more answers
Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t
katrin2010 [14]

Answer:

\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of \triangle ACD and the hypotenuse of \triangle ADB.

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is \angle CAD. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}

Now use this value in the Law of Sines to find AD:

\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}

Recall that \sin 45^{\circ}=\frac{\sqrt{2}}{2} and \sin 60^{\circ}=\frac{\sqrt{3}}{2}:

AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}

Now that we have the length of AD, we can find the length of AB. The right triangle \triangle ADB is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio x:x\sqrt{3}:2x, where x is the side opposite to the 30 degree angle and 2x is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent 2x in this ratio and since AB is the side opposite to the 30 degree angle, it must represent x in this ratio (Derive from basic trig for a right triangle and \sin 30^{\circ}=\frac{1}{2}).

Therefore, AB must be exactly half of AD:

AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24

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3 years ago
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umka21 [38]

Answer:

The slope of the line is -1

I've attached a screenshot of a website that can solve function.

May I have brainliest please? :)

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